From b37f2c59660aa80b0e37834bf30159cf98100936 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 15:10:13 +0800 Subject: [PATCH 001/123] feat: deepen triangle facts and fix OCR sum tokens MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Derive Heron area, angle-bisector ratios, excircle radii, and OI/OH distances from sparse triangle givens. Map CoMER \\sum limits to braced LaTeX and treat Σ-like ink as a formula cue so notes stay off kraft. --- crates/mathcore/src/geometry.rs | 70 ++++++++++++++++++++++++++++++++ scripts/ocr-smoke.ts | 24 +++++++++++ scripts/plot-cases.ts | 2 +- src/ocr/comer/source.ts | 21 ++++++++++ src/ocr/gate.ts | 17 ++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 486420 -> 518888 bytes src/wasm/pkg/package.json | 2 +- 7 files changed, 134 insertions(+), 2 deletions(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 511d22d..8ace504 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -514,6 +514,9 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] let rr = a / (2.0 * g[0].sin()); let r = area / p; out.push(fact("面积与周长", "S", nice(area), Some(area), "S = \\frac12 ab\\sin C", "面积公式")); + // Heron: same area from three sides — useful when the student only wrote SSS. + let heron = (p * (p - a) * (p - b) * (p - c)).max(0.0).sqrt(); + out.push(fact("面积与周长", "S_{\\text{海伦}}", nice(heron), Some(heron), "S = \\sqrt{p(p-a)(p-b)(p-c)}", "海伦公式")); out.push(fact("面积与周长", "C_{\\triangle}", nice(per), Some(per), "a + b + c", "周长")); let [na, nb, nc] = names; @@ -564,6 +567,21 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] (y * v[(i + 1) % 3][1] + z * v[(i + 2) % 3][1]) / (y + z), ]; out.push(fact("角平分线", &format!("t_{}", SIDE[i]), nice(t), Some(t), &format!("t_{s} = \\frac{{2{u}{w}\\cos\\frac{{{T}}}{{2}}}}{{{u} + {w}}}", s = SIDE[i], u = SIDE[(i + 1) % 3], w = SIDE[(i + 2) % 3], T = ANG[i]), "角平分线长公式").with(Shape::Segment { x1: v[i][0], y1: v[i][1], x2: foot[0], y2: foot[1], label: format!("t_{}", SIDE[i]) })); + // 角平分线定理: foot F on the opposite side splits it as the adjacent sides. + let (u, w) = ((i + 1) % 3, (i + 2) % 3); + let d_u = dist2(v[u], foot); + let d_w = dist2(foot, v[w]); + if d_w > 1e-12 { + let ratio = d_u / d_w; + out.push(fact( + "角平分线", + &format!("\\frac{{|{nu}F_{{{s}}}|}}{{|F_{{{s}}}{nw}|}}", s = SIDE[i], nu = names[u], nw = names[w]), + nice(ratio), + Some(ratio), + &format!("\\frac{{{w}}}{{{u}}}", u = SIDE[u], w = SIDE[w]), + "角平分线定理:分对边成邻边比", + )); + } } out.push(fact("特殊点", "G", pt(centroid[0], centroid[1]), None, "G = \\frac{A + B + C}{3}", "重心(中线交点)").with(Shape::Point { x: centroid[0], y: centroid[1], label: "G 重心".into() })); @@ -571,6 +589,37 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] out.push(fact("特殊点", "I", pt(inc[0], inc[1]), None, "I = \\frac{aA + bB + cC}{a + b + c}", "内心(角平分线交点)").with(Shape::Point { x: inc[0], y: inc[1], label: "I 内心".into() })); out.push(fact("特殊点", "H", pt(orth[0], orth[1]), None, "\\vec{OH} = \\vec{OA} + \\vec{OB} + \\vec{OC}", "垂心(高线交点)").with(Shape::Point { x: orth[0], y: orth[1], label: "H 垂心".into() })); + // Excircle radii; Euler OI² = R(R − 2r); OH from the orthocenter / circumcenter. + for i in 0..3 { + let ri = area / (p - s[i]); + out.push(fact( + "外接圆与内切圆", + &format!("r_{}", SIDE[i]), + nice(ri), + Some(ri), + &format!("r_{s} = \\frac{{S}}{{p - {s}}}", s = SIDE[i]), + "旁切圆半径", + )); + } + let oi = dist2(circ, inc); + out.push(fact( + "特殊点", + "|OI|", + nice(oi), + Some(oi), + "|OI|^2 = R(R - 2r)", + "欧拉公式(外心与内心的距离)", + ).with(Shape::Segment { x1: circ[0], y1: circ[1], x2: inc[0], y2: inc[1], label: "OI".into() })); + let oh = dist2(circ, orth); + out.push(fact( + "特殊点", + "|OH|", + nice(oh), + Some(oh), + "|OH|^2 = 9R^2 - (a^2 + b^2 + c^2)", + "外心与垂心的距离", + ).with(Shape::Segment { x1: circ[0], y1: circ[1], x2: orth[0], y2: orth[1], label: "OH".into() })); + let mut kinds: Vec = Vec::new(); let maxg = g.iter().cloned().fold(0.0, f64::max); if near(maxg, PI / 2.0) { @@ -1633,6 +1682,27 @@ mod tests { assert!((get("\\frac{|AP|}{|PB|}").num.unwrap() - 0.5).abs() < 1e-9); } + #[test] + fn angle_bisector_theorem_heron_excircles() { + // 3-4-5: Heron S = 6; bisector from C splits AB as b:a = 4:3; r_a = 2, r_b = 3, r_c = 6 + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let get = |label: &str| fs.iter().find(|f| f.label == label).unwrap(); + assert!((get("S_{\\text{海伦}}").num.unwrap() - 6.0).abs() < 1e-9); + let ratio = get("\\frac{|AF_{c}|}{|F_{c}B|}").num.unwrap(); + assert!((ratio - 4.0 / 3.0).abs() < 1e-9, "ratio = {ratio}"); + assert!((get("r_a").num.unwrap() - 2.0).abs() < 1e-9); + assert!((get("r_b").num.unwrap() - 3.0).abs() < 1e-9); + assert!((get("r_c").num.unwrap() - 6.0).abs() < 1e-9); + // OI² = R(R − 2r) = 2.5 · (2.5 − 2) = 1.25 → OI = √1.25 + let oi = get("|OI|").num.unwrap(); + assert!((oi * oi - 1.25).abs() < 1e-9, "OI = {oi}"); + // right triangle: H at C, O midpoint of AB → |OH| = R = 2.5 + assert!((get("|OH|").num.unwrap() - 2.5).abs() < 1e-9); + } + #[test] fn vector_projection_vector() { let vs = vec![NamedVec { name: "a".into(), v: vec![3.0, 4.0] }, NamedVec { name: "b".into(), v: vec![1.0, 0.0] }]; diff --git a/scripts/ocr-smoke.ts b/scripts/ocr-smoke.ts index a987c0c..06a858b 100644 --- a/scripts/ocr-smoke.ts +++ b/scripts/ocr-smoke.ts @@ -310,6 +310,10 @@ assert.equal(tokensToSource(['a', '^', '{', '2', '}', '=', 'b']), 'a^2 = b') assert.equal(tokensToSource(['\\frac', '{', 'a', '}', '{', 'b', '}']), '(a)/(b)') assert.equal(tokensToSource(['\\sqrt', '{', 'x', '}']), 'sqrt(x)') assert.equal(tokensToSource(['\\vec', '{', 'a', '}']), '\\vec{a}') +assert.equal(tokensToSource(['\\sum', '_', '{', 'i', '=', '1', '}', '^', '{', 'n', '}', 'i']), '\\sum_{i = 1}^{n} i') +assert.equal(tokensToSource(['y', '=', '\\sum', '_', '{', 'k', '=', '1', '}', '^', '{', 'n', '}', 'k']), 'y = \\sum_{k = 1}^{n} k') +assert.equal(tokensToSource(['\\sum', 'i']), '\\sum i') + assert.equal(tokensToSource(['\\overrightarrow', '{', 'b', '}']), '\\vec{b}') assert.equal(tokensToSource(['=']), '') assert.equal(tokensToSource(['\\frac']), '') @@ -430,8 +434,28 @@ assert.equal(bindInk(arrowed, 'a = (1, 2, 2)'), boundVec) assert.doesNotMatch(boundVec, /1,\s*2,\s*2/) console.log('ocr bind ok', { point: bindInk(y2strokes, 'A(1,2)'), vec: boundVec }) + +function sumLikeSigma(): InkStroke[] { + const bowl: InkStroke = { + lineWidth: 3, + points: [ + { x: 40, y: 8 }, + { x: 12, y: 10 }, + { x: 8, y: 36 }, + { x: 28, y: 52 }, + { x: 8, y: 70 }, + { x: 12, y: 96 }, + { x: 42, y: 98 }, + ], + } + const top: InkStroke = { lineWidth: 2, points: [{ x: 48, y: 14 }, { x: 62, y: 12 }] } + const bot: InkStroke = { lineWidth: 2, points: [{ x: 48, y: 92 }, { x: 64, y: 94 }] } + return [bowl, top, bot] +} + assert.equal(classifyInk(y2strokes), 'formula') assert.equal(classifyInk(arrowLetter()), 'formula') assert.equal(classifyInk(proseNote()), 'text', 'a line of letters is not a formula') +assert.equal(classifyInk(sumLikeSigma()), 'formula', 'Σ with limits is a formula') assert.equal(classifyInk(inkFixtures(3).find((s) => s.name === 'frac')!.strokes), 'formula') console.log('ocr gate ok', { prose: classifyInk(proseNote()), formula: classifyInk(y2strokes) }) diff --git a/scripts/plot-cases.ts b/scripts/plot-cases.ts index 08d2b23..e3db0c1 100644 --- a/scripts/plot-cases.ts +++ b/scripts/plot-cases.ts @@ -47,7 +47,7 @@ export const cases: [string, string, Expect][] = [ ['直线过两点', 'y = kx + b, 过(1, 3), 过(2, 5)', { solve: { k: 2, b: 1 } }], // ---- triangles / coordinate geometry ---- ['解三角形 SAS', '△ABC: a = 5, b = 7, C = 60°', { dim: 2, facts: ['\\sqrt{39}'], minFacts: 10 }], - ['解三角形 SSS', '△ABC: a=3, b=4, c=5', { dim: 2, facts: ['90'] }], + ['解三角形 SSS', '△ABC: a=3, b=4, c=5', { dim: 2, facts: ['90', 'S_{\\text{海伦}}', '|OI|', 'r_a=', 'AF_{c}'], minFacts: 18 }], ['解三角形 SSA 两解', '△ABC: a = 6, b = 8, A = 40°', { dim: 2 }], ['坐标 + 垂直', 'A(0,0), B(4,0), C(1,t)\nAC ⊥ BC', { dim: 2, solve: { t: Math.sqrt(3) }, inView: [[0, 0], [4, 0]] }], ['平行四边形', 'A(0,0), B(4,0), C(5,3), D(1,3)', { dim: 2, facts: ['平行四边形'], inView: [[5, 3]] }], diff --git a/src/ocr/comer/source.ts b/src/ocr/comer/source.ts index ef6903d..6d816cc 100644 --- a/src/ocr/comer/source.ts +++ b/src/ocr/comer/source.ts @@ -27,6 +27,7 @@ export function decodeTokens(ids: number[], vocab: Vocab): string[] { /** * CoMER tokens → the ASCII this sheet already parses. * `a ^ { 2 } = b` becomes `a^2 = b`. `\vec{a}` stays an arrowed letter. + * `\sum_{i=1}^{n} i` keeps braced LaTeX so KaTeX can show it (not a plottable curve). * A component tuple is kept only when the model actually emitted parentheses. */ export function tokensToSource(tokens: string[]): string { @@ -51,12 +52,32 @@ export function tokensToSource(tokens: string[]): string { } return body } + /** Keep braces around a group so ∑ / subscripts stay valid LaTeX. */ + const readLatexGroup = (): string => { + if (repaired[i] !== '{') return readAtom() + return `{${readGroup()}}` + } const readAtom = (): string => { const cur = repaired[i++] if (!cur || cur === '{' || cur === '}') return '' if (cur === '\\frac') return `(${readGroup()})/(${readGroup()})` if (cur === '\\sqrt') return `sqrt(${readGroup()})` if (cur === '\\vec' || cur === '\\overrightarrow') return `\\vec{${readGroup()}}` + if (cur === '\\sum') { + let out = '\\sum' + if (repaired[i] === '_') { + i++ + out += `_${readLatexGroup()}` + } + if (repaired[i] === '^') { + i++ + out += `^${readLatexGroup()}` + } + // Body: one atom, or a braced group the model put after the limits. + const body = repaired[i] === '{' ? readLatexGroup() : readAtom() + if (body) out += ` ${body}` + return out + } if (cur === '^') return `^${readGroup()}` if (cur === '_') return `_${readGroup()}` if (cur === '\\cdot' || cur === '\\times') return '' diff --git a/src/ocr/gate.ts b/src/ocr/gate.ts index 3c84d81..0f032ae 100644 --- a/src/ocr/gate.ts +++ b/src/ocr/gate.ts @@ -20,6 +20,7 @@ export function mathCues(strokes: InkStroke[]): string[] { if (hasFractionBar(strokes)) cues.push('fraction') if (hasSuperscript(strokes)) cues.push('superscript') if (hasParen(strokes)) cues.push('paren') + if (hasSumLike(strokes)) cues.push('sum') return cues } @@ -46,6 +47,22 @@ export function looksLikeProse(strokes: InkStroke[]): boolean { return similar && aligned && stepped && all.w > all.h * 1.35 } + +/** + * Tall Σ-shaped stroke with optional limit ticks: treat as math even without "=". + * A single tall bowl with small marks above/below on the right is the usual handwritten sum. + */ +function hasSumLike(strokes: InkStroke[]): boolean { + const boxes = strokes.filter((s) => s.points.length >= 4).map((s) => ({ s, b: bounds(s.points) })) + const sigma = boxes.find(({ b }) => b.h > Math.max(28, b.w * 1.35) && b.h / Math.max(1, b.w) > 1.2) + if (!sigma) return false + const others = boxes.filter((x) => x !== sigma) + const topRight = others.some(({ b }) => b.cy < sigma.b.y0 + sigma.b.h * 0.35 && b.cx > sigma.b.cx - 4 && b.h < sigma.b.h * 0.55) + const botRight = 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5077cfa137d23d817ef702dad717045f58cb3813 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 15:14:33 +0800 Subject: [PATCH 002/123] =?UTF-8?q?feat:=20Ceva,=20Menelaus,=20skew=20line?= =?UTF-8?q?s,=20and=20sphere=C3=97plane?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Emit Ceva products for medians, bisectors, altitudes, and Gergonne contacts, plus a Menelaus transversal check. Derive skew-line distance from four 3D points; treat z = c as a plane and report sphere–plane intersection circles. --- crates/mathcore/src/geometry.rs | 265 ++++++++++++++++++++++++++++++++ scripts/plot-cases.ts | 4 +- src/math/scene.ts | 82 +++++++++- src/math/statements.ts | 2 + src/wasm/pkg/mathcore_bg.wasm | Bin 518888 -> 525315 bytes 5 files changed, 345 insertions(+), 8 deletions(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 8ace504..9a24308 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -620,6 +620,126 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "外心与垂心的距离", ).with(Shape::Segment { x1: circ[0], y1: circ[1], x2: orth[0], y2: orth[1], label: "OH".into() })); + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. + // Emit the classical families that are always concurrent from three sides alone. + { + // Medians: each ratio = 1. + out.push(fact( + "塞瓦与梅涅劳斯", + "\\Pi_{\\text{Ceva}}^{\\text{中线}}", + "1".into(), + Some(1.0), + "\\frac{BD}{DC}\\cdot\\frac{CE}{EA}\\cdot\\frac{AF}{FB} = 1\\cdot 1\\cdot 1", + "塞瓦定理:三中线交于重心", + )); + // Angle bisectors: BD/DC = c/b, CE/EA = a/c, AF/FB = b/a. + let bis = (c / b) * (a / c) * (b / a); + out.push(fact( + "塞瓦与梅涅劳斯", + "\\Pi_{\\text{Ceva}}^{\\text{角平分线}}", + nice(bis), + Some(bis), + &format!( + "\\frac{{c}}{{b}}\\cdot\\frac{{a}}{{c}}\\cdot\\frac{{b}}{{a}} = {}", + nice(bis) + ), + "塞瓦定理:三角平分线交于内心", + )); + // Altitudes: feet of the three altitudes; directed product = 1. + let mut alt_prod = 1.0; + let mut alt_ok = true; + for i in 0..3 { + let (p0, q1, q2) = (v[i], v[(i + 1) % 3], v[(i + 2) % 3]); + let dx = q2[0] - q1[0]; + let dy = q2[1] - q1[1]; + let den = dx * dx + dy * dy; + if den < 1e-18 { + alt_ok = false; + break; + } + let t = ((p0[0] - q1[0]) * dx + (p0[1] - q1[1]) * dy) / den; + let foot = [q1[0] + t * dx, q1[1] + t * dy]; + match directed_ratio(q1, q2, foot) { + Some(r) => alt_prod *= r, + None => { + alt_ok = false; + break; + } + } + } + if alt_ok { + out.push(fact( + "塞瓦与梅涅劳斯", + "\\Pi_{\\text{Ceva}}^{\\text{高}}", + nice(alt_prod), + Some(alt_prod), + "\\frac{BD}{DC}\\cdot\\frac{CE}{EA}\\cdot\\frac{AF}{FB} = 1", + "塞瓦定理:三高交于垂心(有向比)", + )); + } + // Gergonne: incircle contact points. BD = s−b, DC = s−c, … + let (ta, tb, tc) = (p - a, p - b, p - c); + if ta > 1e-12 && tb > 1e-12 && tc > 1e-12 { + let ger = (tb / tc) * (tc / ta) * (ta / tb); + out.push(fact( + "塞瓦与梅涅劳斯", + "\\Pi_{\\text{Ceva}}^{\\text{切点}}", + nice(ger), + Some(ger), + "\\frac{s-b}{s-c}\\cdot\\frac{s-c}{s-a}\\cdot\\frac{s-a}{s-b} = 1", + "塞瓦定理:内切圆切点连线交于格尔巩点", + )); + } + } + + // Menelaus: a transversal DEF with D on BC, E on CA, F on AB (or extensions) + // satisfies (BD/DC)(CE/EA)(AF/FB) = −1 (directed). Construct D,E then F = DE ∩ AB. + { + let d_pt = section_point(pb, pc, 2.0, 1.0); // BD:DC = 2:1 + let e_pt = section_point(pc, pa, 2.0, 1.0); // CE:EA = 2:1 + if let Some(f_pt) = line_line_isect2(d_pt, e_pt, pa, pb) { + if let (Some(r_bc), Some(r_ca), Some(r_ab)) = ( + directed_ratio(pb, pc, d_pt), + directed_ratio(pc, pa, e_pt), + directed_ratio(pa, pb, f_pt), + ) { + let prod = r_bc * r_ca * r_ab; + out.push(fact( + "塞瓦与梅涅劳斯", + "\\Pi_{\\text{Menelaus}}", + nice(prod), + Some(prod), + &format!( + "\\frac{{BD}}{{DC}}\\cdot\\frac{{CE}}{{EA}}\\cdot\\frac{{AF}}{{FB}} = {}\\cdot{}\\cdot{} = {}", + nice(r_bc), + nice(r_ca), + nice(r_ab), + nice(prod) + ), + "梅涅劳斯定理:横截线分三边的有向比之积为 −1", + ).with(Shape::Segment { + x1: d_pt[0], + y1: d_pt[1], + x2: e_pt[0], + y2: e_pt[1], + label: "Menelaus 横截线".into(), + })); + out.push(fact( + "塞瓦与梅涅劳斯", + "F_{\\text{Menelaus}}", + pt(f_pt[0], f_pt[1]), + None, + "DE \\cap AB", + "横截线与 AB(延长线)的交点", + ).with(Shape::Point { + x: f_pt[0], + y: f_pt[1], + label: "F Menelaus".into(), + })); + } + } + } + let mut kinds: Vec = Vec::new(); let maxg = g.iter().cloned().fold(0.0, f64::max); if near(maxg, PI / 2.0) { @@ -664,10 +784,44 @@ pub struct NamedPoint { pub p: Vec, } + pub(crate) fn dist2(a: [f64; 2], b: [f64; 2]) -> f64 { ((a[0] - b[0]).powi(2) + (a[1] - b[1]).powi(2)).sqrt() } +/// Directed ratio AP:PB for P on the line AB. P = A + t(B−A) ⇒ AP:PB = t:(1−t). +fn directed_ratio(a: [f64; 2], b: [f64; 2], p: [f64; 2]) -> Option { + let dx = b[0] - a[0]; + let dy = b[1] - a[1]; + let len2 = dx * dx + dy * dy; + if len2 < 1e-18 { + return None; + } + let t = ((p[0] - a[0]) * dx + (p[1] - a[1]) * dy) / len2; + if (1.0 - t).abs() < 1e-14 { + return None; + } + Some(t / (1.0 - t)) +} + +fn section_point(a: [f64; 2], b: [f64; 2], m: f64, n: f64) -> [f64; 2] { + // divides AB in AP:PB = m:n + let den = m + n; + [(n * a[0] + m * b[0]) / den, (n * a[1] + m * b[1]) / den] +} + +fn line_line_isect2(p: [f64; 2], q: [f64; 2], r: [f64; 2], s: [f64; 2]) -> Option<[f64; 2]> { + let d1 = [q[0] - p[0], q[1] - p[1]]; + let d2 = [s[0] - r[0], s[1] - r[1]]; + let det = d1[0] * d2[1] - d1[1] * d2[0]; + if det.abs() < 1e-14 * (d1[0].hypot(d1[1]) * d2[0].hypot(d2[1])).max(1e-18) { + return None; + } + let t = ((r[0] - p[0]) * d2[1] - (r[1] - p[1]) * d2[0]) / det; + Some([p[0] + t * d1[0], p[1] + t * d1[1]]) +} + + fn line_eq_latex(a: f64, b: f64, c: f64) -> String { // a x + b y = c, normalised for display if near(b, 0.0) { @@ -884,6 +1038,75 @@ fn points3_analyze(points: &[NamedPoint]) -> Vec { let h = 3.0 * vol / area; out.push(fact("距离", &format!("d({}, \\text{{平面}})", pts[3].0), nice(h), Some(h), "d = \\frac{3V}{S}", "等体积法")); } + // Skew / intersecting lines AB and CD from the first four points. + let (na, nb, nc, nd) = (&pts[0].0, &pts[1].0, &pts[2].0, &pts[3].0); + let (pa, pb, pc, pd) = (pts[0].1, pts[1].1, pts[2].1, pts[3].1); + let ab = sub3(pb, pa); + let cd = sub3(pd, pc); + let nskew = cross3(ab, cd); + let ln = len3(nskew); + let ac = sub3(pc, pa); + if ln < 1e-12 * len3(ab).max(len3(cd)).max(1e-12) { + let parallel = len3(ab) > 1e-12 && len3(cd) > 1e-12; + if parallel { + let n2 = cross3(ab, ac); + let dpar = len3(n2) / len3(ab); + out.push(fact( + "异面直线", + &format!("{}{} \\parallel {}{}", na, nb, nc, nd), + "\\checkmark".into(), + None, + "\\vec{AB} \\times \\vec{CD} = \\mathbf{0}", + "方向向量共线", + )); + out.push(fact( + "异面直线", + &format!("d({}{}, {}{})", na, nb, nc, nd), + nice(dpar), + Some(dpar), + "d = \\frac{|\\vec{AB}\\times\\vec{AC}|}{|\\vec{AB}|}", + "平行直线间距离", + )); + } + } else { + let triple = dot3(ac, nskew); + let dskew = triple.abs() / ln; + if dskew < 1e-9 { + out.push(fact( + "异面直线", + &format!("{}{} , {}{}", na, nb, nc, nd), + "\\text{共面(相交或平行)}".into(), + Some(0.0), + "\\vec{AC}\\cdot(\\vec{AB}\\times\\vec{CD}) = 0", + "混合积为 0 ⇒ 共面", + )); + } else { + out.push(fact( + "异面直线", + &format!("d({}{}, {}{})", na, nb, nc, nd), + nice(dskew), + Some(dskew), + "d = \\frac{|\\vec{AC}\\cdot(\\vec{AB}\\times\\vec{CD})|}{|\\vec{AB}\\times\\vec{CD}|}", + "异面直线的距离", + ).with(Shape::Line3 { + px: pa[0], + py: pa[1], + pz: pa[2], + dx: ab[0], + dy: ab[1], + dz: ab[2], + label: format!("{na}{nb}"), + })); + out.push(fact( + "异面直线", + &format!("{}{} \\nparallel {}{}", na, nb, nc, nd), + "\\text{异面}".into(), + None, + "\\vec{AB}\\times\\vec{CD}\\ne\\mathbf{0},\\ \\vec{AC}\\cdot(\\vec{AB}\\times\\vec{CD})\\ne 0", + "既不平行也不相交", + )); + } + } } } out @@ -1767,4 +1990,46 @@ mod tests { let sim = out.iter().find(|f| f.label.starts_with("\\text{相似比}")).unwrap(); assert!((sim.num.unwrap() - 1.0 / 3.0).abs() < 1e-9, "k = {}", sim.value); } + + #[test] + fn ceva_and_menelaus_on_345() { + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let get = |label: &str| fs.iter().find(|f| f.label == label).unwrap_or_else(|| panic!("missing {label}")); + assert!((get("\\Pi_{\\text{Ceva}}^{\\text{中线}}").num.unwrap() - 1.0).abs() < 1e-9); + assert!((get("\\Pi_{\\text{Ceva}}^{\\text{角平分线}}").num.unwrap() - 1.0).abs() < 1e-9); + // right triangle: an altitude foot sits on a vertex → skip 高 family + assert!(fs.iter().all(|f| f.label != "\\Pi_{\\text{Ceva}}^{\\text{高}}")); + assert!((get("\\Pi_{\\text{Ceva}}^{\\text{切点}}").num.unwrap() - 1.0).abs() < 1e-9); + let men = get("\\Pi_{\\text{Menelaus}}").num.unwrap(); + assert!((men + 1.0).abs() < 1e-9, "Menelaus = {men}"); + } + + #[test] + fn ceva_altitudes_acute() { + // 6-5-5 acute isosceles: all altitude feet interior → Ceva product = 1 + let k = TriangleKnown { a: Some(6.0), b: Some(5.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let alt = fs.iter().find(|f| f.label == "\\Pi_{\\text{Ceva}}^{\\text{高}}").unwrap(); + assert!((alt.num.unwrap() - 1.0).abs() < 1e-9, "alt = {}", alt.value); + } + + #[test] + fn skew_lines_distance() { + // AB = (0,0,0)->(1,0,0), CD = (0,1,0)->(0,1,1): skew, distance = 1 + let pts = vec![ + NamedPoint { name: "A".into(), p: vec![0.0, 0.0, 0.0] }, + NamedPoint { name: "B".into(), p: vec![1.0, 0.0, 0.0] }, + NamedPoint { name: "C".into(), p: vec![0.0, 1.0, 0.0] }, + NamedPoint { name: "D".into(), p: vec![0.0, 1.0, 1.0] }, + ]; + let out = points_analyze(&pts); + let d = out.iter().find(|f| f.label == "d(AB, CD)").unwrap(); + assert!((d.num.unwrap() - 1.0).abs() < 1e-9, "d = {}", d.value); + assert!(out.iter().any(|f| f.value.contains("异面"))); + } } diff --git a/scripts/plot-cases.ts b/scripts/plot-cases.ts index e3db0c1..c928a80 100644 --- a/scripts/plot-cases.ts +++ b/scripts/plot-cases.ts @@ -47,7 +47,7 @@ export const cases: [string, string, Expect][] = [ ['直线过两点', 'y = kx + b, 过(1, 3), 过(2, 5)', { solve: { k: 2, b: 1 } }], // ---- triangles / coordinate geometry ---- ['解三角形 SAS', '△ABC: a = 5, b = 7, C = 60°', { dim: 2, facts: ['\\sqrt{39}'], minFacts: 10 }], - ['解三角形 SSS', '△ABC: a=3, b=4, c=5', { dim: 2, facts: ['90', 'S_{\\text{海伦}}', '|OI|', 'r_a=', 'AF_{c}'], minFacts: 18 }], + ['解三角形 SSS', '△ABC: a=3, b=4, c=5', { dim: 2, facts: ['90', 'S_{\\text{海伦}}', '|OI|', 'r_a=', 'AF_{c}', '\\Pi_{\\text{Ceva}}', '\\Pi_{\\text{Menelaus}}'], minFacts: 22 }], ['解三角形 SSA 两解', '△ABC: a = 6, b = 8, A = 40°', { dim: 2 }], ['坐标 + 垂直', 'A(0,0), B(4,0), C(1,t)\nAC ⊥ BC', { dim: 2, solve: { t: Math.sqrt(3) }, inView: [[0, 0], [4, 0]] }], ['平行四边形', 'A(0,0), B(4,0), C(5,3), D(1,3)', { dim: 2, facts: ['平行四边形'], inView: [[5, 3]] }], @@ -88,6 +88,8 @@ export const cases: [string, string, Expect][] = [ ['碗面 z = x² + y²', 'z = x^2 + y^2', { dim: 3 }], ['两平面交线', 'x + y + z = 3\nx - y + 2z = 1', { dim: 3, facts: ['α \\cap β'] }], ['球面', 'x^2 + y^2 + z^2 = 4', { dim: 3, facts: ['r=2'] }], + ['球面 ∩ 平面', 'x^2 + y^2 + z^2 = 4\nz = 1', { dim: 3, facts: ['\\rho_', '\\text{圆}'] }], + ['异面直线四点', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,1,1)', { dim: 3, facts: ['d(AB, CD)=1', '异面'] }], ['空间螺旋线', 'r(t) = (cos(t), sin(t), t/3)', { dim: 3 }], ['空间三点', 'P(1,2,3), Q(0,1,-1), R(2,0,1)', { dim: 3 }], ] diff --git a/src/math/scene.ts b/src/math/scene.ts index a4acb40..92e3f59 100644 --- a/src/math/scene.ts +++ b/src/math/scene.ts @@ -647,6 +647,7 @@ export function analyze(cards: CardInput[], solutionIndex = 0): Analysis { // ---- 3D: planes / surfaces / implicit ------------------------------------------------------ const planes: { name: string; n: number[]; d: number }[] = [] + const spheres: { name: string; c: number[]; r: number }[] = [] for (const i of good) { if (i.st.kind === 'implicit3') { const co = engine.linearCoeffs(i.st.F, ['x', 'y', 'z'], env) @@ -657,8 +658,11 @@ export function analyze(cards: CardInput[], solutionIndex = 0): Analysis { } else { const name = i.st.name ?? nextName(['Σ'], (k) => `Σ_${k}`) objects.push({ type: 'implicit3', name, F: i.st.F, color: nextColor() }) - const sphere = sphereFacts(i.st.F, env) - if (sphere.length) sections.push({ id: `sph-${i.idx}`, title: `曲面 ${name}`, subtitle: '球面识别', tone: 'func', facts: sphere }) + const sph = parseSphere(i.st.F, env) + if (sph) { + spheres.push({ name, c: sph.c, r: sph.r }) + sections.push({ id: `sph-${i.idx}`, title: `曲面 ${name}`, subtitle: '球面识别', tone: 'func', facts: sphereFactsFrom(sph) }) + } } } else if (i.st.kind === 'surface') { const name = names.get(i)! @@ -697,6 +701,66 @@ export function analyze(cards: CardInput[], solutionIndex = 0): Analysis { } if (planes.length) sections.push({ id: 'planes', title: `平面 ${planes.map((p) => p.name).join(', ')}`, subtitle: '法向量 · 夹角 · 交线 / 交点', tone: 'geo', facts: engine.planes(planes, pts3) }) + if (spheres.length && planes.length) { + const facts: RustFact[] = [] + for (const s of spheres) { + for (const p of planes) { + const ln = Math.hypot(p.n[0], p.n[1], p.n[2]) + if (ln < 1e-12) continue + const signed = (p.n[0] * s.c[0] + p.n[1] * s.c[1] + p.n[2] * s.c[2] - p.d) / ln + const dist = Math.abs(signed) + const label = `${s.name} \\cap ${p.name}` + if (dist > s.r + 1e-9) { + facts.push({ group: '球面与平面', label, value: '\\varnothing', num: null, how: 'd > r', why: '球心到平面的距离大于半径,不相交', shape: null }) + } else if (Math.abs(dist - s.r) < 1e-9) { + const t = -signed + const q = [s.c[0] + (t * p.n[0]) / ln, s.c[1] + (t * p.n[1]) / ln, s.c[2] + (t * p.n[2]) / ln] + facts.push({ + group: '球面与平面', + label, + value: `\\text{相切于 }\\left(${fmt(q[0])},\\ ${fmt(q[1])},\\ ${fmt(q[2])}\\right)`, + num: 0, + how: 'd = r', + why: '球心到平面的距离等于半径', + shape: { type: 'point3', x: q[0], y: q[1], z: q[2], label: `${s.name}∩${p.name}` }, + }) + } else { + const rho = Math.sqrt(Math.max(0, s.r * s.r - dist * dist)) + const t = -signed + const q = [s.c[0] + (t * p.n[0]) / ln, s.c[1] + (t * p.n[1]) / ln, s.c[2] + (t * p.n[2]) / ln] + facts.push({ + group: '球面与平面', + label: `\\text{交圆圆心}_{${s.name},${p.name}}`, + value: `\\left(${fmt(q[0])},\\ ${fmt(q[1])},\\ ${fmt(q[2])}\\right)`, + num: null, + how: "O' = O - \\dfrac{ax_0+by_0+cz_0-d}{|n|^2}\\vec n", + why: '球心在平面上的投影', + shape: { type: 'point3', x: q[0], y: q[1], z: q[2], label: '交圆圆心' }, + }) + facts.push({ + group: '球面与平面', + label: `\\rho_{${s.name}\\cap ${p.name}}`, + value: engine.nice(rho), + num: rho, + how: '\\rho = \\sqrt{r^2 - d^2}', + why: '交圆半径', + shape: null, + }) + facts.push({ + group: '球面与平面', + label, + value: '\\text{圆}', + num: rho, + how: 'd < r', + why: '球面被平面截得一圆', + shape: null, + }) + } + } + } + if (facts.length) sections.push({ id: 'sphere-plane', title: '球面 ∩ 平面', subtitle: '交圆 · 相切 · 相离', tone: 'geo', facts }) + } + if (marks.length) objects.push({ type: 'marks', pts: marks }) // ---- dimension --------------------------------------------------------------------------- @@ -831,24 +895,28 @@ function equationFacts(st: Extract, name: stri return { facts, roots: zs } } -function sphereFacts(F: string, env: Env): RustFact[] { +function parseSphere(F: string, env: Env): { c: number[]; r: number } | null { // F = x² + y² + z² + Dx + Ey + Fz + G (up to a common factor) const f = (x: number, y: number, z: number) => engine.eval(F, { ...env, x, y, z }) const g = f(0, 0, 0) const ax = (f(1, 0, 0) + f(-1, 0, 0)) / 2 - g const ay = (f(0, 1, 0) + f(0, -1, 0)) / 2 - g const az = (f(0, 0, 1) + f(0, 0, -1)) / 2 - g - if (!(Math.abs(ax - ay) < 1e-9 && Math.abs(ay - az) < 1e-9 && Math.abs(ax) > 1e-12)) return [] + if (!(Math.abs(ax - ay) < 1e-9 && Math.abs(ay - az) < 1e-9 && Math.abs(ax) > 1e-12)) return null const D = (f(1, 0, 0) - f(-1, 0, 0)) / 2 / ax const E = (f(0, 1, 0) - f(0, -1, 0)) / 2 / ax const G = (f(0, 0, 1) - f(0, 0, -1)) / 2 / ax const c = [-D / 2, -E / 2, -G / 2] const test = f(2.3, -1.1, 0.7) / ax const pred = 2.3 ** 2 + 1.1 ** 2 + 0.7 ** 2 + D * 2.3 - E * 1.1 + G * 0.7 + g / ax - if (Math.abs(test - pred) > 1e-7 * (1 + Math.abs(test))) return [] + if (Math.abs(test - pred) > 1e-7 * (1 + Math.abs(test))) return null const r2 = c[0] ** 2 + c[1] ** 2 + c[2] ** 2 - g / ax - if (r2 <= 0) return [] - const r = Math.sqrt(r2) + if (r2 <= 0) return null + return { c, r: Math.sqrt(r2) } +} + +function sphereFactsFrom(sph: { c: number[]; r: number }): RustFact[] { + const { c, r } = sph return [ { group: '球面', label: '\\text{类型}', value: '\\text{球面}', num: null, how: '(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2', why: '配方', shape: null }, { group: '球面', label: '\\text{球心}', value: `\\left(${fmt(c[0])},\\ ${fmt(c[1])},\\ ${fmt(c[2])}\\right)`, num: null, how: '', why: '配方', shape: { type: 'point3', x: c[0], y: c[1], z: c[2], label: '球心' } }, diff --git a/src/math/statements.ts b/src/math/statements.ts index f093a28..b42ffc9 100644 --- a/src/math/statements.ts +++ b/src/math/statements.ts @@ -244,6 +244,8 @@ function classifyPart(part: string): Statement[] { const v = vars(rhs) if (!v) return [err(src, engine.inspect(rhs).error ?? '无法解析')] if (v.includes('z')) return [{ kind: 'implicit3', F: `(z) - (${rhs})`, src }] + // z = c (no x/y) is the horizontal plane; keep it as implicit3 so plane tools apply. + if (v.length === 0) return [{ kind: 'implicit3', F: `(z) - (${rhs})`, src }] return [{ kind: 'surface', name: named ? named[1] : undefined, expr: rhs, src }] } diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 55940d0cadd52fec1c489fb371885e2aa9f9248c..27916f6065fe5df47f283ca38c049e7d0c9aa260 100644 GIT binary patch delta 56669 zcmce<30ziH{y+ZQbMM0@=;H&=8-^J9&mke3AHRiH8@xSIMtZ%6Q zzmD+n8spk~bmQ)O#tq!2Wb2Bq@!G{TzQBhn_oYXR4gXLEN9k%NYg3GtdnU0~#Tb-( zy!dFLk{D9CGL3&o~H~JubU`cSGKCo0z)Cc3q*qxgcLVvt@@dh7{ z()~J30X63;dVgN~IDjMhPD%y@o>JHx>aJ4>qEaSnS58R4SiBvB=RC2&7g+4?L+}no zXFOl|t36db2F^&P1#t!I=u~utXJ)6{^AB`I>F5J12|N^~YkCwa1*48nVDY{_eUR69 z<>SVxd(#PNb@$E>5o&nX!y9}ScIK+nB=!hvZCEx2Y4Bl`R>Brw+bme7gFt|qC1@&Z zqEsT&MtmXgBiC*rH<#JS1>8a|POP!pVWLafQ51_P%=ag1au{1bDV!V>#M3vk$s_FmA766 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From 4cfd4d72835bbd927b8ee0b347652c261524c725 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 15:17:05 +0800 Subject: [PATCH 003/123] =?UTF-8?q?feat:=20Stewart,=20line=E2=80=93plane?= =?UTF-8?q?=20angle,=20and=20two-sphere=20radical=20plane?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Verify Stewart for medians/bisectors in triangle_derived; emit line–plane θ (∥/⊥) from 3D point pairs in planes_analyze; compute radical plane, center distance, and intersection circle for sphere pairs in scene. --- crates/mathcore/src/geometry.rs | 148 ++++++++++++++++++++++++++++++++ scripts/plot-cases.ts | 4 +- src/math/scene.ts | 90 +++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 525315 -> 530606 bytes 4 files changed, 241 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 9a24308..828d583 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -740,6 +740,61 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // Stewart: for a cevian AD to side a=BC with BD=m, DC=n (m+n=a), + // a(d² + mn) = b²m + c²n. Verify for medians and angle bisectors. + { + for i in 0..3 { + let (aa, bb, cc) = (s[i], s[(i + 1) % 3], s[(i + 2) % 3]); + // median: m = n = a/2 + let m = aa / 2.0; + let n = aa / 2.0; + let d = 0.5 * (2.0 * bb * bb + 2.0 * cc * cc - aa * aa).max(0.0).sqrt(); + let lhs = bb * bb * m + cc * cc * n; + let rhs = aa * (d * d + m * n); + if (lhs - rhs).abs() < 1e-6 * (1.0 + lhs.abs()) { + out.push(fact( + "斯特瓦尔特定理", + &format!("\\text{{Stewart}}_{{m_{}}}", SIDE[i]), + nice(lhs), + Some(lhs), + &format!( + "{b}^2\\cdot\\frac{{{a}}}{{2}} + {c}^2\\cdot\\frac{{{a}}}{{2}} = {a}\\left(m_{s}^2 + \\left(\\frac{{{a}}}{{2}}\\right)^2\\right)", + a = SIDE[i], + b = SIDE[(i + 1) % 3], + c = SIDE[(i + 2) % 3], + s = SIDE[i], + ), + "斯特瓦尔特定理(中线)", + )); + } + // angle bisector: BD:DC = c:b → m = c/(b+c)·a, n = b/(b+c)·a + let den = bb + cc; + if den > 1e-12 { + let m = cc / den * aa; + let n = bb / den * aa; + let d = 2.0 * bb * cc * (g[i] / 2.0).cos() / den; + let lhs = bb * bb * m + cc * cc * n; + let rhs = aa * (d * d + m * n); + if (lhs - rhs).abs() < 1e-6 * (1.0 + lhs.abs()) { + out.push(fact( + "斯特瓦尔特定理", + &format!("\\text{{Stewart}}_{{t_{}}}", SIDE[i]), + nice(lhs), + Some(lhs), + &format!( + "{b}^2 m + {c}^2 n = {a}(t_{s}^2 + mn),\\ m:n = {c}:{b}", + a = SIDE[i], + b = SIDE[(i + 1) % 3], + c = SIDE[(i + 2) % 3], + s = SIDE[i], + ), + "斯特瓦尔特定理(角平分线)", + )); + } + } + } + } + let mut kinds: Vec = Vec::new(); let maxg = g.iter().cloned().fold(0.0, f64::max); if near(maxg, PI / 2.0) { @@ -1447,6 +1502,65 @@ pub fn planes_analyze(ps: &[NamedPlane], points: &[NamedPoint]) -> Vec { out.push(fact("点与平面", &format!("d({}, {})", q.name, p.name), nice(d), Some(d), "\\frac{|ax_0+by_0+cz_0-d|}{\\sqrt{a^2+b^2+c^2}}", "点到平面距离")); } } + // Line–plane angle: every pair of 3D points defines a line. + { + let pts3: Vec<(String, [f64; 3])> = points + .iter() + .filter(|q| q.p.len() >= 3) + .map(|q| (q.name.clone(), [q.p[0], q.p[1], q.p[2]])) + .collect(); + let mut pair_count = 0usize; + 'pairs: for i in 0..pts3.len() { + for j in i + 1..pts3.len() { + if pair_count >= 6 { + break 'pairs; + } + let (ref na, pa) = pts3[i]; + let (ref nb, pb) = pts3[j]; + let dir = sub3(pb, pa); + let ld = len3(dir); + if ld < 1e-12 { + continue; + } + pair_count += 1; + for p in ps { + let ln = len3(p.n); + if ln < 1e-12 { + continue; + } + let sin_phi = (dot3(dir, p.n).abs() / (ld * ln)).clamp(0.0, 1.0); + let phi = sin_phi.asin(); // angle between line and plane ∈ [0, π/2] + out.push(fact( + "线面角", + &format!("\\theta({}{}, {})", na, nb, p.name), + deg(phi), + Some(phi), + "\\sin\\theta = \\dfrac{|\\vec v\\cdot\\vec n|}{|\\vec v||\\vec n|}", + "直线与平面所成的角", + )); + if sin_phi < 1e-9 { + out.push(fact( + "线面角", + &format!("{}{} \\parallel {}", na, nb, p.name), + "\\checkmark".into(), + None, + "\\vec v\\cdot\\vec n = 0", + "直线平行于平面(或落在平面上)", + )); + } else if (1.0 - sin_phi).abs() < 1e-9 { + out.push(fact( + "线面角", + &format!("{}{} \\perp {}", na, nb, p.name), + "\\checkmark".into(), + None, + "|\\vec v\\cdot\\vec n| = |\\vec v||\\vec n|", + "直线垂直于平面", + )); + } + } + } + } + } for i in 0..ps.len() { for j in i + 1..ps.len() { let (p, q) = (&ps[i], &ps[j]); @@ -2032,4 +2146,38 @@ mod tests { assert!((d.num.unwrap() - 1.0).abs() < 1e-9, "d = {}", d.value); assert!(out.iter().any(|f| f.value.contains("异面"))); } + + #[test] + fn stewart_median_and_bisector() { + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + // median to c=5: m=n=2.5, d=2.5; LHS = 3²·2.5 + 4²·2.5 = 62.5 + let med = fs.iter().find(|f| f.label == "\\text{Stewart}_{m_c}").unwrap(); + assert!((med.num.unwrap() - 62.5).abs() < 1e-6, "med = {}", med.value); + let bis = fs.iter().find(|f| f.label == "\\text{Stewart}_{t_c}").unwrap(); + assert!(bis.num.unwrap().is_finite()); + // both sides of Stewart agree for every median/bisector we emitted + assert_eq!(fs.iter().filter(|f| f.label.starts_with("\\text{Stewart}_")).count(), 6); + } + + #[test] + fn line_plane_angle_perpendicular() { + // AB = vertical (0,0,0)->(0,0,1); plane z = 0 → θ = 90° + let ps = vec![NamedPlane { name: "α".into(), n: [0.0, 0.0, 1.0], d: 0.0 }]; + let pts = vec![ + NamedPoint { name: "A".into(), p: vec![0.0, 0.0, 0.0] }, + NamedPoint { name: "B".into(), p: vec![0.0, 0.0, 1.0] }, + NamedPoint { name: "C".into(), p: vec![1.0, 0.0, 0.0] }, + ]; + let out = planes_analyze(&ps, &pts); + let th = out.iter().find(|f| f.label == "\\theta(AB, α)").unwrap(); + assert!((th.num.unwrap() - PI / 2.0).abs() < 1e-9, "θ = {}", th.value); + assert!(out.iter().any(|f| f.label == "AB \\perp α")); + // AC lies in / parallel to the plane → θ = 0 + let th2 = out.iter().find(|f| f.label == "\\theta(AC, α)").unwrap(); + assert!(th2.num.unwrap().abs() < 1e-9, "θ(AC) = {}", th2.value); + assert!(out.iter().any(|f| f.label == "AC \\parallel α")); + } } diff --git a/scripts/plot-cases.ts b/scripts/plot-cases.ts index c928a80..a93ea87 100644 --- a/scripts/plot-cases.ts +++ b/scripts/plot-cases.ts @@ -47,7 +47,7 @@ export const cases: [string, string, Expect][] = [ ['直线过两点', 'y = kx + b, 过(1, 3), 过(2, 5)', { solve: { k: 2, b: 1 } }], // ---- triangles / coordinate geometry ---- ['解三角形 SAS', '△ABC: a = 5, b = 7, C = 60°', { dim: 2, facts: ['\\sqrt{39}'], minFacts: 10 }], - ['解三角形 SSS', '△ABC: a=3, b=4, c=5', { dim: 2, facts: ['90', 'S_{\\text{海伦}}', '|OI|', 'r_a=', 'AF_{c}', '\\Pi_{\\text{Ceva}}', '\\Pi_{\\text{Menelaus}}'], minFacts: 22 }], + ['解三角形 SSS', '△ABC: a=3, b=4, c=5', { dim: 2, facts: ['90', 'S_{\\text{海伦}}', '|OI|', 'r_a=', 'AF_{c}', '\\Pi_{\\text{Ceva}}', '\\Pi_{\\text{Menelaus}}', '\\text{Stewart}_{m_'], minFacts: 26 }], ['解三角形 SSA 两解', '△ABC: a = 6, b = 8, A = 40°', { dim: 2 }], ['坐标 + 垂直', 'A(0,0), B(4,0), C(1,t)\nAC ⊥ BC', { dim: 2, solve: { t: Math.sqrt(3) }, inView: [[0, 0], [4, 0]] }], ['平行四边形', 'A(0,0), B(4,0), C(5,3), D(1,3)', { dim: 2, facts: ['平行四边形'], inView: [[5, 3]] }], @@ -90,6 +90,8 @@ export const cases: [string, string, Expect][] = [ ['球面', 'x^2 + y^2 + z^2 = 4', { dim: 3, facts: ['r=2'] }], ['球面 ∩ 平面', 'x^2 + y^2 + z^2 = 4\nz = 1', { dim: 3, facts: ['\\rho_', '\\text{圆}'] }], ['异面直线四点', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,1,1)', { dim: 3, facts: ['d(AB, CD)=1', '异面'] }], + ['线面角', 'A(0,0,0)\nB(0,0,1)\nC(1,0,0)\nz = 0', { dim: 3, facts: ['\\theta(AB, α)', 'AB \\perp α', 'AC \\parallel α'] }], + ['两球根面', 'x^2 + y^2 + z^2 = 4\n(x-3)^2 + y^2 + z^2 = 4', { dim: 3, facts: ['\\pi_', '\\rho_'] }], ['空间螺旋线', 'r(t) = (cos(t), sin(t), t/3)', { dim: 3 }], ['空间三点', 'P(1,2,3), Q(0,1,-1), R(2,0,1)', { dim: 3 }], ] diff --git a/src/math/scene.ts b/src/math/scene.ts index 92e3f59..b8be871 100644 --- a/src/math/scene.ts +++ b/src/math/scene.ts @@ -761,6 +761,96 @@ export function analyze(cards: CardInput[], solutionIndex = 0): Analysis { if (facts.length) sections.push({ id: 'sphere-plane', title: '球面 ∩ 平面', subtitle: '交圆 · 相切 · 相离', tone: 'geo', facts }) } + + if (spheres.length >= 2) { + const facts: RustFact[] = [] + for (let i = 0; i < spheres.length; i++) { + for (let j = i + 1; j < spheres.length; j++) { + const A = spheres[i] + const B = spheres[j] + const n = [B.c[0] - A.c[0], B.c[1] - A.c[1], B.c[2] - A.c[2]] + const ln = Math.hypot(n[0], n[1], n[2]) + const d = + (B.c[0] ** 2 + B.c[1] ** 2 + B.c[2] ** 2 - A.c[0] ** 2 - A.c[1] ** 2 - A.c[2] ** 2 - B.r ** 2 + A.r ** 2) / 2 + if (ln < 1e-12) { + facts.push({ + group: '根面', + label: `${A.name}, ${B.name}`, + value: Math.abs(A.r - B.r) < 1e-9 ? '\\text{同心等半径(重合)}' : '\\text{同心不等半径(无根面)}', + num: null, + how: '\\vec{O_1O_2} = \\mathbf{0}', + why: '两球球心重合', + shape: null, + }) + continue + } + const terms: string[] = [] + ;(['x', 'y', 'z'] as const).forEach((ax, k) => { + if (Math.abs(n[k]) < 1e-12) return + const coef = Math.abs(n[k] - 1) < 1e-9 ? '' : Math.abs(n[k] + 1) < 1e-9 ? '-' : fmt(n[k]) + terms.push(`${coef}${ax}`) + }) + let eq = terms.join(' + ').replace('+ -', '- ') + if (!eq) eq = '0' + eq = `${eq} = ${fmt(d)}` + facts.push({ + group: '根面', + label: `\\pi_{${A.name}${B.name}}`, + value: eq, + num: null, + how: '(\\vec{O_2}-\\vec{O_1})\\cdot\\vec{x} = \\frac{|O_2|^2-|O_1|^2-r_2^2+r_1^2}{2}', + why: '两球面方程相减得根面', + shape: null, + }) + objects.push({ type: 'plane', name: `π_${A.name}${B.name}`, n, d, color: nextColor() }) + const signed = (n[0] * A.c[0] + n[1] * A.c[1] + n[2] * A.c[2] - d) / ln + const dist = Math.abs(signed) + facts.push({ + group: '根面', + label: `d(O_{${A.name}}, \\pi_{${A.name}${B.name}})`, + value: engine.nice(dist), + num: dist, + how: '\\dfrac{|\\vec n\\cdot O_1 - d|}{|\\vec n|}', + why: '球心到根面的距离', + shape: null, + }) + const rho2 = A.r * A.r - signed * signed + if (rho2 > 1e-9) { + facts.push({ + group: '根面', + label: `\\rho_{${A.name}\\cap ${B.name}}`, + value: engine.nice(Math.sqrt(rho2)), + num: Math.sqrt(rho2), + how: '\\rho = \\sqrt{r_1^2 - d_1^2}', + why: '两球交圆落在根面上', + shape: null, + }) + } else if (Math.abs(rho2) <= 1e-9) { + facts.push({ + group: '根面', + label: `${A.name} \\cap ${B.name}`, + value: '\\text{相切}', + num: 0, + how: 'd_1 = \\pm r_1', + why: '两球相切,交点在根面上', + shape: null, + }) + } else { + facts.push({ + group: '根面', + label: `${A.name}, ${B.name}`, + value: '\\text{相离(根面仍在)}', + num: null, + how: 'r_1^2 - d_1^2 < 0', + why: '无实交圆;根面是等幂点的轨迹', + shape: null, + }) + } + } + } + if (facts.length) sections.push({ id: 'radical', title: '两球根面', subtitle: '等幂点轨迹 · 交圆平面', tone: 'geo', facts }) + } + if (marks.length) objects.push({ type: 'marks', pts: marks }) // ---- dimension --------------------------------------------------------------------------- diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 27916f6065fe5df47f283ca38c049e7d0c9aa260..77dd6f92bf79bc33140af77cab925a5a8a5d0395 100644 GIT binary patch delta 103936 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Content-Transfer-Encoding: 8bit Angle-bisector length and power-of-a-point were already covered; add Van Obel (incenter AI/ID=(b+c)/a) and Apollonius circles per vertex, line–sphere intersection points in scene, clearer tetrahedron volume label, and an explicit dihedral-angle fact beside plane–plane θ. --- crates/mathcore/src/geometry.rs | 164 +++++++++++++++++++++++++++++++- scripts/plot-cases.ts | 5 +- src/math/scene.ts | 86 +++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 530606 -> 534420 bytes 4 files changed, 253 insertions(+), 2 deletions(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 828d583..08f22fb 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -795,6 +795,119 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // Van Obel (incenter form): AI/ID = (b+c)/a. + { + for i in 0..3 { + let (aa, bb, cc) = (s[i], s[(i + 1) % 3], s[(i + 2) % 3]); + let den = bb + cc; + if den < 1e-12 || aa < 1e-12 { + continue; + } + let foot = [ + (bb * v[(i + 1) % 3][0] + cc * v[(i + 2) % 3][0]) / den, + (bb * v[(i + 1) % 3][1] + cc * v[(i + 2) % 3][1]) / den, + ]; + let ai = dist2(v[i], inc); + let idlen = dist2(inc, foot); + if idlen < 1e-12 { + continue; + } + let ratio = ai / idlen; + let expect = den / aa; + if (ratio - expect).abs() < 1e-6 * (1.0 + expect) { + out.push(fact( + "凡奥培尔定理", + &format!("\\dfrac{{|{n}I|}}{{|ID_{{{s}}}|}}", n = names[i], s = SIDE[i]), + nice(ratio), + Some(ratio), + &format!( + "\\dfrac{{{b} + {c}}}{{{a}}} = \\dfrac{{AF}}{{FB}} + \\dfrac{{AE}}{{EC}}", + a = SIDE[i], + b = SIDE[(i + 1) % 3], + c = SIDE[(i + 2) % 3], + ), + "凡奥培尔定理(内心):角平分线分对边的内分比之和", + ).with(Shape::Segment { + x1: v[i][0], + y1: v[i][1], + x2: foot[0], + y2: foot[1], + label: format!("{}I", names[i]), + })); + } + } + } + + // Apollonius circle at vertex i. + { + for i in 0..3 { + let b_pt = v[(i + 1) % 3]; + let c_pt = v[(i + 2) % 3]; + let side_to_b = s[(i + 2) % 3]; + let side_to_c = s[(i + 1) % 3]; + let opp = s[i]; + if side_to_c < 1e-12 { + continue; + } + let k = side_to_b / side_to_c; + if (k - 1.0).abs() < 1e-9 { + let mid = [(b_pt[0] + c_pt[0]) / 2.0, (b_pt[1] + c_pt[1]) / 2.0]; + out.push(fact( + "阿波罗尼奥斯圆", + &format!("\\mathcal{{A}}_{{{}}}", names[i]), + "\\text{中垂线}".into(), + None, + &format!( + "\\frac{{|P{nb}|}}{{|P{nc}|}} = 1", + nb = names[(i + 1) % 3], + nc = names[(i + 2) % 3], + ), + "阿波罗尼奥斯圆退化为对边的中垂线", + ).with(Shape::Point { + x: mid[0], + y: mid[1], + label: format!("A_{} 中点", names[i]), + })); + continue; + } + let k2 = k * k; + let o = [ + (k2 * c_pt[0] - b_pt[0]) / (k2 - 1.0), + (k2 * c_pt[1] - b_pt[1]) / (k2 - 1.0), + ]; + let rad = (k * opp / (k2 - 1.0).abs()).abs(); + let d_v = dist2(v[i], o); + if (d_v - rad).abs() > 1e-4 * (1.0 + rad) { + continue; + } + out.push(fact( + "阿波罗尼奥斯圆", + &format!("\\mathcal{{A}}_{{{}}}", names[i]), + format!( + "O=\\left({},\\ {}\\right),\\ R={}", + nice_short(o[0]), + nice_short(o[1]), + nice(rad) + ), + Some(rad), + &format!( + "\\frac{{|P{nb}|}}{{|P{nc}|}} = \\frac{{{c}}}{{{b}}} = {k}", + nb = names[(i + 1) % 3], + nc = names[(i + 2) % 3], + b = SIDE[(i + 1) % 3], + c = SIDE[(i + 2) % 3], + k = nice(k), + ), + "阿波罗尼奥斯圆:到两定点距离成定比的轨迹", + ).with(Shape::Circle { + cx: o[0], + cy: o[1], + r: rad, + label: format!("阿氏圆 {}", names[i]), + })); + } + } + let mut kinds: Vec = Vec::new(); let maxg = g.iter().cloned().fold(0.0, f64::max); if near(maxg, PI / 2.0) { @@ -1088,7 +1201,7 @@ fn points3_analyze(points: &[NamedPoint]) -> Vec { if pts.len() >= 4 { let dpt = pts[3].1; let vol = dot3(sub3(dpt, a), nrm).abs() / 6.0; - out.push(fact("体积", "V", nice(vol), Some(vol), "V = \\frac16\\left|\\vec{AD}\\cdot(\\vec{AB}\\times\\vec{AC})\\right|", "混合积")); + out.push(fact("体积", "V_{\\text{四面体}}", nice(vol), Some(vol), "V = \\frac16\\left|\\vec{AD}\\cdot(\\vec{AB}\\times\\vec{AC})\\right|", "混合积")); if area > 1e-12 { let h = 3.0 * vol / area; out.push(fact("距离", &format!("d({}, \\text{{平面}})", pts[3].0), nice(h), Some(h), "d = \\frac{3V}{S}", "等体积法")); @@ -1577,6 +1690,14 @@ pub fn planes_analyze(ps: &[NamedPlane], points: &[NamedPoint]) -> Vec { } let ang = (dot3(p.n, q.n).abs() / (lp * lq)).clamp(-1.0, 1.0).acos(); out.push(fact("两平面", &format!("\\theta({}, {})", p.name, q.name), deg(ang), Some(ang), "\\cos\\theta = \\frac{|\\vec n_1\\cdot\\vec n_2|}{|\\vec n_1||\\vec n_2|}", "二面角(锐角)")); + out.push(fact( + "两平面", + &format!("\\text{{二面角}}({}, {})", p.name, q.name), + deg(ang), + Some(ang), + "\\cos\\theta = \\frac{|\\vec n_1\\cdot\\vec n_2|}{|\\vec n_1||\\vec n_2|}", + "二面角等于两法向量夹角(取锐角)", + )); if dot3(p.n, q.n).abs() < 1e-9 * lp * lq { out.push(fact("两平面", &format!("{} \\perp {}", p.name, q.name), "\\checkmark".into(), None, "\\vec n_1\\cdot\\vec n_2 = 0", "法向量垂直")); } @@ -2180,4 +2301,45 @@ mod tests { assert!(th2.num.unwrap().abs() < 1e-9, "θ(AC) = {}", th2.value); assert!(out.iter().any(|f| f.label == "AC \\parallel α")); } + + #[test] + fn van_obel_and_apollonius_on_345() { + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let vo_a = fs.iter().find(|f| f.label.contains("ID_{a}")).expect("Van Obel A"); + assert!((vo_a.num.unwrap() - 3.0).abs() < 1e-6, "Van Obel A = {}", vo_a.value); + let vo_b = fs.iter().find(|f| f.label.contains("ID_{b}")).expect("Van Obel B"); + assert!((vo_b.num.unwrap() - 2.0).abs() < 1e-6, "Van Obel B = {}", vo_b.value); + assert_eq!(fs.iter().filter(|f| f.label.contains("ID_")).count(), 3); + let ap = fs.iter().filter(|f| f.group == "阿波罗尼奥斯圆").count(); + assert_eq!(ap, 3, "Apollonius count"); + } + + #[test] + fn tetrahedron_volume_unit() { + let pts = vec![ + NamedPoint { name: "A".into(), p: vec![0.0, 0.0, 0.0] }, + NamedPoint { name: "B".into(), p: vec![1.0, 0.0, 0.0] }, + NamedPoint { name: "C".into(), p: vec![0.0, 1.0, 0.0] }, + NamedPoint { name: "D".into(), p: vec![0.0, 0.0, 1.0] }, + ]; + let out = points_analyze(&pts); + let v = out.iter().find(|f| f.label.contains("四面体")).expect("tetra volume"); + assert!((v.num.unwrap() - 1.0 / 6.0).abs() < 1e-9, "V = {}", v.value); + } + + #[test] + fn dihedral_angle_xy_planes() { + let ps = vec![ + NamedPlane { name: "α".into(), n: [1.0, 0.0, 0.0], d: 0.0 }, + NamedPlane { name: "β".into(), n: [0.0, 1.0, 0.0], d: 0.0 }, + ]; + let out = planes_analyze(&ps, &[]); + let th = out.iter().find(|f| f.label == "\\theta(α, β)").expect("theta"); + assert!((th.num.unwrap() - PI / 2.0).abs() < 1e-9); + assert!(out.iter().any(|f| f.label.contains("二面角"))); + assert!(out.iter().any(|f| f.label == "α \\perp β")); + } } diff --git a/scripts/plot-cases.ts b/scripts/plot-cases.ts index a93ea87..2e5142f 100644 --- a/scripts/plot-cases.ts +++ b/scripts/plot-cases.ts @@ -47,7 +47,7 @@ export const cases: [string, string, Expect][] = [ ['直线过两点', 'y = kx + b, 过(1, 3), 过(2, 5)', { solve: { k: 2, b: 1 } }], // ---- triangles / coordinate geometry ---- ['解三角形 SAS', '△ABC: a = 5, b = 7, C = 60°', { dim: 2, facts: ['\\sqrt{39}'], minFacts: 10 }], - ['解三角形 SSS', '△ABC: a=3, b=4, c=5', { dim: 2, facts: ['90', 'S_{\\text{海伦}}', '|OI|', 'r_a=', 'AF_{c}', '\\Pi_{\\text{Ceva}}', '\\Pi_{\\text{Menelaus}}', '\\text{Stewart}_{m_'], minFacts: 26 }], + ['解三角形 SSS', '△ABC: a=3, b=4, c=5', { dim: 2, facts: ['90', 'S_{\\text{海伦}}', '|OI|', 'r_a=', 'AF_{c}', '\\Pi_{\\text{Ceva}}', '\\Pi_{\\text{Menelaus}}', '\\text{Stewart}_{m_', 'ID_{a}', '\\mathcal{A}_'], minFacts: 30 }], ['解三角形 SSA 两解', '△ABC: a = 6, b = 8, A = 40°', { dim: 2 }], ['坐标 + 垂直', 'A(0,0), B(4,0), C(1,t)\nAC ⊥ BC', { dim: 2, solve: { t: Math.sqrt(3) }, inView: [[0, 0], [4, 0]] }], ['平行四边形', 'A(0,0), B(4,0), C(5,3), D(1,3)', { dim: 2, facts: ['平行四边形'], inView: [[5, 3]] }], @@ -92,6 +92,9 @@ export const cases: [string, string, Expect][] = [ ['异面直线四点', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,1,1)', { dim: 3, facts: ['d(AB, CD)=1', '异面'] }], ['线面角', 'A(0,0,0)\nB(0,0,1)\nC(1,0,0)\nz = 0', { dim: 3, facts: ['\\theta(AB, α)', 'AB \\perp α', 'AC \\parallel α'] }], ['两球根面', 'x^2 + y^2 + z^2 = 4\n(x-3)^2 + y^2 + z^2 = 4', { dim: 3, facts: ['\\pi_', '\\rho_'] }], + ['四面体体积', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,0,1)', { dim: 3, facts: ['V_{\\text{四面体}}'] }], + ['二面角', 'x + 0*z = 0\ny + 0*z = 0', { dim: 3, facts: ['\\text{二面角}', '\\perp'] }], + ['直线交球面', 'A(0,0,0)\nB(4,0,0)\nx^2 + y^2 + z^2 = 4', { dim: 3, facts: ['P_{AB\\cap', '|P_1P_2|'] }], ['空间螺旋线', 'r(t) = (cos(t), sin(t), t/3)', { dim: 3 }], ['空间三点', 'P(1,2,3), Q(0,1,-1), R(2,0,1)', { dim: 3 }], ] diff --git a/src/math/scene.ts b/src/math/scene.ts index b8be871..d13fa6c 100644 --- a/src/math/scene.ts +++ b/src/math/scene.ts @@ -851,6 +851,92 @@ export function analyze(cards: CardInput[], solutionIndex = 0): Analysis { if (facts.length) sections.push({ id: 'radical', title: '两球根面', subtitle: '等幂点轨迹 · 交圆平面', tone: 'geo', facts }) } + // Line–sphere: every pair of 3D points defines a line; intersect with each sphere. + if (spheres.length && pts3.length >= 2) { + const facts: RustFact[] = [] + const maxPairs = 6 + let pairs = 0 + for (let i = 0; i < pts3.length; i++) { + for (let j = i + 1; j < pts3.length; j++) { + if (pairs >= maxPairs) break + const A = pts3[i] + const B = pts3[j] + const d = [B.p[0] - A.p[0], B.p[1] - A.p[1], B.p[2] - A.p[2]] + const dd = d[0] * d[0] + d[1] * d[1] + d[2] * d[2] + if (dd < 1e-16) continue + pairs++ + for (const s of spheres) { + const ac = [A.p[0] - s.c[0], A.p[1] - s.c[1], A.p[2] - s.c[2]] + const qa = dd + const qb = 2 * (d[0] * ac[0] + d[1] * ac[1] + d[2] * ac[2]) + const qc = ac[0] * ac[0] + ac[1] * ac[1] + ac[2] * ac[2] - s.r * s.r + const disc = qb * qb - 4 * qa * qc + const lab = `${A.name}${B.name}` + if (disc < -1e-9) { + facts.push({ + group: '直线与球面', + label: `${lab} \\cap ${s.name}`, + value: '\\varnothing', + num: null, + how: '\\Delta < 0', + why: '直线与球面相离', + shape: null, + }) + } else if (Math.abs(disc) <= 1e-9) { + const t0 = -qb / (2 * qa) + const q = [A.p[0] + t0 * d[0], A.p[1] + t0 * d[1], A.p[2] + t0 * d[2]] + facts.push({ + group: '直线与球面', + label: `${lab} \\cap ${s.name}`, + value: '\\text{相切}', + num: 0, + how: '\\Delta = 0', + why: '直线与球面相切', + shape: { type: 'point3', x: q[0], y: q[1], z: q[2], label: `${lab}∩${s.name}` }, + }) + } else { + const sq = Math.sqrt(disc) + const t1 = (-qb - sq) / (2 * qa) + const t2 = (-qb + sq) / (2 * qa) + const q1 = [A.p[0] + t1 * d[0], A.p[1] + t1 * d[1], A.p[2] + t1 * d[2]] + const q2 = [A.p[0] + t2 * d[0], A.p[1] + t2 * d[1], A.p[2] + t2 * d[2]] + facts.push({ + group: '直线与球面', + label: `P_{${lab}\\cap ${s.name},1}`, + value: `\\left(${fmt(q1[0])},\\ ${fmt(q1[1])},\\ ${fmt(q1[2])}\\right)`, + num: null, + how: '|A + t(B-A) - O|^2 = r^2', + why: '直线与球面的交点', + shape: { type: 'point3', x: q1[0], y: q1[1], z: q1[2], label: `${lab}∩${s.name}` }, + }) + facts.push({ + group: '直线与球面', + label: `P_{${lab}\\cap ${s.name},2}`, + value: `\\left(${fmt(q2[0])},\\ ${fmt(q2[1])},\\ ${fmt(q2[2])}\\right)`, + num: null, + how: '|A + t(B-A) - O|^2 = r^2', + why: '直线与球面的交点', + shape: { type: 'point3', x: q2[0], y: q2[1], z: q2[2], label: `${lab}∩${s.name}` }, + }) + const chord = Math.hypot(q2[0] - q1[0], q2[1] - q1[1], q2[2] - q1[2]) + facts.push({ + group: '直线与球面', + label: `|P_1P_2|_{${lab}\\cap ${s.name}}`, + value: engine.nice(chord), + num: chord, + how: '两交点距离', + why: '弦长', + shape: null, + }) + } + } + } + if (pairs >= maxPairs) break + } + if (facts.length) sections.push({ id: 'line-sphere', title: '直线 ∩ 球面', subtitle: '交点 · 相切 · 相离', tone: 'geo', facts }) + } + + if (marks.length) objects.push({ type: 'marks', pts: marks }) // ---- dimension --------------------------------------------------------------------------- diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 77dd6f92bf79bc33140af77cab925a5a8a5d0395..0950811cc383cb01721861992ee99cbe7acc0dcd 100644 GIT binary patch delta 51710 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z{Pst5+wMB+47_%mjWp?V_*s7PU(Ehld{ddmj5OMKk=rp9s@UzA5ZaDy4n_mpxz+9H zCny~S8sUy8L1}qQyMKJRqfq{^wK>u;$r#TCjgCINbc6%H2W7(F1-is_ Date: Sun, 1 Nov 2026 15:24:01 +0800 Subject: [PATCH 005/123] =?UTF-8?q?feat:=20Descartes=20circles,=20Euler=20?= =?UTF-8?q?line/nine-point,=20cylinder=E2=88=A9plane=20ellipse?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit OI² = R(R−2r) was already exact; add Euler-line collinearity OG:GH=1:2 and nine-point circle. Descartes ± Soddy radii for three mutually tangent circles; cylinder∥z ∩ plane ellipse semi-axes a=R/sinθ, b=R. --- crates/mathcore/src/circle.rs | 68 +++++++++++++++++++++++++ crates/mathcore/src/geometry.rs | 87 ++++++++++++++++++++++++++++++++ scripts/plot-cases.ts | 4 +- src/math/scene.ts | 70 +++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 534420 -> 537911 bytes 5 files changed, 228 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/circle.rs b/crates/mathcore/src/circle.rs index 9843831..82c328a 100644 --- a/crates/mathcore/src/circle.rs +++ b/crates/mathcore/src/circle.rs @@ -473,6 +473,56 @@ pub fn circles_analyze(circles: &[NamedCircle], points: &[NamedPoint]) -> Vec = out.iter().filter(|f| f.group == "笛卡尔圆定理").collect(); + assert_eq!(ds.len(), 2, "expected ± Descartes radii, got {:?}", ds.iter().map(|f| &f.label).collect::>()); + let nums: Vec = ds.iter().map(|f| f.num.unwrap()).collect(); + let expect = [1.0 / (3.0 + 2.0 * sq3), 1.0 / (3.0 - 2.0 * sq3)]; + for e in expect { + assert!(nums.iter().any(|n| (n - e).abs() < 1e-9), "missing {e}, have {nums:?}"); + } + } } diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 08f22fb..9ac5550 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -620,6 +620,79 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "外心与垂心的距离", ).with(Shape::Segment { x1: circ[0], y1: circ[1], x2: orth[0], y2: orth[1], label: "OH".into() })); + // Euler line: O, G, H collinear with OG:GH = 1:2 (and |OH| = 3|OG|). + // Note: |OI|^2 = R(R−2r) is the Euler distance formula for the incenter (already above); + // it is not |OH|^2. + { + let og = dist2(circ, centroid); + let gh = dist2(centroid, orth); + let cross = (centroid[0] - circ[0]) * (orth[1] - circ[1]) - (centroid[1] - circ[1]) * (orth[0] - circ[0]); + let scale = (1.0 + og) * (1.0 + oh); + if cross.abs() < 1e-6 * scale { + out.push(fact( + "欧拉线", + "O,\\ G,\\ H", + "\\text{共线}".into(), + None, + "\\vec{OH} = 3\\vec{OG}", + "欧拉线:外心、重心、垂心共线", + )); + if og > 1e-12 { + let ratio = gh / og; + out.push(fact( + "欧拉线", + "OG:GH", + format!("1:{}", nice(ratio)), + Some(ratio), + "OG:GH = 1:2", + "重心按 1:2 分 OH", + )); + out.push(fact( + "欧拉线", + "|OG|", + nice(og), + Some(og), + "|OH| = 3|OG|", + "欧拉线上的线段", + ).with(Shape::Segment { + x1: circ[0], + y1: circ[1], + x2: centroid[0], + y2: centroid[1], + label: "OG".into(), + })); + } + } + // Nine-point circle: center N = midpoint of OH, radius R/2. + let n9 = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; + let r9 = rr / 2.0; + out.push(fact( + "欧拉线", + "N", + pt(n9[0], n9[1]), + None, + "N = \\text{中点}(O, H)", + "九点圆圆心(欧拉圆)", + ).with(Shape::Point { + x: n9[0], + y: n9[1], + label: "N 九点圆圆心".into(), + })); + out.push(fact( + "欧拉线", + "R_{\\text{九点}}", + nice(r9), + Some(r9), + "R_N = R/2", + "九点圆半径", + ).with(Shape::Circle { + cx: n9[0], + cy: n9[1], + r: r9, + label: "九点圆".into(), + })); + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -2342,4 +2415,18 @@ mod tests { assert!(out.iter().any(|f| f.label.contains("二面角"))); assert!(out.iter().any(|f| f.label == "α \\perp β")); } + + #[test] + fn euler_line_and_nine_point() { + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + let fs = &r.cases[0].facts; + assert!(fs.iter().any(|f| f.label.contains("O,") && f.value.contains("共线"))); + let og_gh = fs.iter().find(|f| f.label == "OG:GH").unwrap(); + assert!((og_gh.num.unwrap() - 2.0).abs() < 1e-6, "OG:GH = {}", og_gh.value); + let r9 = fs.iter().find(|f| f.label.contains("九点")).unwrap(); + assert!((r9.num.unwrap() - 1.25).abs() < 1e-9, "R9 = {}", r9.value); // R=2.5 + // OI² = R(R-2r) already covered; ensure |OI| present + assert!(fs.iter().any(|f| f.label == "|OI|")); + } } diff --git a/scripts/plot-cases.ts b/scripts/plot-cases.ts index 2e5142f..6cc8a61 100644 --- a/scripts/plot-cases.ts +++ b/scripts/plot-cases.ts @@ -47,7 +47,7 @@ export const cases: [string, string, Expect][] = [ ['直线过两点', 'y = kx + b, 过(1, 3), 过(2, 5)', { solve: { k: 2, b: 1 } }], // ---- triangles / coordinate geometry ---- ['解三角形 SAS', '△ABC: a = 5, b = 7, C = 60°', { dim: 2, facts: ['\\sqrt{39}'], minFacts: 10 }], - ['解三角形 SSS', '△ABC: a=3, b=4, c=5', { dim: 2, facts: ['90', 'S_{\\text{海伦}}', '|OI|', 'r_a=', 'AF_{c}', '\\Pi_{\\text{Ceva}}', '\\Pi_{\\text{Menelaus}}', '\\text{Stewart}_{m_', 'ID_{a}', '\\mathcal{A}_'], minFacts: 30 }], + ['解三角形 SSS', '△ABC: a=3, b=4, c=5', { dim: 2, facts: ['90', 'S_{\\text{海伦}}', '|OI|', 'r_a=', 'AF_{c}', '\\Pi_{\\text{Ceva}}', '\\Pi_{\\text{Menelaus}}', '\\text{Stewart}_{m_', 'ID_{a}', '\\mathcal{A}_', 'OG:GH', 'R_{\\text{九点}}'], minFacts: 34 }], ['解三角形 SSA 两解', '△ABC: a = 6, b = 8, A = 40°', { dim: 2 }], ['坐标 + 垂直', 'A(0,0), B(4,0), C(1,t)\nAC ⊥ BC', { dim: 2, solve: { t: Math.sqrt(3) }, inView: [[0, 0], [4, 0]] }], ['平行四边形', 'A(0,0), B(4,0), C(5,3), D(1,3)', { dim: 2, facts: ['平行四边形'], inView: [[5, 3]] }], @@ -95,6 +95,8 @@ export const cases: [string, string, Expect][] = [ ['四面体体积', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,0,1)', { dim: 3, facts: ['V_{\\text{四面体}}'] }], ['二面角', 'x + 0*z = 0\ny + 0*z = 0', { dim: 3, facts: ['\\text{二面角}', '\\perp'] }], ['直线交球面', 'A(0,0,0)\nB(4,0,0)\nx^2 + y^2 + z^2 = 4', { dim: 3, facts: ['P_{AB\\cap', '|P_1P_2|'] }], + ['笛卡尔圆', 'A(0,0)\nB(2,0)\nC(1,1.7320508075688772)\n⊙A: r = 1\n⊙B: r = 1\n⊙C: r = 1', { dim: 2, facts: ['\\text{Descartes}'], minFacts: 2 }], + ['圆柱截椭圆', 'x^2 + y^2 = 4\nx - z = 0', { dim: 3, facts: ['a_', 'b_', '\\text{椭圆}'] }], ['空间螺旋线', 'r(t) = (cos(t), sin(t), t/3)', { dim: 3 }], ['空间三点', 'P(1,2,3), Q(0,1,-1), R(2,0,1)', { dim: 3 }], ] diff --git a/src/math/scene.ts b/src/math/scene.ts index d13fa6c..42ba5cb 100644 --- a/src/math/scene.ts +++ b/src/math/scene.ts @@ -936,6 +936,76 @@ export function analyze(cards: CardInput[], solutionIndex = 0): Analysis { if (facts.length) sections.push({ id: 'line-sphere', title: '直线 ∩ 球面', subtitle: '交点 · 相切 · 相离', tone: 'geo', facts }) } + // Right circular cylinder ∥ z (circle in xy) ∩ plane → ellipse semi-axes. + if (planes.length) { + const cyls = [...sheetCircles.values(), ...detectedCircles] + const facts: RustFact[] = [] + for (const cyl of cyls) { + if (!(cyl.r > 0)) continue + for (const p of planes) { + const ln = Math.hypot(p.n[0], p.n[1], p.n[2]) + if (ln < 1e-12) continue + const sinTheta = Math.abs(p.n[2]) / ln + const label = `\\mathrm{Cyl}_{${cyl.name}} \\cap ${p.name}` + if (sinTheta < 1e-9) { + facts.push({ + group: '圆柱与平面', + label, + value: '\\text{平行(无界)}', + num: null, + how: '\\vec n \\cdot \\vec k = 0', + why: '平面平行于母线,交线是直线或空', + shape: null, + }) + continue + } + const b = cyl.r + const a = cyl.r / sinTheta + if (Math.abs(sinTheta - 1) < 1e-9) { + facts.push({ + group: '圆柱与平面', + label, + value: `\\text{圆},\\ r = ${fmt(b)}`, + num: b, + how: '\\vec n \\parallel \\vec k', + why: '平面垂直于轴,交线是圆', + shape: null, + }) + } else { + facts.push({ + group: '圆柱与平面', + label: `a_{${cyl.name}\\cap ${p.name}}`, + value: engine.nice(a), + num: a, + how: 'a = R / \\sin\\theta', + why: '椭圆长半轴(θ = 轴与平面的线面角)', + shape: null, + }) + facts.push({ + group: '圆柱与平面', + label: `b_{${cyl.name}\\cap ${p.name}}`, + value: engine.nice(b), + num: b, + how: 'b = R', + why: '椭圆短半轴等于圆柱半径', + shape: null, + }) + facts.push({ + group: '圆柱与平面', + label, + value: '\\text{椭圆}', + num: a, + how: '\\sin\\theta = |\\vec n \\cdot \\vec k| / |\\vec n|', + why: '圆柱被斜平面截得椭圆', + shape: null, + }) + } + } + } + if (facts.length) sections.push({ id: 'cyl-plane', title: '圆柱 ∩ 平面', subtitle: '椭圆半轴 · 线面角', tone: 'geo', facts }) + } + + if (marks.length) objects.push({ type: 'marks', pts: marks }) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 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znH12BGdR^VV6}tx>+pdRqmOMXwF_rhUR&?)HX7SKw>R=}=UK4-Bb$tE6Ms-IBnSp2 zBZ=I^%ONjL0wxDI3zUorrzcbMvvTG-a~EdiVNuXosH z;r=HusMiI)3ryQx0xPJXEN=r$gT<6zqz)h>R)e(-4RU+J)Ap)GfLpHplMANLJjp>L|>&dYdh z;s2KLltVz#MK(OD%(KK&cET#4VwFMR`Bjo+#H{*{G! zc;DD%j_+G zxbktWz_kun6|O_Lj^nz3s}5HqF6C`xjO$Tci*T*QwG-DtTt{)8!Sxxg8@PVLrJ`a! zxWaHn?Q)E^jls<{Tyt?1;o5*}8?M8+YHHS8)n<+#Y`PD%@!G9)9mC)*Q9?Ty-6eoi*&?>R%O=w06T2b@{$a@e7dS#mJs3A-G|w*s;sm3xPI`7Ion13h{RCo}Fr zkDONlUw4c7@$5V7q2c3Q(^Dpo8J#j>%;+&wCPOHc3URMW_zdnTb0Md|9p&3v=I}*w9Hr@1Vsu^7Tf6G@lANwUByH z;CMH@-%8J`e}X~IJI*hI`Uw56%?5z)Y=XfFet$Scxg309Z;NuW-SFRmCrI_U1w2;A zyt)bH7M$dln_xDeZSNR3{tgBPaM>OBi76lQ+B^8<+vguTY)+)R{UJ~K86RBhf68!F z!$B!PoN1Zkq;5UU%*pUUQ#~3N8mGPrDJ6>T?W~=I7I($cpsBAF!_eLazaQTKUWcrN$jO z&1XNrIqtq6IrPy^lN6b6-;cEF2kcwbC+PPMee-xcm{jqg-}9}Wt)i6d-)o Date: Sun, 1 Nov 2026 07:24:01 +0000 Subject: [PATCH 006/123] feat: Euler line, altitude Stewart, plane feet, and radical axis MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Keep Van Obel, Apollonius circles, and line–sphere from the stack. Add the Euler division and nine-point circle, Stewart checks for altitudes, the angle between skew directions, the foot of a point on a plane, and the radical axis of two circles. Co-authored-by: DNT_OF --- README.md | 3 +- crates/mathcore/src/circle.rs | 75 +++++++++++++++++++- crates/mathcore/src/geometry.rs | 119 +++++++++++++++++++++++++++++++- scripts/plot-cases.ts | 7 +- src/math/scene.ts | 8 ++- src/wasm/pkg/mathcore_bg.wasm | Bin 534420 -> 531160 bytes 6 files changed, 202 insertions(+), 10 deletions(-) diff --git a/README.md b/README.md index 191a0fd..4e8ab0c 100644 --- a/README.md +++ b/README.md @@ -191,7 +191,8 @@ AC ⊥ BC - 3D 曲面:z 轴范围跟随曲面的取值范围,例如 z = x² + y² 不会被立方体顶面截掉。 - 拖动或缩放后,曲线会在新的范围里由 Rust 重新采样。 - **函数**:定义域(扫描断点和渐近线)、零点(变号二分 + 切点检测)、极值(黄金分割 + 渐近线剔除)、两两之间的交点。 -- **向量与平面**:点积、叉积、夹角、投影(数量)、**投影向量与垂直分量**(a = 投影 + 垂直)、混合积。向量还可以用语句定义:`𝐜 = 𝐚 + 𝐛`、`𝐩 = 投影(𝐚, 𝐛)`,定义出的向量参与同一套推导。平面的法向量、两平面夹角、交线、三平面交点、点到平面的距离。 +- **向量与平面**:点积、叉积、夹角、投影(数量)、**投影向量与垂直分量**(a = 投影 + 垂直)、混合积。向量还可以用语句定义:`𝐜 = 𝐚 + 𝐛`、`𝐩 = 投影(𝐚, 𝐛)`,定义出的向量参与同一套推导。平面的法向量、两平面夹角、交线、三平面交点、点到平面的距离和垂足。直线与平面的夹角由 \(\sin\theta = |\vec v\cdot\vec n| / (|\vec v||\vec n|)\) 给出。空间四点给出异面直线的距离和方向夹角。两个球面给出根面和交圆半径;两个圆给出根轴、圆心距和公共弦。 +- **欧拉线与九点圆**:解出三角形后给出 \(|OG|:|GH| = 1:2\)、九点圆圆心 \(N\)(\(OH\) 中点)和半径 \(R/2\)。中线、角平分线和高都用斯特瓦尔特定理核对等式(高用有向线段)。角平分线上还有 Van Obel 比 \(AI/ID = (b+c)/a\),以及每个顶点的 Apollonius 圆。空间直线与球面给出交点、切点或相离。 - **精确形式**:数值结果会被尽量还原成 √、分数、π 的形式,例如 \(\sqrt{39}\)、\(\frac{35\sqrt3}{4}\)、\(\frac{\pi}{3}\)。 坐标系面板右侧依次列出三部分:「已知 N 条 → 推出 M 项」、每一项的推导依据,以及一个可以在图上标出该项的眼睛开关。纸上同一维度的所有式子都在同一个坐标系里,它们之间的交点会自动求出(`src/math/page.ts` 负责把纸上的式子分到平面 / 空间两个共享坐标系)。 diff --git a/crates/mathcore/src/circle.rs b/crates/mathcore/src/circle.rs index 9843831..838992c 100644 --- a/crates/mathcore/src/circle.rs +++ b/crates/mathcore/src/circle.rs @@ -3,7 +3,7 @@ //! chord lengths, centre-to-chord distances, central angles, and a canonical picture of //! the whole configuration. Plus cross inference between circles and named points. -use crate::geometry::{deg, dist2, near, nice, Fact, NamedPoint, Shape}; +use crate::geometry::{deg, dist2, line_eq_latex, near, nice, Fact, NamedPoint, Shape}; use serde::{Deserialize, Serialize}; use std::collections::HashMap; @@ -473,6 +473,54 @@ pub fn circles_analyze(circles: &[NamedCircle], points: &[NamedPoint]) -> Vec sum { + "外离" + } else if ln + 1e-9 < diff { + "内含" + } else { + "相交" + }; + out.push(fact(g, &format!("\\odot {} ,\\ \\odot {}", a.name, b.name), format!("\\text{{{rel}}}"), None, "|O_1O_2| \\text{ 与 } r_1\\pm r_2", "两圆位置关系")); + if rho2 > 1e-9 { + let chord = 2.0 * rho2.sqrt(); + out.push(seg_fact(g, &format!("|\\text{{公共弦}}_{{{}{}}}|", a.name, b.name), chord, "2\\sqrt{r_1^2 - d^2}", "公共弦长(落在根轴上)")); + } + } + } out } @@ -597,4 +645,29 @@ mod tests { // C is on the circle assert!(out.iter().any(|x| x.label == "C \\in \\odot O" && x.value.contains("圆上"))); } + + #[test] + fn radical_axis_of_two_circles() { + // unit circles at (0,0) and (1,0): radical axis x = 1/2, common chord √3 + let circles = vec![ + NamedCircle { name: "A".into(), cx: 0.0, cy: 0.0, r: 1.0 }, + NamedCircle { name: "B".into(), cx: 1.0, cy: 0.0, r: 1.0 }, + ]; + let out = circles_analyze(&circles, &[]); + let axis = out.iter().find(|f| f.label == "l_{AB}").unwrap(); + assert!(axis.value.contains("\\frac{1}{2}") || axis.value.contains("0.5"), "axis = {}", axis.value); + let chord = out.iter().find(|f| f.label == "|\\text{公共弦}_{AB}|").unwrap(); + assert!((chord.num.unwrap() - 3f64.sqrt()).abs() < 1e-9, "chord = {}", chord.value); + assert!(out.iter().any(|f| f.value.contains("相交"))); + // separate equal circles: x = 3/2, no chord + let circles = vec![ + NamedCircle { name: "A".into(), cx: 0.0, cy: 0.0, r: 1.0 }, + NamedCircle { name: "B".into(), cx: 3.0, cy: 0.0, r: 1.0 }, + ]; + let out = circles_analyze(&circles, &[]); + let axis = out.iter().find(|f| f.label == "l_{AB}").unwrap(); + assert!(axis.value.contains("\\frac{3}{2}"), "axis = {}", axis.value); + assert!(out.iter().all(|f| f.label != "|\\text{公共弦}_{AB}|")); + assert!(out.iter().any(|f| f.value.contains("外离"))); + } } diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 08f22fb..22b5e41 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -620,6 +620,36 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "外心与垂心的距离", ).with(Shape::Segment { x1: circ[0], y1: circ[1], x2: orth[0], y2: orth[1], label: "OH".into() })); + // Euler line: G divides OH with OG:GH = 1:2. Nine-point center N is the midpoint of OH, radius R/2. + { + let og = dist2(circ, centroid); + let gh = dist2(centroid, orth); + let nx = (circ[0] + orth[0]) / 2.0; + let ny = (circ[1] + orth[1]) / 2.0; + let r9 = rr / 2.0; + if oh > 1e-9 { + out.push(fact("特殊点", "|OG|", nice(og), Some(og), "|OG| = \\frac13|OH|", "欧拉线:重心分外心与垂心为 1:2")); + out.push(fact("特殊点", "|GH|", nice(gh), Some(gh), "|GH| = \\frac23|OH|", "欧拉线")); + let ratio = og / oh; + out.push(fact( + "特殊点", + "\\frac{|OG|}{|OH|}", + nice(ratio), + Some(ratio), + "\\frac{|OG|}{|OH|} = \\frac13", + "欧拉线分比", + )); + } + let ogv = [centroid[0] - circ[0], centroid[1] - circ[1]]; + let ohv = [orth[0] - circ[0], orth[1] - circ[1]]; + let colin = (ogv[0] * ohv[1] - ogv[1] * ohv[0]).abs() <= 1e-6 * (1.0 + oh); + if colin { + out.push(fact("特殊点", "\\text{欧拉线}", "\\checkmark".into(), None, "G,\\ O,\\ H \\text{ 共线}", "欧拉线")); + } + out.push(fact("特殊点", "N", pt(nx, ny), None, "N = \\frac{O + H}{2}", "九点圆圆心(OH 中点)").with(Shape::Circle { cx: nx, cy: ny, r: r9, label: "九点圆".into() })); + out.push(fact("外接圆与内切圆", "R_{9}", nice(r9), Some(r9), "R_9 = \\frac{R}{2}", "九点圆半径")); + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -792,6 +822,36 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] )); } } + // altitude: signed segments along side i (foot may lie on the extension) + let bpt = v[(i + 1) % 3]; + let cpt = v[(i + 2) % 3]; + let apt = v[i]; + let (dx, dy) = (cpt[0] - bpt[0], cpt[1] - bpt[1]); + let den2 = dx * dx + dy * dy; + if den2 > 1e-18 && aa > 1e-12 { + let t = ((apt[0] - bpt[0]) * dx + (apt[1] - bpt[1]) * dy) / den2; + let m = t * aa; + let nseg = (1.0 - t) * aa; + let d = 2.0 * area / aa; + let lhs = bb * bb * m + cc * cc * nseg; + let rhs = aa * (d * d + m * nseg); + if (lhs - rhs).abs() < 1e-6 * (1.0 + lhs.abs()) { + out.push(fact( + "斯特瓦尔特定理", + &format!("\\text{{Stewart}}_{{h_{}}}", SIDE[i]), + nice(lhs), + Some(lhs), + &format!( + "{b}^2 m + {c}^2 n = {a}(h_{s}^2 + mn)", + a = SIDE[i], + b = SIDE[(i + 1) % 3], + c = SIDE[(i + 2) % 3], + s = SIDE[i], + ), + "斯特瓦尔特定理(高,有向线段)", + )); + } + } } } @@ -990,7 +1050,7 @@ fn line_line_isect2(p: [f64; 2], q: [f64; 2], r: [f64; 2], s: [f64; 2]) -> Optio } -fn line_eq_latex(a: f64, b: f64, c: f64) -> String { +pub(crate) fn line_eq_latex(a: f64, b: f64, c: f64) -> String { // a x + b y = c, normalised for display if near(b, 0.0) { return format!("x = {}", nice_short(c / a)); @@ -1211,6 +1271,19 @@ fn points3_analyze(points: &[NamedPoint]) -> Vec { let (pa, pb, pc, pd) = (pts[0].1, pts[1].1, pts[2].1, pts[3].1); let ab = sub3(pb, pa); let cd = sub3(pd, pc); + let (lab, lcd) = (len3(ab), len3(cd)); + if lab > 1e-12 && lcd > 1e-12 { + let cosang = (dot3(ab, cd).abs() / (lab * lcd)).clamp(0.0, 1.0); + let theta = cosang.acos(); + out.push(fact( + "异面直线", + &format!("\\theta({}{}, {}{})", na, nb, nc, nd), + deg(theta), + Some(theta), + "\\cos\\theta = \\frac{|\\vec{AB}\\cdot\\vec{CD}|}{|\\vec{AB}||\\vec{CD}|}", + "两直线方向的夹角(取锐角或直角)", + )); + } let nskew = cross3(ab, cd); let ln = len3(nskew); let ac = sub3(pc, pa); @@ -1613,6 +1686,18 @@ pub fn planes_analyze(ps: &[NamedPlane], points: &[NamedPoint]) -> Vec { let x = [q.p[0], *q.p.get(1).unwrap_or(&0.0), *q.p.get(2).unwrap_or(&0.0)]; let d = (dot3(p.n, x) - p.d).abs() / ln; out.push(fact("点与平面", &format!("d({}, {})", q.name, p.name), nice(d), Some(d), "\\frac{|ax_0+by_0+cz_0-d|}{\\sqrt{a^2+b^2+c^2}}", "点到平面距离")); + if ln > 1e-12 && d > 1e-8 && d.is_finite() { + let lam = (p.d - dot3(p.n, x)) / (ln * ln); + let foot = [x[0] + lam * p.n[0], x[1] + lam * p.n[1], x[2] + lam * p.n[2]]; + out.push(fact( + "点与平面", + &format!("\\text{{foot}}({}, {})", q.name, p.name), + pt3(foot), + None, + "P + \\frac{d - \\vec n\\cdot P}{|\\vec n|^2}\\vec n", + "点到平面的垂足", + ).with(Shape::Point3 { x: foot[0], y: foot[1], z: foot[2], label: format!("foot {} {}", q.name, p.name) })); + } } } // Line–plane angle: every pair of 3D points defines a line. @@ -2279,8 +2364,16 @@ mod tests { assert!((med.num.unwrap() - 62.5).abs() < 1e-6, "med = {}", med.value); let bis = fs.iter().find(|f| f.label == "\\text{Stewart}_{t_c}").unwrap(); assert!(bis.num.unwrap().is_finite()); - // both sides of Stewart agree for every median/bisector we emitted - assert_eq!(fs.iter().filter(|f| f.label.starts_with("\\text{Stewart}_")).count(), 6); + // altitude to the hypotenuse: m = 16/5, n = 9/5, h = 12/5 → LHS = 57.6 + let alt = fs.iter().find(|f| f.label == "\\text{Stewart}_{h_c}").unwrap(); + assert!((alt.num.unwrap() - 57.6).abs() < 1e-6, "alt = {}", alt.value); + // medians, bisectors, and altitudes + assert_eq!(fs.iter().filter(|f| f.label.starts_with("\\text{Stewart}_")).count(), 9); + let ratio = fs.iter().find(|f| f.label == "\\frac{|OG|}{|OH|}").unwrap(); + assert!((ratio.num.unwrap() - 1.0 / 3.0).abs() < 1e-9, "OG/OH = {}", ratio.value); + let r9 = fs.iter().find(|f| f.label == "R_{9}").unwrap(); + assert!((r9.num.unwrap() - 1.25).abs() < 1e-9, "R9 = {}", r9.value); + assert!(fs.iter().any(|f| f.label == "\\text{欧拉线}")); } #[test] @@ -2300,6 +2393,26 @@ mod tests { let th2 = out.iter().find(|f| f.label == "\\theta(AC, α)").unwrap(); assert!(th2.num.unwrap().abs() < 1e-9, "θ(AC) = {}", th2.value); assert!(out.iter().any(|f| f.label == "AC \\parallel α")); + let foot = out.iter().find(|f| f.label == "\\text{foot}(B, α)").unwrap(); + assert!(foot.value.contains('0'), "foot = {}", foot.value); + if let Shape::Point3 { x, y, z, .. } = foot.shape.as_ref().unwrap() { + assert!(x.abs() < 1e-9 && y.abs() < 1e-9 && z.abs() < 1e-9); + } else { + panic!("foot should be a point"); + } + } + + #[test] + fn skew_line_angle() { + let pts = vec![ + NamedPoint { name: "A".into(), p: vec![0.0, 0.0, 0.0] }, + NamedPoint { name: "B".into(), p: vec![1.0, 0.0, 0.0] }, + NamedPoint { name: "C".into(), p: vec![0.0, 1.0, 0.0] }, + NamedPoint { name: "D".into(), p: vec![0.0, 1.0, 1.0] }, + ]; + let out = points_analyze(&pts); + let th = out.iter().find(|f| f.label == "\\theta(AB, CD)").unwrap(); + assert!((th.num.unwrap() - PI / 2.0).abs() < 1e-9, "θ = {}", th.value); } #[test] diff --git a/scripts/plot-cases.ts b/scripts/plot-cases.ts index 2e5142f..e26f94b 100644 --- a/scripts/plot-cases.ts +++ b/scripts/plot-cases.ts @@ -47,7 +47,7 @@ export const cases: [string, string, Expect][] = [ ['直线过两点', 'y = kx + b, 过(1, 3), 过(2, 5)', { solve: { k: 2, b: 1 } }], // ---- triangles / coordinate geometry ---- ['解三角形 SAS', '△ABC: a = 5, b = 7, C = 60°', { dim: 2, facts: ['\\sqrt{39}'], minFacts: 10 }], - ['解三角形 SSS', '△ABC: a=3, b=4, c=5', { dim: 2, facts: ['90', 'S_{\\text{海伦}}', '|OI|', 'r_a=', 'AF_{c}', '\\Pi_{\\text{Ceva}}', '\\Pi_{\\text{Menelaus}}', '\\text{Stewart}_{m_', 'ID_{a}', '\\mathcal{A}_'], minFacts: 30 }], + ['解三角形 SSS', '△ABC: a=3, b=4, c=5', { dim: 2, facts: ['90', 'S_{\\text{海伦}}', '|OI|', 'r_a=', 'AF_{c}', '\\Pi_{\\text{Ceva}}', '\\Pi_{\\text{Menelaus}}', '\\text{Stewart}_{m_', 'ID_{a}', '\\mathcal{A}_', 'R_{9}', '\\text{欧拉线}'], minFacts: 36 }], ['解三角形 SSA 两解', '△ABC: a = 6, b = 8, A = 40°', { dim: 2 }], ['坐标 + 垂直', 'A(0,0), B(4,0), C(1,t)\nAC ⊥ BC', { dim: 2, solve: { t: Math.sqrt(3) }, inView: [[0, 0], [4, 0]] }], ['平行四边形', 'A(0,0), B(4,0), C(5,3), D(1,3)', { dim: 2, facts: ['平行四边形'], inView: [[5, 3]] }], @@ -89,8 +89,9 @@ export const cases: [string, string, Expect][] = [ ['两平面交线', 'x + y + z = 3\nx - y + 2z = 1', { dim: 3, facts: ['α \\cap β'] }], ['球面', 'x^2 + y^2 + z^2 = 4', { dim: 3, facts: ['r=2'] }], ['球面 ∩ 平面', 'x^2 + y^2 + z^2 = 4\nz = 1', { dim: 3, facts: ['\\rho_', '\\text{圆}'] }], - ['异面直线四点', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,1,1)', { dim: 3, facts: ['d(AB, CD)=1', '异面'] }], - ['线面角', 'A(0,0,0)\nB(0,0,1)\nC(1,0,0)\nz = 0', { dim: 3, facts: ['\\theta(AB, α)', 'AB \\perp α', 'AC \\parallel α'] }], + ['异面直线四点', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,1,1)', { dim: 3, facts: ['d(AB, CD)=1', '异面', '\\theta(AB, CD)'] }], + ['线面角', 'A(0,0,0)\nB(0,0,1)\nC(1,0,0)\nz = 0', { dim: 3, facts: ['\\theta(AB, α)', 'AB \\perp α', 'AC \\parallel α', '\\text{foot}(B, α)'] }], + ['两圆根轴', 'x^2 + y^2 = 4\n(x-3)^2 + y^2 = 4', { dim: 2, facts: ['l_{', '相交', '公共弦'] }], ['两球根面', 'x^2 + y^2 + z^2 = 4\n(x-3)^2 + y^2 + z^2 = 4', { dim: 3, facts: ['\\pi_', '\\rho_'] }], ['四面体体积', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,0,1)', { dim: 3, facts: ['V_{\\text{四面体}}'] }], ['二面角', 'x + 0*z = 0\ny + 0*z = 0', { dim: 3, facts: ['\\text{二面角}', '\\perp'] }], diff --git a/src/math/scene.ts b/src/math/scene.ts index d13fa6c..1c2e8af 100644 --- a/src/math/scene.ts +++ b/src/math/scene.ts @@ -629,9 +629,13 @@ export function analyze(cards: CardInput[], solutionIndex = 0): Analysis { // ---- circles × named points: powers, chords, central / inscribed angles -------------- const allCircles = [...sheetCircles.values(), ...detectedCircles] - if (allCircles.length && pts2.length) { + if ((allCircles.length && pts2.length) || allCircles.length >= 2) { const facts = engine.circles(allCircles, pts2) - if (facts.length) sections.push({ id: 'circle-points', title: `圆与点 ${allCircles.map((c) => `⊙${c.name}`).join(' ')}`, subtitle: '点的幂 · 弦 · 圆周角', tone: 'geo', facts }) + if (facts.length) { + const title = pts2.length ? `圆与点 ${allCircles.map((c) => `⊙${c.name}`).join(' ')}` : `两圆 ${allCircles.map((c) => `⊙${c.name}`).join(' ')}` + const subtitle = allCircles.length >= 2 ? '点的幂 · 弦 · 根轴' : '点的幂 · 弦 · 圆周角' + sections.push({ id: 'circle-points', title, subtitle, tone: 'geo', facts }) + } } // ---- vectors ---------------------------------------------------------------------------- diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 0950811cc383cb01721861992ee99cbe7acc0dcd..aea25ded0824051ff6eec6c90d0341c69c6964bf 100644 GIT binary patch delta 212495 zcmc$H3w#|_wfC8s^J-2WCu!0oP1DRwlQv0doAT%rX{VOg6~xE=d|VYMP?ZYhRZ*1d z1SwFoU}cI)ZLcJ0)d~dzRH$07L8}%)30kFSk)TB@_DazDS+vOa|F6Ag&Lc@%(EIyR zID2N#W3RpTdhfOOtbfAZ`!%~Hw(OeAjaV#Z{Q3TpTa5Je#`PDP{wHF=Mq{F7`PTiF8XURg3$}t3c1yJ5s5Z<_^3(-jSJ9I^LQm zugb(LN^9|#O3lVyaR8DkFOTy9JXVp4$1|z&v}FPGR0n=4cqR8&l}-by(s>r3I027W zrTkPn-7Gg$0^}+H5U;36m6xKb92iTd@DdAP18~%*(pB?P8LJAzR9?OSu!eu_snY4v zDBjG!lT=X&)TGnw7KefFN|n#cl*U5PrHqOKzqv(mwl z_z4x`Cu`G5NX9N=e^Q1I|w-x*;#Go?xd}6Xc zFP4s3@p0yr#`))85nG*3SVpWeS#SA<*V#D`%lI*G__6OwxtC??n{hXJ`SQ!JxcWLX zmbhT~waYGxJ!Or%_|mH{zHIpgSG+&=`$VZex#o(?u3aAcd!j;}Uvt5-mCG)>?qkbi 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[PATCH 007/123] feat: British flag, Varignon, radical axis/center, Viviani, parallelogram law MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - Rectangle British flag PA²+PC²=PB²+PD² (origin check) - Varignon midpoint parallelogram for any quad - Circle radical axes + radical center of three - Viviani for equilateral △ (3r=h) and regular tetra (4ρ=h) - Vector parallelogram law |a+b|²+|a−b|²=2(|a|²+|b|²) - WASM rebuilt; rust 51/51; smoke 91/91 + 19/19; smoke:ocr ok --- crates/mathcore/src/circle.rs | 83 ++++++++++++ crates/mathcore/src/geometry.rs | 232 ++++++++++++++++++++++++++++++++ scripts/plot-cases.ts | 5 + src/wasm/pkg/mathcore_bg.wasm | Bin 533051 -> 549399 bytes 4 files changed, 320 insertions(+) diff --git a/crates/mathcore/src/circle.rs b/crates/mathcore/src/circle.rs index bde33d7..9e221fb 100644 --- a/crates/mathcore/src/circle.rs +++ b/crates/mathcore/src/circle.rs @@ -4,6 +4,7 @@ //! the whole configuration. Plus cross inference between circles and named points. use crate::geometry::{deg, dist2, line_eq_latex, near, nice, Fact, NamedPoint, Shape}; +use crate::numeric::solve_linear_pub; use serde::{Deserialize, Serialize}; use std::collections::HashMap; @@ -522,6 +523,61 @@ pub fn circles_analyze(circles: &[NamedCircle], points: &[NamedPoint]) -> Vec Option<(f64, f64, f64)> { + let aa = 2.0 * (q.cx - p.cx); + let bb = 2.0 * (q.cy - p.cy); + let cc = (q.cx * q.cx + q.cy * q.cy - q.r * q.r) - (p.cx * p.cx + p.cy * p.cy - p.r * p.r); + if aa.abs() + bb.abs() < 1e-12 { + None + } else { + Some((aa, bb, cc)) + } + }; + let (Some((a1, b1, d1)), Some((a2, b2, d2))) = (ax(c0, c1), ax(c0, c2)) else { + continue; + }; + let Some(xy) = solve_linear_pub(vec![vec![a1, b1], vec![a2, b2]], vec![d1, d2]) else { + continue; + }; + if !xy[0].is_finite() || !xy[1].is_finite() { + continue; + } + let (x, y) = (xy[0], xy[1]); + let tag = format!("{}{}{}", c0.name, c1.name, c2.name); + // common power value + let pow = (x - c0.cx).powi(2) + (y - c0.cy).powi(2) - c0.r * c0.r; + out.push(fact( + "根心", + &format!("R_{{\\odot {}}}", tag), + format!("\\left({},\\ {}\\right)", nice(x), nice(y)), + None, + "\\pi_{12} \\cap \\pi_{13}", + "三圆根心:三根轴交于一点", + ).with(Shape::Point { x, y, label: format!("根心 {}", tag) })); + out.push(fact( + "根心", + &format!("\\text{{幂}}_{{{}}}", tag), + nice(pow), + Some(pow), + "|OR|^2 - r^2", + "根心对三圆有相同的幂", + )); + } + } + } + } + // Descartes: k_4 = k_1+k_2+k_3 ± 2√(Σ k_i k_j) for three mutually tangent circles. { let n = circles.len().min(4); @@ -738,4 +794,31 @@ mod tests { assert!(nums.iter().any(|n| (n - e).abs() < 1e-9), "missing {e}, have {nums:?}"); } } + + #[test] + fn radical_axis_and_center() { + // Unit circles at (0,0) and (2,0): radical axis x = 1. + // Third at (1, √3) r=1: radical center = circumcenter of centers = (1, √3/3). + let sq3 = 3f64.sqrt(); + let circles = vec![ + NamedCircle { name: "A".into(), cx: 0.0, cy: 0.0, r: 1.0 }, + NamedCircle { name: "B".into(), cx: 2.0, cy: 0.0, r: 1.0 }, + NamedCircle { name: "C".into(), cx: 1.0, cy: sq3, r: 1.0 }, + ]; + let out = circles_analyze(&circles, &[]); + assert!(out.iter().filter(|f| f.group == "两圆根轴" && f.label.starts_with("l_")).count() >= 3); + let axis_ab = out.iter().find(|f| f.label == "l_{AB}").expect("axis AB"); + assert!(axis_ab.value.contains("x = 1") || axis_ab.value == "x = 1", "AB axis = {}", axis_ab.value); + let rc = out.iter().find(|f| f.group == "根心" && f.label.starts_with("R_")).expect("radical center"); + match &rc.shape { + Some(Shape::Point { x, y, .. }) => { + assert!((x - 1.0).abs() < 1e-9, "x={x}"); + assert!((y - sq3 / 3.0).abs() < 1e-9, "y={y}"); + } + other => panic!("expected Point shape, got {other:?}"), + } + let pow = out.iter().find(|f| f.group == "根心" && f.label.contains("幂")).unwrap(); + assert!((pow.num.unwrap() - 1.0 / 3.0).abs() < 1e-9, "power = {}", pow.value); + } + } diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index deb77d9..6a4569c 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -1027,6 +1027,27 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] kinds.push("等腰".into()); } out.push(fact("形状判断", "\\text{类型}", format!("\\text{{{}}}", kinds.join("、")), None, "", "由三个角与三边比较")); + // Viviani (equilateral): sum of distances to the three sides equals the altitude; at I this is 3r = h. + if near(a, b) && near(b, c) { + let h = 2.0 * area / a; + let sum = 3.0 * r; + out.push(fact( + "维维安尼定理", + "d_a + d_b + d_c", + nice(sum), + Some(sum), + "d_a + d_b + d_c = h", + "等边三角形:内点到三边距离之和等于高(内心处为 3r)", + )); + out.push(fact( + "维维安尼定理", + "h", + nice(h), + Some(h), + "3r = h", + "等边:内切圆半径是高的三分之一", + )); + } if near(maxg, PI / 2.0) { out.push(fact("形状判断", "R", nice(rr), Some(rr), "R = \\frac{\\text{斜边}}{2}", "直角三角形外心在斜边中点")); // altitude onto the hypotenuse and the two leg projections (射影定理). @@ -1262,6 +1283,93 @@ pub fn points_analyze(points: &[NamedPoint]) -> Vec { } else { "一般凸四边形" }; + // Varignon: midpoints of the four sides form a parallelogram. + { + let mids = [ + [(a[0] + b[0]) / 2.0, (a[1] + b[1]) / 2.0], + [(b[0] + c[0]) / 2.0, (b[1] + c[1]) / 2.0], + [(c[0] + d[0]) / 2.0, (c[1] + d[1]) / 2.0], + [(d[0] + a[0]) / 2.0, (d[1] + a[1]) / 2.0], + ]; + let side = |i: usize, j: usize| { + let (u, w) = (mids[i], mids[j]); + [w[0] - u[0], w[1] - u[1]] + }; + let (u01, u23) = (side(0, 1), side(3, 2)); + let (u12, u30) = (side(1, 2), side(0, 3)); + let para = |p: [f64; 2], q: [f64; 2]| { + let cr = p[0] * q[1] - p[1] * q[0]; + let sc = (p[0].hypot(p[1])) * (q[0].hypot(q[1])); + sc < 1e-12 || cr.abs() < 1e-9 * sc + }; + if para(u01, u23) && para(u12, u30) { + let l01 = u01[0].hypot(u01[1]); + let l12 = u12[0].hypot(u12[1]); + out.push(fact( + "瓦里农定理", + "\\text{Varignon}", + "\\text{平行四边形}".into(), + None, + "M_i = \\text{中点}(P_iP_{i+1})", + "任意四边形各边中点连成平行四边形", + )); + out.push(fact( + "瓦里农定理", + "|M_0M_1|", + nice(l01), + Some(l01), + "", + "Varignon 边长", + ).with(Shape::Segment { + x1: mids[0][0], y1: mids[0][1], x2: mids[1][0], y2: mids[1][1], + label: "Varignon".into(), + })); + out.push(fact( + "瓦里农定理", + "|M_1M_2|", + nice(l12), + Some(l12), + "", + "Varignon 邻边", + )); + for (i, m) in mids.iter().enumerate() { + out.push(fact( + "瓦里农定理", + &format!("M_{}", i), + pt(m[0], m[1]), + None, + "", + "边中点", + ).with(Shape::Point { x: m[0], y: m[1], label: format!("M{}", i) })); + } + } + } + // British flag theorem: for rectangle/square, PA²+PC² = PB²+PD² for any P (verify at origin). + if is_para && right { + let p0 = [0.0, 0.0]; + let dsq = |q: [f64; 2]| (q[0] - p0[0]).powi(2) + (q[1] - p0[1]).powi(2); + let lhs = dsq(a) + dsq(c); + let rhs = dsq(b) + dsq(d); + if near(lhs, rhs) { + out.push(fact( + "英国国旗定理", + "PA^2 + PC^2", + nice(lhs), + Some(lhs), + "PA^2 + PC^2 = PB^2 + PD^2", + "矩形上任一点(取原点验证):对角顶点到点的平方和相等", + )); + out.push(fact( + "英国国旗定理", + "PB^2 + PD^2", + nice(rhs), + Some(rhs), + "PA^2 + PC^2 = PB^2 + PD^2", + "英国国旗定理", + )); + } + } + out.push(fact("形状判断", "\\text{类型}", format!("\\text{{{}}}", kind), None, "", "由对边平行、直角、边长相等判断")); } else { out.push(fact("形状判断", "\\text{类型}", format!("\\text{{{}{}边形}}", if convex { "凸" } else { "凹" }, n), None, "", "内角和 (n-2)·180°")); @@ -1309,6 +1417,40 @@ fn points3_analyze(points: &[NamedPoint]) -> Vec { let h = 3.0 * vol / area; out.push(fact("距离", &format!("d({}, \\text{{平面}})", pts[3].0), nice(h), Some(h), "d = \\frac{3V}{S}", "等体积法")); } + + // Viviani for regular tetrahedron: sum of distances from an interior point to the four faces = altitude. + { + let edges = [ + len3(sub3(pts[1].1, pts[0].1)), + len3(sub3(pts[2].1, pts[0].1)), + len3(sub3(pts[3].1, pts[0].1)), + len3(sub3(pts[2].1, pts[1].1)), + len3(sub3(pts[3].1, pts[1].1)), + len3(sub3(pts[3].1, pts[2].1)), + ]; + let e0 = edges[0]; + if e0 > 1e-12 && edges.iter().all(|e| near(*e, e0)) && vol > 1e-12 { + // Regular tetra: altitude h = √6 / 3 · a; inradius ρ = h/4 + let h_reg = (6.0f64).sqrt() / 3.0 * e0; + let rho = h_reg / 4.0; + out.push(fact( + "维维安尼定理", + "\\sum d_{\\text{面}}", + nice(h_reg), + Some(h_reg), + "d_1+d_2+d_3+d_4 = h", + "正四面体:内点到四面距离之和等于高(形心处为 4ρ)", + )); + out.push(fact( + "维维安尼定理", + "\\rho", + nice(rho), + Some(rho), + "\\rho = h/4", + "正四面体内切球半径", + )); + } + } // Skew / intersecting lines AB and CD from the first four points. let (na, nb, nc, nd) = (&pts[0].0, &pts[1].0, &pts[2].0, &pts[3].0); let (pa, pb, pc, pd) = (pts[0].1, pts[1].1, pts[2].1, pts[3].1); @@ -1486,6 +1628,23 @@ pub fn vectors_analyze(vs: &[NamedVec]) -> Vec { let dif: Vec = (0..3).map(|k| a[k] - b[k]).collect(); out.push(fact("两向量关系", &format!("{} + {}", na, nb), fmt(&sum), None, "", "坐标相加")); out.push(fact("两向量关系", &format!("{} - {}", na, nb), fmt(&dif), None, "", "坐标相减")); + // Parallelogram law: |a+b|² + |a−b|² = 2(|a|²+|b|²) + { + let sum_len2 = sum[0] * sum[0] + sum[1] * sum[1] + sum[2] * sum[2]; + let dif_len2 = dif[0] * dif[0] + dif[1] * dif[1] + dif[2] * dif[2]; + let rhs = 2.0 * (la * la + lb * lb); + let lhs = sum_len2 + dif_len2; + if (lhs - rhs).abs() < 1e-6 * (1.0 + rhs) { + out.push(fact( + "平行四边形法则", + &format!("|{0}+{1}|^2 + |{0}-{1}|^2", vs[i].name, vs[j].name), + nice(lhs), + Some(lhs), + "|\\vec a+\\vec b|^2 + |\\vec a-\\vec b|^2 = 2(|\\vec a|^2+|\\vec b|^2)", + "平行四边形法则(向量形式)", + )); + } + } } } if vs.len() >= 3 && is3 { @@ -2507,4 +2666,77 @@ mod tests { // OI² = R(R-2r) already covered; ensure |OI| present assert!(fs.iter().any(|f| f.label == "|OI|")); } + + #[test] + fn british_flag_on_rectangle() { + let pts = vec![ + NamedPoint { name: "A".into(), p: vec![0.0, 0.0] }, + NamedPoint { name: "B".into(), p: vec![4.0, 0.0] }, + NamedPoint { name: "C".into(), p: vec![4.0, 3.0] }, + NamedPoint { name: "D".into(), p: vec![0.0, 3.0] }, + ]; + let out = points_analyze(&pts); + assert!(out.iter().any(|f| f.value.contains("矩形"))); + let lhs = out.iter().find(|f| f.group == "英国国旗定理" && f.label == "PA^2 + PC^2").expect("british lhs"); + let rhs = out.iter().find(|f| f.group == "英国国旗定理" && f.label == "PB^2 + PD^2").expect("british rhs"); + assert!((lhs.num.unwrap() - 25.0).abs() < 1e-9); + assert!((rhs.num.unwrap() - 25.0).abs() < 1e-9); + } + + #[test] + fn varignon_parallelogram() { + let pts = vec![ + NamedPoint { name: "A".into(), p: vec![0.0, 0.0] }, + NamedPoint { name: "B".into(), p: vec![4.0, 0.0] }, + NamedPoint { name: "C".into(), p: vec![5.0, 3.0] }, + NamedPoint { name: "D".into(), p: vec![1.0, 3.0] }, + ]; + let out = points_analyze(&pts); + assert!(out.iter().any(|f| f.group == "瓦里农定理" && f.value.contains("平行四边形"))); + assert_eq!(out.iter().filter(|f| f.group == "瓦里农定理" && f.label.starts_with("M_")).count(), 4); + } + + #[test] + fn viviani_equilateral() { + let k = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let sum = fs.iter().find(|f| f.group == "维维安尼定理" && f.label.contains("d_a")).expect("viviani sum"); + let h = fs.iter().find(|f| f.group == "维维安尼定理" && f.label == "h").expect("viviani h"); + assert!((sum.num.unwrap() - h.num.unwrap()).abs() < 1e-9); + // h = √3 for side 2 + assert!((h.num.unwrap() - 3f64.sqrt()).abs() < 1e-9, "h = {}", h.value); + } + + #[test] + fn parallelogram_law_vectors() { + let vs = vec![ + NamedVec { name: "a".into(), v: vec![3.0, 4.0] }, + NamedVec { name: "b".into(), v: vec![1.0, 0.0] }, + ]; + let out = vectors_analyze(&vs); + let f = out.iter().find(|f| f.group == "平行四边形法则").expect("parallelogram law"); + // |a+b|² + |a-b|² = 2(25+1) = 52 + assert!((f.num.unwrap() - 52.0).abs() < 1e-9, "got {}", f.value); + } + + #[test] + fn viviani_regular_tetra() { + // Regular tetra with edge √2: (1,1,1),(1,-1,-1),(-1,1,-1),(-1,-1,1) + let pts = vec![ + NamedPoint { name: "A".into(), p: vec![1.0, 1.0, 1.0] }, + NamedPoint { name: "B".into(), p: vec![1.0, -1.0, -1.0] }, + NamedPoint { name: "C".into(), p: vec![-1.0, 1.0, -1.0] }, + NamedPoint { name: "D".into(), p: vec![-1.0, -1.0, 1.0] }, + ]; + let out = points_analyze(&pts); + let sum = out.iter().find(|f| f.group == "维维安尼定理" && f.label.contains("面")).expect("tetra viviani"); + let edge = 2f64.sqrt() * 2.0 / 1.0; // |A-B| = √[(0)²+(2)²+(2)²] = √8 = 2√2 + let e = (0.0f64.powi(2) + 2.0f64.powi(2) + 2.0f64.powi(2)).sqrt(); // √8 = 2√2 + let h_reg = (6.0f64).sqrt() / 3.0 * e; + assert!((sum.num.unwrap() - h_reg).abs() < 1e-9, "sum={} expect {}", sum.value, h_reg); + let _ = edge; + } + } diff --git a/scripts/plot-cases.ts b/scripts/plot-cases.ts index dd562e0..a5c1b94 100644 --- a/scripts/plot-cases.ts +++ b/scripts/plot-cases.ts @@ -98,6 +98,11 @@ export const cases: [string, string, Expect][] = [ ['直线交球面', 'A(0,0,0)\nB(4,0,0)\nx^2 + y^2 + z^2 = 4', { dim: 3, facts: ['P_{AB\\cap', '|P_1P_2|'] }], ['笛卡尔圆', 'A(0,0)\nB(2,0)\nC(1,1.7320508075688772)\n⊙A: r = 1\n⊙B: r = 1\n⊙C: r = 1', { dim: 2, facts: ['\\text{Descartes}'], minFacts: 2 }], ['圆柱截椭圆', 'x^2 + y^2 = 4\nx - z = 0', { dim: 3, facts: ['a_', 'b_', '\\text{椭圆}'] }], + ['英国国旗定理', 'A(0,0), B(4,0), C(4,3), D(0,3)', { dim: 2, facts: ['矩形', 'PA^2 + PC^2'], minFacts: 4 }], + ['瓦里农平行四边形', 'A(0,0), B(4,0), C(5,3), D(1,3)', { dim: 2, facts: ['\\text{Varignon}', 'M_0'] }], + ['三圆根心', 'A(0,0)\nB(2,0)\nC(1,1.7320508075688772)\n⊙A: r = 1\n⊙B: r = 1\n⊙C: r = 1', { dim: 2, facts: ['l_{', 'R_{\\odot', '\\text{幂}'], minFacts: 5 }], + ['维维安尼等边', '△ABC: a = 2, b = 2, c = 2', { dim: 2, facts: ['d_a + d_b + d_c'], minFacts: 4 }], + ['平行四边形法则', '𝐚 = (3, 4); 𝐛 = (1, 0)', { dim: 2, kinds: ['vector', 'vector'], facts: ['|a+b|^2 + |a-b|^2'] }], ['空间螺旋线', 'r(t) = (cos(t), sin(t), t/3)', { dim: 3 }], ['空间三点', 'P(1,2,3), Q(0,1,-1), R(2,0,1)', { dim: 3 }], ] diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index c828471d35fd52601b7415d59cb64b560c17ae8f..72b67411acee63a17dbd5b4e6febfb5335392adc 100644 GIT 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z2LrhyQ^8N}kV?pX*>_51?&yKmp}S=KK2($VPbCyI1PHoFML)XO(e3O!)zfEdxvmt2LG~1lgbr_~CsrzR;Sz zUp9uQgFPS>ez0nnRX6GfxSTI>Yx#=mI6quj9cS8KRUPO5uC9*r`)jIf`KZ*#* zx-4OosqiQr7UVmM8FWO!Ss$w^S6wSdrdKy(rt7uUsX;dkcxvAauUo>2)pD+@c6Mb$S~UjEIjHTUQ2?A5PYxt8R-2WFkByz)Q?+7jErPsXu0C{Z z0~IdrIo^j*kQsERJmjPe)ybt+!t)ucOzM{n&p3rAkQ|P|te$i-!cDV>kw_lfcp)En z!>0VN=UdvjuSycfztJY;U_92^aV`sZH9ANoSKj zqlui!a~i*!v>c9%1J;5t_1*0oc5kNtsjk*+;SceSmpAS>wTnsHu^F(c0*)qT7g|xc bu)Je4A1z%PSCaRn7 From 5e4eedc36cbdc416d2ee37a77e6b4dc854aa4bd4 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 15:30:32 +0800 Subject: [PATCH 008/123] feat: Ptolemy, Brahmagupta, Napoleon, sphere common chord MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - Cyclic quad: opposite angles → Ptolemy AC·BD = AB·CD+AD·BC - Brahmagupta area √((s-a)(s-b)(s-c)(s-d)) - Napoleon outward equilateral centroids form equilateral - Two-sphere radical plane: common chord 2ρ + intersection centre - WASM rebuilt; rust 55/55; smoke 94/94 + 19/19; smoke:ocr ok --- crates/mathcore/src/geometry.rs | 133 ++++++++++++++++++++++++++++++++ scripts/plot-cases.ts | 4 +- src/math/scene.ts | 30 ++++++- src/wasm/pkg/mathcore_bg.wasm | Bin 549399 -> 552647 bytes 4 files changed, 164 insertions(+), 3 deletions(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 6a4569c..636e04e 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -1064,6 +1064,59 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] out.push(fact("射影定理", &format!("\\text{{射影}}_{{{}}}", SIDE[u]), nice(lu * lu / hyp), Some(lu * lu / hyp), &format!("\\frac{{{u}^2}}{{{c}}}", u = SIDE[u], c = SIDE[ri]), "直角边² = 斜边 × 这条直角边的射影").with(Shape::Segment { x1: v[w][0], y1: v[w][1], x2: foot[0], y2: foot[1], label: format!("射影 {}", SIDE[u]) })); out.push(fact("射影定理", &format!("\\text{{射影}}_{{{}}}", SIDE[w]), nice(lw * lw / hyp), Some(lw * lw / hyp), &format!("\\frac{{{w}^2}}{{{c}}}", w = SIDE[w], c = SIDE[ri]), "直角边² = 斜边 × 这条直角边的射影").with(Shape::Segment { x1: v[u][0], y1: v[u][1], x2: foot[0], y2: foot[1], label: format!("射影 {}", SIDE[w]) })); } + // Napoleon: outward equilateral on each side → centroids form an equilateral triangle. + { + // Orient: positive cross (pa→pb)×(pa→pc) means CCW; outward on edge B→C is clockwise (−60°). + let orient = (pb[0] - pa[0]) * (pc[1] - pa[1]) - (pb[1] - pa[1]) * (pc[0] - pa[0]); + let sign = if orient >= 0.0 { -1.0 } else { 1.0 }; // outward + let cos60 = 0.5; + let sin60 = sign * (3.0f64).sqrt() / 2.0; + let rot = |u: [f64; 2]| -> [f64; 2] { + [u[0] * cos60 - u[1] * sin60, u[0] * sin60 + u[1] * cos60] + }; + let mut cents = [[0.0; 2]; 3]; + for i in 0..3 { + let b = v[(i + 1) % 3]; + let c = v[(i + 2) % 3]; + let w = rot([c[0] - b[0], c[1] - b[1]]); + let dpt = [b[0] + w[0], b[1] + w[1]]; + cents[i] = [(b[0] + c[0] + dpt[0]) / 3.0, (b[1] + c[1] + dpt[1]) / 3.0]; + } + let e01 = dist2(cents[0], cents[1]); + let e12 = dist2(cents[1], cents[2]); + let e20 = dist2(cents[2], cents[0]); + if e01 > 1e-12 && near(e01, e12) && near(e12, e20) { + out.push(fact( + "拿破仑定理", + "\\text{Napoleon}", + "\\text{等边}".into(), + None, + "G_aG_bG_c\\text{ 等边}", + "各边向外作等边三角形,其重心连成等边三角形", + )); + out.push(fact( + "拿破仑定理", + "|G_aG_b|", + nice(e01), + Some(e01), + "", + "拿破仑三角形边长", + ).with(Shape::Segment { + x1: cents[0][0], y1: cents[0][1], x2: cents[1][0], y2: cents[1][1], + label: "Napoleon".into(), + })); + for (i, gcent) in cents.iter().enumerate() { + out.push(fact( + "拿破仑定理", + &format!("G_{{{}}}", SIDE[i]), + pt(gcent[0], gcent[1]), + None, + "", + "外侧等边三角形的重心", + ).with(Shape::Point { x: gcent[0], y: gcent[1], label: format!("G{}", SIDE[i]) })); + } + } + } out } @@ -1370,6 +1423,53 @@ pub fn points_analyze(points: &[NamedPoint]) -> Vec { } } + // Cyclic quad: opposite angles sum to π → Ptolemy + Brahmagupta. + { + let cyclic = convex + && near(angles[0] + angles[2], PI) + && near(angles[1] + angles[3], PI); + if cyclic { + out.push(fact( + "圆内接四边形", + "\\text{共圆}", + "\\checkmark".into(), + None, + "\\angle A + \\angle C = \\angle B + \\angle D = 180^\\circ", + "对角互补 ⇒ 四点共圆", + )); + let (ab, bc, cd, da) = (sides[0], sides[1], sides[2], sides[3]); + let (ac, bd) = (d1, d2); + let lhs = ac * bd; + let rhs = ab * cd + da * bc; + out.push(fact( + "托勒密定理", + "AC \\cdot BD", + nice(lhs), + Some(lhs), + "AC\\cdot BD = AB\\cdot CD + AD\\cdot BC", + "圆内接四边形的托勒密定理", + )); + out.push(fact( + "托勒密定理", + "AB\\cdot CD + AD\\cdot BC", + nice(rhs), + Some(rhs), + "AC\\cdot BD = AB\\cdot CD + AD\\cdot BC", + "托勒密:对角线积 = 对边积之和", + )); + let ssemi = (ab + bc + cd + da) / 2.0; + let brahm = ((ssemi - ab) * (ssemi - bc) * (ssemi - cd) * (ssemi - da)).max(0.0).sqrt(); + out.push(fact( + "婆罗摩笈多公式", + "S_{\\text{Brahmagupta}}", + nice(brahm), + Some(brahm), + "S = \\sqrt{(s-a)(s-b)(s-c)(s-d)}", + "圆内接四边形面积(婆罗摩笈多)", + )); + } + } + out.push(fact("形状判断", "\\text{类型}", format!("\\text{{{}}}", kind), None, "", "由对边平行、直角、边长相等判断")); } else { out.push(fact("形状判断", "\\text{类型}", format!("\\text{{{}{}边形}}", if convex { "凸" } else { "凹" }, n), None, "", "内角和 (n-2)·180°")); @@ -2739,4 +2839,37 @@ mod tests { let _ = edge; } + + #[test] + fn ptolemy_and_brahmagupta_rectangle() { + // 3-4-5 rectangle: sides 4,3,4,3; diagonals 5,5; area 12 + let pts = vec![ + NamedPoint { name: "A".into(), p: vec![0.0, 0.0] }, + NamedPoint { name: "B".into(), p: vec![4.0, 0.0] }, + NamedPoint { name: "C".into(), p: vec![4.0, 3.0] }, + NamedPoint { name: "D".into(), p: vec![0.0, 3.0] }, + ]; + let out = points_analyze(&pts); + assert!(out.iter().any(|f| f.group == "圆内接四边形")); + let acbd = out.iter().find(|f| f.group == "托勒密定理" && f.label.contains("AC")).unwrap(); + assert!((acbd.num.unwrap() - 25.0).abs() < 1e-9, "AC·BD = {}", acbd.value); + let rhs = out.iter().find(|f| f.group == "托勒密定理" && f.label.contains("AB")).unwrap(); + assert!((rhs.num.unwrap() - 25.0).abs() < 1e-9); + let s = out.iter().find(|f| f.group == "婆罗摩笈多公式").unwrap(); + assert!((s.num.unwrap() - 12.0).abs() < 1e-9, "Brahmagupta = {}", s.value); + } + + #[test] + fn napoleon_equilateral_centroids() { + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + assert!(fs.iter().any(|f| f.group == "拿破仑定理" && f.value.contains("等边"))); + let side = fs.iter().find(|f| f.label == "|G_aG_b|").unwrap(); + assert!(side.num.unwrap() > 0.0); + assert_eq!(fs.iter().filter(|f| f.group == "拿破仑定理" && f.label.starts_with("G_")).count(), 3); + } + + } diff --git a/scripts/plot-cases.ts b/scripts/plot-cases.ts index a5c1b94..385efd1 100644 --- a/scripts/plot-cases.ts +++ b/scripts/plot-cases.ts @@ -92,7 +92,7 @@ export const cases: [string, string, Expect][] = [ ['异面直线四点', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,1,1)', { dim: 3, facts: ['d(AB, CD)=1', '异面', '\\theta(AB, CD)'] }], ['线面角', 'A(0,0,0)\nB(0,0,1)\nC(1,0,0)\nz = 0', { dim: 3, facts: ['\\theta(AB, α)', 'AB \\perp α', 'AC \\parallel α', '\\text{foot}(B, α)'] }], ['两圆根轴', 'x^2 + y^2 = 4\n(x-3)^2 + y^2 = 4', { dim: 2, facts: ['l_{', '相交', '公共弦'] }], - ['两球根面', 'x^2 + y^2 + z^2 = 4\n(x-3)^2 + y^2 + z^2 = 4', { dim: 3, facts: ['\\pi_', '\\rho_'] }], + ['两球根面', 'x^2 + y^2 + z^2 = 4\n(x-3)^2 + y^2 + z^2 = 4', { dim: 3, facts: ['\\pi_', '\\rho_', '公共弦'] }], ['四面体体积', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,0,1)', { dim: 3, facts: ['V_{\\text{四面体}}'] }], ['二面角', 'x + 0*z = 0\ny + 0*z = 0', { dim: 3, facts: ['\\text{二面角}', '\\perp'] }], ['直线交球面', 'A(0,0,0)\nB(4,0,0)\nx^2 + y^2 + z^2 = 4', { dim: 3, facts: ['P_{AB\\cap', '|P_1P_2|'] }], @@ -103,6 +103,8 @@ export const cases: [string, string, Expect][] = [ ['三圆根心', 'A(0,0)\nB(2,0)\nC(1,1.7320508075688772)\n⊙A: r = 1\n⊙B: r = 1\n⊙C: r = 1', { dim: 2, facts: ['l_{', 'R_{\\odot', '\\text{幂}'], minFacts: 5 }], ['维维安尼等边', '△ABC: a = 2, b = 2, c = 2', { dim: 2, facts: ['d_a + d_b + d_c'], minFacts: 4 }], ['平行四边形法则', '𝐚 = (3, 4); 𝐛 = (1, 0)', { dim: 2, kinds: ['vector', 'vector'], facts: ['|a+b|^2 + |a-b|^2'] }], + ['托勒密与婆罗摩笈多', 'A(0,0), B(4,0), C(4,3), D(0,3)', { dim: 2, facts: ['\\text{共圆}', 'AC \\cdot BD', 'S_{\\text{Brahmagupta}}'], minFacts: 4 }], + ['拿破仑定理', '△ABC: a = 3, b = 4, c = 5', { dim: 2, facts: ['\\text{Napoleon}', '|G_aG_b|'], minFacts: 3 }], ['空间螺旋线', 'r(t) = (cos(t), sin(t), t/3)', { dim: 3 }], ['空间三点', 'P(1,2,3), Q(0,1,-1), R(2,0,1)', { dim: 3 }], ] diff --git a/src/math/scene.ts b/src/math/scene.ts index 9cddc0b..487074b 100644 --- a/src/math/scene.ts +++ b/src/math/scene.ts @@ -820,15 +820,41 @@ export function analyze(cards: CardInput[], solutionIndex = 0): Analysis { }) const rho2 = A.r * A.r - signed * signed if (rho2 > 1e-9) { + const rho = Math.sqrt(rho2) facts.push({ group: '根面', label: `\\rho_{${A.name}\\cap ${B.name}}`, - value: engine.nice(Math.sqrt(rho2)), - num: Math.sqrt(rho2), + value: engine.nice(rho), + num: rho, how: '\\rho = \\sqrt{r_1^2 - d_1^2}', why: '两球交圆落在根面上', shape: null, }) + // Common chord in a plane through the line of centres = diameter of the intersection circle. + const chord = 2 * rho + facts.push({ + group: '根面', + label: `|\\text{公共弦}_{${A.name}${B.name}}|`, + value: engine.nice(chord), + num: chord, + how: '2\\rho = 2\\sqrt{r_1^2 - d_1^2}', + why: '过两球心的平面截交圆得公共弦(交圆直径)', + shape: null, + }) + // Centre of the intersection circle on the radical plane, along O1O2. + const tParam = -signed / ln + const cx = A.c[0] + tParam * n[0] + const cy = A.c[1] + tParam * n[1] + const cz = A.c[2] + tParam * n[2] + facts.push({ + group: '根面', + label: `C_{${A.name}\\cap ${B.name}}`, + value: `\\left(${engine.nice(cx)},\\ ${engine.nice(cy)},\\ ${engine.nice(cz)}\\right)`, + num: null, + how: 'O_1 + \\dfrac{-\\mathrm{signed}}{|O_1O_2|}\\vec{O_1O_2}', + why: '交圆圆心:根面与球心连线的交点', + shape: null, + }) } else if (Math.abs(rho2) <= 1e-9) { facts.push({ group: '根面', diff --git 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zG4{~jhxPIH-nF*Co@E2Wmaum%IpXzO*0y`8OM>2yXa4G^1f{g}iqLTCpVdjJje=*nrq;Knw1t-%7z$mKi;BRu=*N(@;SHa^IJ-!Ez4lt#qpxq^h$&-R* zgLrk2Po!XDfTIS$PPmTHqyhTU@UM^9GzZGvJwgow^a=JMM-4+Y1~GewvyRg6RNdK6 zrdI~@S0d(dm=%l%qY`v2@U!=5&B|1Lu*JTv&UmT27Kb0ZhU@C6;V~Gk_+#|=K>R7V zMaRfDP#>Ls_Lwbjkt@ZFvB#(~U&JKm!n@!}mi&5%R}In!#*8~|9IMk2!@6tPh}r0t z9H-1ddWLfam<{b)h*_O|i1~Ovj2Jbs+^#`-T#S^vgLJ<2lpyB5?LI~~(T+XsOIS-V z8xUT-X*nZL0rnqgM*_r`y!w;bejS zZ%MXaY=JI25j#koo%0La From 13b4e80bea102280520a9166e13b00a3810f34dc Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 15:32:10 +0800 Subject: [PATCH 009/123] =?UTF-8?q?feat:=20Morley,=20Carnot,=20|OH|=C2=B2?= =?UTF-8?q?=20Euler=20form,=20isogonal=20O=E2=86=94H?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - Explicit |OH|² = 9R²−(a²+b²+c²) and |OI|² = R(R−2r) (distinct) - Carnot: signed δ_a+δ_b+δ_c = R+r - Morley trisector triangle equilateral - Isogonal conjugates H↔O and I↔I - WASM rebuilt; rust 56/56; smoke 96/96 + 19/19; smoke:ocr ok --- crates/mathcore/src/geometry.rs | 211 +++++++++++++++++++++++++++++++- scripts/plot-cases.ts | 2 + src/wasm/pkg/mathcore_bg.wasm | Bin 552647 -> 557752 bytes 3 files changed, 212 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 636e04e..b4f2fff 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -619,8 +619,104 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "|OH|^2 = 9R^2 - (a^2 + b^2 + c^2)", "外心与垂心的距离", ).with(Shape::Segment { x1: circ[0], y1: circ[1], x2: orth[0], y2: orth[1], label: "OH".into() })); + // Explicit Euler OH² identity (distinct from |OI|² = R(R−2r)). + { + let oh2 = oh * oh; + let oh2_form = 9.0 * rr * rr - (a * a + b * b + c * c); + out.push(fact( + "特殊点", + "|OH|^2", + nice(oh2), + Some(oh2), + "|OH|^2 = 9R^2 - (a^2 + b^2 + c^2)", + "欧拉:外心与垂心距离的平方公式", + )); + if (oh2 - oh2_form).abs() < 1e-6 * (1.0 + oh2.abs()) { + out.push(fact( + "特殊点", + "9R^2 - (a^2+b^2+c^2)", + nice(oh2_form), + Some(oh2_form), + "|OH|^2 = 9R^2 - (a^2 + b^2 + c^2)", + "与 |OH|^2 一致", + )); + } + let oi2_form = rr * (rr - 2.0 * r); + out.push(fact( + "特殊点", + "|OI|^2", + nice(oi * oi), + Some(oi * oi), + "|OI|^2 = R(R - 2r)", + "欧拉:外心与内心(勿与 |OH|^2 混淆)", + )); + let _ = oi2_form; + } + // Isogonal conjugates: O and H are isogonal conjugates of each other; I is self-conjugate. + out.push(fact( + "等角共轭", + "H \\leftrightarrow O", + "\\text{等角共轭}".into(), + None, + "\\text{反射角平分线}", + "垂心与外心互为等角共轭;内心是自身的等角共轭", + )); + out.push(fact( + "等角共轭", + "I \\leftrightarrow I", + "\\checkmark".into(), + None, + "", + "内心的等角共轭是自身", + )); + - // Euler line: O, G, H collinear with OG:GH = 1:2 (and |OH| = 3|OG|). + // Carnot: signed distances from O to the three sides sum to R + r. + { + let mut sum_d = 0.0; + for i in 0..3 { + let q1 = v[(i + 1) % 3]; + let q2 = v[(i + 2) % 3]; + let dx = q2[0] - q1[0]; + let dy = q2[1] - q1[1]; + let len = (dx * dx + dy * dy).sqrt(); + if len < 1e-12 { + continue; + } + // cross z-component for (q2-q1)×(P-q1) + let cross_o = dx * (circ[1] - q1[1]) - dy * (circ[0] - q1[0]); + let cross_v = dx * (v[i][1] - q1[1]) - dy * (v[i][0] - q1[0]); + let dist = cross_o.abs() / len; + let signed = if cross_o * cross_v >= 0.0 { dist } else { -dist }; + sum_d += signed; + out.push(fact( + "卡诺定理", + &format!("\\delta_{{{}}}", SIDE[i]), + nice(signed), + Some(signed), + "d(O,\\text{边})\\text{(有向)}", + "外心到边的有向距离(与对顶同侧为正)", + )); + } + out.push(fact( + "卡诺定理", + "\\delta_a+\\delta_b+\\delta_c", + nice(sum_d), + Some(sum_d), + "\\delta_a+\\delta_b+\\delta_c = R+r", + "卡诺定理:外心到三边有向距离之和等于 R+r", + )); + out.push(fact( + "卡诺定理", + "R+r", + nice(rr + r), + Some(rr + r), + "R + r", + "与有向距离之和对照", + )); + } + + // Euler line: O, G, H collinear with OG:GH = 1:2 (and |OH| = 3|OG|). // Note: |OI|^2 = R(R−2r) is the Euler distance formula for the incenter (already above); // it is not |OH|^2. { @@ -1064,6 +1160,91 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] out.push(fact("射影定理", &format!("\\text{{射影}}_{{{}}}", SIDE[u]), nice(lu * lu / hyp), Some(lu * lu / hyp), &format!("\\frac{{{u}^2}}{{{c}}}", u = SIDE[u], c = SIDE[ri]), "直角边² = 斜边 × 这条直角边的射影").with(Shape::Segment { x1: v[w][0], y1: v[w][1], x2: foot[0], y2: foot[1], label: format!("射影 {}", SIDE[u]) })); out.push(fact("射影定理", &format!("\\text{{射影}}_{{{}}}", SIDE[w]), nice(lw * lw / hyp), Some(lw * lw / hyp), &format!("\\frac{{{w}^2}}{{{c}}}", w = SIDE[w], c = SIDE[ri]), "直角边² = 斜边 × 这条直角边的射影").with(Shape::Segment { x1: v[u][0], y1: v[u][1], x2: foot[0], y2: foot[1], label: format!("射影 {}", SIDE[w]) })); } + // Morley: adjacent angle trisectors meet at an equilateral triangle. + { + let unit = |u: [f64; 2]| { + let l = u[0].hypot(u[1]); + if l < 1e-12 { + [0.0, 0.0] + } else { + [u[0] / l, u[1] / l] + } + }; + let rot = |u: [f64; 2], ang: f64| { + let (c, s) = (ang.cos(), ang.sin()); + [u[0] * c - u[1] * s, u[0] * s + u[1] * c] + }; + let sang = |u: [f64; 2], w: [f64; 2]| (u[0] * w[1] - u[1] * w[0]).atan2(u[0] * w[0] + u[1] * w[1]); + let mut mverts = [[0.0; 2]; 3]; + let mut ok = true; + for s in 0..3 { + let i = s; + let j = (s + 1) % 3; + let k = (s + 2) % 3; + let (pi, pj) = (v[i], v[j]); + let u_ij = unit([pj[0] - pi[0], pj[1] - pi[1]]); + let u_ik = unit([v[k][0] - pi[0], v[k][1] - pi[1]]); + let ai = sang(u_ij, u_ik); + let dir_i = rot(u_ij, ai / 3.0); + let u_ji = unit([pi[0] - pj[0], pi[1] - pj[1]]); + let u_jk = unit([v[k][0] - pj[0], v[k][1] - pj[1]]); + let aj = sang(u_ji, u_jk); + let dir_j = rot(u_ji, aj / 3.0); + let mat = vec![vec![dir_i[0], -dir_j[0]], vec![dir_i[1], -dir_j[1]]]; + if let Some(st) = solve_linear_pub(mat, vec![pj[0] - pi[0], pj[1] - pi[1]]) { + if st[0].is_finite() && st[0] > 1e-9 { + mverts[s] = [pi[0] + st[0] * dir_i[0], pi[1] + st[0] * dir_i[1]]; + } else { + ok = false; + } + } else { + ok = false; + } + } + if ok { + let e01 = dist2(mverts[0], mverts[1]); + let e12 = dist2(mverts[1], mverts[2]); + let e20 = dist2(mverts[2], mverts[0]); + if e01 > 1e-9 && near(e01, e12) && near(e12, e20) { + out.push(fact( + "莫利定理", + "\\text{Morley}", + "\\text{等边}".into(), + None, + "\\text{邻角三等分线交点}", + "相邻角的三等分线交出等边三角形", + )); + out.push(fact( + "莫利定理", + "|M_0M_1|", + nice(e01), + Some(e01), + "", + "莫利三角形边长", + ).with(Shape::Segment { + x1: mverts[0][0], + y1: mverts[0][1], + x2: mverts[1][0], + y2: mverts[1][1], + label: "Morley".into(), + })); + for (ii, mv) in mverts.iter().enumerate() { + out.push(fact( + "莫利定理", + &format!("M_{}", ii), + pt(mv[0], mv[1]), + None, + "", + "莫利三角形顶点", + ).with(Shape::Point { + x: mv[0], + y: mv[1], + label: format!("M{}", ii), + })); + } + } + } + } // Napoleon: outward equilateral on each side → centroids form an equilateral triangle. { // Orient: positive cross (pa→pb)×(pa→pc) means CCW; outward on edge B→C is clockwise (−60°). @@ -2872,4 +3053,32 @@ mod tests { } + + #[test] + fn oh2_carnot_isogonal_morley() { + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let oh2 = fs.iter().find(|f| f.label == "|OH|^2").expect("|OH|^2"); + assert!((oh2.num.unwrap() - 6.25).abs() < 1e-9, "OH² = {}", oh2.value); + let form = fs.iter().find(|f| f.label.starts_with("9R^2")).expect("9R^2 form"); + assert!((form.num.unwrap() - 6.25).abs() < 1e-9); + let oi2 = fs.iter().find(|f| f.label == "|OI|^2").expect("|OI|^2"); + assert!((oi2.num.unwrap() - 1.25).abs() < 1e-9, "OI² = {}", oi2.value); + assert!(fs.iter().any(|f| f.group == "等角共轭" && f.label.contains("H"))); + let sum = fs + .iter() + .find(|f| f.group == "卡诺定理" && f.label.contains("delta_a") && f.label.contains('+')) + .expect("Carnot sum"); + let rr = fs.iter().find(|f| f.group == "卡诺定理" && f.label == "R+r").unwrap(); + assert!((sum.num.unwrap() - rr.num.unwrap()).abs() < 1e-6, "Carnot {} vs {}", sum.value, rr.value); + assert!( + fs.iter().any(|f| f.group == "莫利定理" && f.value.contains("等边")), + "Morley missing" + ); + let ms = fs.iter().find(|f| f.group == "莫利定理" && f.label == "|M_0M_1|").unwrap(); + assert!(ms.num.unwrap() > 0.0); + } + } diff --git a/scripts/plot-cases.ts b/scripts/plot-cases.ts index 385efd1..f4c4bd0 100644 --- a/scripts/plot-cases.ts +++ b/scripts/plot-cases.ts @@ -105,6 +105,8 @@ export const cases: [string, string, Expect][] = [ ['平行四边形法则', '𝐚 = (3, 4); 𝐛 = (1, 0)', { dim: 2, kinds: ['vector', 'vector'], facts: ['|a+b|^2 + |a-b|^2'] }], ['托勒密与婆罗摩笈多', 'A(0,0), B(4,0), C(4,3), D(0,3)', { dim: 2, facts: ['\\text{共圆}', 'AC \\cdot BD', 'S_{\\text{Brahmagupta}}'], minFacts: 4 }], ['拿破仑定理', '△ABC: a = 3, b = 4, c = 5', { dim: 2, facts: ['\\text{Napoleon}', '|G_aG_b|'], minFacts: 3 }], + ['欧拉OH²与卡诺', '△ABC: a = 3, b = 4, c = 5', { dim: 2, facts: ['|OH|^2', '9R^2', 'R+r', 'H \\leftrightarrow O'], minFacts: 6 }], + ['莫利定理', '△ABC: a = 3, b = 4, c = 5', { dim: 2, facts: ['\\text{Morley}', '|M_0M_1|'], minFacts: 3 }], ['空间螺旋线', 'r(t) = (cos(t), sin(t), t/3)', { dim: 3 }], ['空间三点', 'P(1,2,3), Q(0,1,-1), R(2,0,1)', { dim: 3 }], ] diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index a7286d92f3b7b183816ecc9b6d0502c8fab73788..ff70108c9c51fd0317f6bf2673941385245a4271 100644 GIT binary patch delta 53665 zcmd4434B$>6+iy&-1}bk@}uEZthX>Uf+cg551wV zUO9vQ(ci^uBaE*jd0Me&zMii4)6?d-fZZxH?KA>jY?w09^;m%Ta{|# zjUmYd{3mK;uWB}*A3a{{;t9O!TO^4njjW;3=Ue4;*{sz_uxKY0jkAhYM9)FdZ42jetrC=%!!lLX5{gx39O0AcqXt$O5-N52Ewxmte#RD z7O_y7m|?sU+nYGIab(XJLJzmOtHdQu1dQO(1S808JN^Ctgq<3gW> ziuaNfHp_^am~0G*=k^GVh4G`624heBc-Hi|@mc&I=ahi4yzTLQt_dijyJssCSs9_! z39Jh9NSv#r)XgiE`4ccIJTIp{GT05<#RGs3gqV!x8 zti%HqEVm0tVo`wxh9V#smC-n!J2X63Q%5awFc_RQnDPkY0dIOvc?7a(?m7$iL8kQ{ zI<<*mK_14_Kr15jB%Z$onF*Fafbg^MvI3nFFUu*F4cWXz$AE2KN-0Uu-GhzPL|v&j zrX`LW(oXV{u8-EUO8vIJY+LhW{(LBtzx|F)`@CBfRa$A+*qD;Q%(`h 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17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 15:34:37 +0800 Subject: [PATCH 010/123] =?UTF-8?q?feat:=20Simson,=20OH=20nine-point=20dia?= =?UTF-8?q?meter,=20=CF=84(I),=20Cayley=E2=80=93Menger=20V?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- crates/mathcore/src/geometry.rs | 271 ++++++++++++++++++++++++++++++++ scripts/plot-cases.ts | 4 +- src/wasm/pkg/mathcore_bg.wasm | Bin 557752 -> 564393 bytes 3 files changed, 274 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index b4f2fff..1928264 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -787,6 +787,36 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] r: r9, label: "九点圆".into(), })); + // OH is always a diameter of the circle centred at N through O (and H); + // it coincides with the nine-point circle precisely when |OH| = R (right triangles). + let oh_len = dist2(circ, orth); + out.push(fact( + "欧拉线", + "|OH| = 2|ON|", + nice(oh_len), + Some(oh_len), + "|OH| = 2|ON| = 2|NH|", + "N 平分 OH,故 OH 是以 N 为圆心、半径 |OH|/2 的圆的直径", + )); + if near(oh_len, rr) { + out.push(fact( + "欧拉线", + "OH\\text{ 九点圆直径}", + "\\checkmark".into(), + None, + "|OH| = R = 2R_N", + "直角三角形:欧拉圆(九点圆)以 OH 为直径", + )); + } else { + out.push(fact( + "欧拉线", + "OH\\text{ 与九点圆}", + format!("|OH|/2 = {},\\ R_N = {}", nice(oh_len / 2.0), nice(r9)), + None, + "|OH|/2 \\ne R/2", + "一般三角形 OH 不是九点圆直径(仅当直角时重合)", + )); + } } // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. @@ -1298,6 +1328,161 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } } + + // Simson line: feet from a circumcircle point P onto the three sides are collinear. + // Take P = antipode of A on the circumcircle (always on (O)). + { + let p_sim = [2.0 * circ[0] - pa[0], 2.0 * circ[1] - pa[1]]; + let foot_line = |p: [f64; 2], q1: [f64; 2], q2: [f64; 2]| -> Option<[f64; 2]> { + let dx = q2[0] - q1[0]; + let dy = q2[1] - q1[1]; + let den = dx * dx + dy * dy; + if den < 1e-18 { + return None; + } + let t = ((p[0] - q1[0]) * dx + (p[1] - q1[1]) * dy) / den; + Some([q1[0] + t * dx, q1[1] + t * dy]) + }; + // feet onto BC, CA, AB + let sides = [(pb, pc), (pc, pa), (pa, pb)]; + let mut feet = [[0.0; 2]; 3]; + let mut ok = true; + for (i, (q1, q2)) in sides.into_iter().enumerate() { + if let Some(f) = foot_line(p_sim, q1, q2) { + feet[i] = f; + } else { + ok = false; + } + } + if ok { + let cross = (feet[1][0] - feet[0][0]) * (feet[2][1] - feet[0][1]) + - (feet[1][1] - feet[0][1]) * (feet[2][0] - feet[0][0]); + if cross.abs() < 1e-6 * (1.0 + rr) { + out.push(fact( + "西姆松线", + "\\text{Simson}", + "\\text{共线}".into(), + None, + "P\\in\\odot(O)\\Rightarrow\\text{三垂足共线}", + "西姆松线:外接圆上一点到三边垂足共线(P 取 A 的对径点)", + )); + out.push(fact( + "西姆松线", + "P_{\\text{Simson}}", + pt(p_sim[0], p_sim[1]), + None, + "P = 2O - A", + "外接圆上 A 的对径点", + ).with(Shape::Point { + x: p_sim[0], + y: p_sim[1], + label: "P Simson".into(), + })); + for (i, f) in feet.iter().enumerate() { + let side_name = SIDE[i]; + out.push(fact( + "西姆松线", + &format!("F_{{{}}}", side_name), + pt(f[0], f[1]), + None, + "", + &format!("P 到边 {} 的垂足", side_name), + ).with(Shape::Point { + x: f[0], + y: f[1], + label: format!("F{}", side_name), + })); + } + // line through F_a and F_b + let (f0, f1) = (feet[0], feet[1]); + let la = f1[1] - f0[1]; + let lb = f0[0] - f1[0]; + let lc = la * f0[0] + lb * f0[1]; + if la.hypot(lb) > 1e-12 { + out.push(fact( + "西姆松线", + "l_{\\text{Simson}}", + line_eq_latex(la, lb, lc), + None, + "三垂足所在直线", + "西姆松线方程", + ).with(Shape::Segment { + x1: f0[0], + y1: f0[1], + x2: f1[0], + y2: f1[1], + label: "Simson".into(), + })); + } + } + } + } + + // Trilinear polar of the incenter I (barycentrics a:b:c): X/a + Y/b + Z/c = 0. + { + let mut poles: Vec<[f64; 2]> = Vec::new(); + // Intersection with side opposite vertex i (bary coord of that vertex = 0). + for i in 0..3 { + let sj = s[(i + 1) % 3]; + let sk = s[(i + 2) % 3]; + // On side jk: α_i = 0, β_j + β_k = 1, β_j/sj + β_k/sk = 0. + if (sj - sk).abs() < 1e-12 { + continue; // polar ∥ this side + } + let bj = sj / (sj - sk); + let bk = 1.0 - bj; + let pj = v[(i + 1) % 3]; + let pk = v[(i + 2) % 3]; + let pt_i = [bj * pj[0] + bk * pk[0], bj * pj[1] + bk * pk[1]]; + if pt_i[0].is_finite() && pt_i[1].is_finite() { + poles.push(pt_i); + } + } + out.push(fact( + "三线极线", + "\\tau(I)", + "\\frac{X}{a}+\\frac{Y}{b}+\\frac{Z}{c}=0".into(), + None, + "I=(a:b:c)_{\\text{bary}}", + "内心的三线极线(重心坐标方程)", + )); + if poles.len() >= 2 { + let (p0, p1) = (poles[0], poles[1]); + let la = p1[1] - p0[1]; + let lb = p0[0] - p1[0]; + let lc = la * p0[0] + lb * p0[1]; + if la.hypot(lb) > 1e-12 { + out.push(fact( + "三线极线", + "l_{\\tau(I)}", + line_eq_latex(la, lb, lc), + None, + "\\frac{X}{a}+\\frac{Y}{b}+\\frac{Z}{c}=0", + "内心三线极线的直角坐标方程", + ).with(Shape::Segment { + x1: p0[0], + y1: p0[1], + x2: p1[0], + y2: p1[1], + label: "τ(I)".into(), + })); + } + for (k, pp) in poles.iter().take(3).enumerate() { + out.push(fact( + "三线极线", + &format!("Q_{{{}}}", k), + pt(pp[0], pp[1]), + None, + "", + "三线极线与边的交点", + ).with(Shape::Point { + x: pp[0], + y: pp[1], + label: format!("Q{}", k), + })); + } + } + } out } @@ -1694,6 +1879,64 @@ fn points3_analyze(points: &[NamedPoint]) -> Vec { let dpt = pts[3].1; let vol = dot3(sub3(dpt, a), nrm).abs() / 6.0; out.push(fact("体积", "V_{\\text{四面体}}", nice(vol), Some(vol), "V = \\frac16\\left|\\vec{AD}\\cdot(\\vec{AB}\\times\\vec{AC})\\right|", "混合积")); + // Cayley–Menger: volume from the six edge lengths alone. + { + let p0 = pts[0].1; + let p1 = pts[1].1; + let p2 = pts[2].1; + let p3 = pts[3].1; + let d12 = len3(sub3(p1, p0)); + let d13 = len3(sub3(p2, p0)); + let d14 = len3(sub3(p3, p0)); + let d23 = len3(sub3(p2, p1)); + let d24 = len3(sub3(p3, p1)); + let d34 = len3(sub3(p3, p2)); + let s = |x: f64| x * x; + let mut m = [ + [0.0, 1.0, 1.0, 1.0, 1.0], + [1.0, 0.0, s(d12), s(d13), s(d14)], + [1.0, s(d12), 0.0, s(d23), s(d24)], + [1.0, s(d13), s(d23), 0.0, s(d34)], + [1.0, s(d14), s(d24), s(d34), 0.0], + ]; + // Gaussian elimination → det + let mut det = 1.0_f64; + for i in 0..5 { + let mut piv = i; + for r in (i + 1)..5 { + if m[r][i].abs() > m[piv][i].abs() { + piv = r; + } + } + if m[piv][i].abs() < 1e-18 { + det = 0.0; + break; + } + if piv != i { + m.swap(piv, i); + det = -det; + } + det *= m[i][i]; + for r in (i + 1)..5 { + let f = m[r][i] / m[i][i]; + for c in i..5 { + m[r][c] -= f * m[i][c]; + } + } + } + let v_cm2 = det.abs() / 288.0; + if v_cm2 >= 0.0 { + let v_cm = v_cm2.sqrt(); + out.push(fact( + "体积", + "V_{\\text{Cayley--Menger}}", + nice(v_cm), + Some(v_cm), + "288V^2 = |\\det M_5|", + "凯莱–门杰行列式:由六棱长求四面体体积", + )); + } + } if area > 1e-12 { let h = 3.0 * vol / area; out.push(fact("距离", &format!("d({}, \\text{{平面}})", pts[3].0), nice(h), Some(h), "d = \\frac{3V}{S}", "等体积法")); @@ -2919,6 +3162,8 @@ mod tests { let out = points_analyze(&pts); let v = out.iter().find(|f| f.label.contains("四面体")).expect("tetra volume"); assert!((v.num.unwrap() - 1.0 / 6.0).abs() < 1e-9, "V = {}", v.value); + let cm = out.iter().find(|f| f.label.contains("Cayley")).expect("Cayley-Menger"); + assert!((cm.num.unwrap() - 1.0 / 6.0).abs() < 1e-9, "V_CM = {}", cm.value); } #[test] @@ -2946,6 +3191,13 @@ mod tests { assert!((r9.num.unwrap() - 1.25).abs() < 1e-9, "R9 = {}", r9.value); // R=2.5 // OI² = R(R-2r) already covered; ensure |OI| present assert!(fs.iter().any(|f| f.label == "|OI|")); + // 3-4-5 is right: OH is nine-point diameter + assert!( + fs.iter().any(|f| f.label.contains("九点圆直径")), + "OH nine-point diameter fact missing for right triangle" + ); + let oh2on = fs.iter().find(|f| f.label == "|OH| = 2|ON|").expect("OH=2ON"); + assert!((oh2on.num.unwrap() - 2.5).abs() < 1e-9); } #[test] @@ -3081,4 +3333,23 @@ mod tests { assert!(ms.num.unwrap() > 0.0); } + #[test] + fn simson_and_trilinear_polar() { + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + assert!( + fs.iter().any(|f| f.group == "西姆松线" && f.value.contains("共线")), + "Simson collinear missing" + ); + assert!(fs.iter().any(|f| f.group == "西姆松线" && f.label.contains("Simson"))); + assert_eq!(fs.iter().filter(|f| f.group == "西姆松线" && f.label.starts_with("F_")).count(), 3); + assert!( + fs.iter().any(|f| f.group == "三线极线" && f.label.contains("tau")), + "trilinear polar of I missing" + ); + assert!(fs.iter().any(|f| f.group == "三线极线" && f.label.contains("l_"))); + } + } diff --git a/scripts/plot-cases.ts b/scripts/plot-cases.ts index f4c4bd0..e633d84 100644 --- a/scripts/plot-cases.ts +++ b/scripts/plot-cases.ts @@ -93,7 +93,7 @@ export const cases: [string, string, Expect][] = [ ['线面角', 'A(0,0,0)\nB(0,0,1)\nC(1,0,0)\nz = 0', { dim: 3, facts: ['\\theta(AB, α)', 'AB \\perp α', 'AC \\parallel α', '\\text{foot}(B, α)'] }], ['两圆根轴', 'x^2 + y^2 = 4\n(x-3)^2 + y^2 = 4', { dim: 2, facts: ['l_{', '相交', '公共弦'] }], ['两球根面', 'x^2 + y^2 + z^2 = 4\n(x-3)^2 + y^2 + z^2 = 4', { dim: 3, facts: ['\\pi_', '\\rho_', '公共弦'] }], - ['四面体体积', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,0,1)', { dim: 3, facts: ['V_{\\text{四面体}}'] }], + ['四面体体积', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,0,1)', { dim: 3, facts: ['V_{\\text{四面体}}', 'V_{\\text{Cayley'] }], ['二面角', 'x + 0*z = 0\ny + 0*z = 0', { dim: 3, facts: ['\\text{二面角}', '\\perp'] }], ['直线交球面', 'A(0,0,0)\nB(4,0,0)\nx^2 + y^2 + z^2 = 4', { dim: 3, facts: ['P_{AB\\cap', '|P_1P_2|'] }], ['笛卡尔圆', 'A(0,0)\nB(2,0)\nC(1,1.7320508075688772)\n⊙A: r = 1\n⊙B: r = 1\n⊙C: r = 1', { dim: 2, facts: ['\\text{Descartes}'], minFacts: 2 }], @@ -107,6 +107,8 @@ export const cases: [string, string, Expect][] = [ ['拿破仑定理', '△ABC: a = 3, b = 4, c = 5', { dim: 2, facts: ['\\text{Napoleon}', '|G_aG_b|'], minFacts: 3 }], ['欧拉OH²与卡诺', '△ABC: a = 3, b = 4, c = 5', { dim: 2, facts: ['|OH|^2', '9R^2', 'R+r', 'H \\leftrightarrow O'], minFacts: 6 }], ['莫利定理', '△ABC: a = 3, b = 4, c = 5', { dim: 2, facts: ['\\text{Morley}', '|M_0M_1|'], minFacts: 3 }], + ['西姆松与三线极线', '△ABC: a = 3, b = 4, c = 5', { dim: 2, facts: ['\\text{Simson}', 'l_{\\text{Simson}}', '\\tau(I)', 'OH\\text{ 九点圆直径}'], minFacts: 6 }], + ['凯莱门杰四面体', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,0,1)', { dim: 3, facts: ['V_{\\text{四面体}}', 'V_{\\text{Cayley'] }], ['空间螺旋线', 'r(t) = (cos(t), sin(t), t/3)', { dim: 3 }], ['空间三点', 'P(1,2,3), Q(0,1,-1), R(2,0,1)', { dim: 3 }], ] diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index ff70108c9c51fd0317f6bf2673941385245a4271..59b90526d04a930a6f0ea7582fa40293ed77d1b2 100644 GIT binary patch delta 62901 zcmcG131Ae}{r|q1&E_VXJ0v8TT?izEBjJ>r7Z9;Zy{lI1eN?nnto3NM8#HQEkibMH zXv9s3uwcNb(TxfkFx9B2(WV+L)nKtkMH?&DR8jw*?|U<|vmv1EzdvmA?(2KM?|W~y z?Nee@DW^|=KC$fQvD_rOj|KjFv@XghV9I1IUV4UXRHSCI|0*6?s 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zb_=3-K4Qxqa@-#^L4Iq7pY&P>l4*$JHYA^L|jk zh9`l>f|+k@=K69A$NMG~j?bOtD?mKABuP-@3b<%M-eav7{?rxnC46JRe|C-huRs3> DipYe1 From cf2767f2e207e0185bc87b8007bdea685b9b9841 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 07:35:37 +0000 Subject: [PATCH 011/123] feat: write confident over-arrow, sum, and isolated sigma Lift CoMER when an over-arrow, summation, or Greek name agrees with the ink. A lone sigma is the symbol and does not open the axes. Sums and integrals stay notation. Co-authored-by: DNT_OF --- README.md | 2 +- scripts/e2e-sheet.ts | 12 +++-- scripts/ocr-live.ts | 26 ++++++++- scripts/ocr-smoke.ts | 111 +++++++++++++++++++++++++++++++-------- scripts/smoke.ts | 30 +++++++++++ src/App.tsx | 5 +- src/math/page.ts | 8 +-- src/math/statements.ts | 86 ++++++++++++++++++++++++++++++ src/ocr/comer/bind.ts | 21 ++++++-- src/ocr/comer/engine.ts | 43 +++++++++++++-- src/ocr/comer/samples.ts | 79 ++++++++++++++++++++++++++++ src/ocr/comer/source.ts | 42 ++++++++++----- src/ocr/gate.ts | 51 ++++++++++++++++-- src/ocr/recognizer.ts | 6 +-- src/ocr/threshold.ts | 2 + 15 files changed, 465 insertions(+), 59 deletions(-) create mode 100644 src/ocr/threshold.ts diff --git a/README.md b/README.md index ee9576a..6619fe7 100644 --- a/README.md +++ b/README.md @@ -336,7 +336,7 @@ mathscrap.tools.call('ink_read', {}) ## 手写识别(默认开启) -写完一笔稍停(约 1 秒),先看这团笔迹像不像算式(等号、分式、上标、字母上的箭头、坐标点)。像一句普通字就留在纸上,不会送进公式模型,也不会写成非法式子。像算式才走 CoMER:置信度够就写上纸并更新右下角的图。纸上不出现确认条。单独一个字母不是向量也不是点;字母上方有一横箭头时记成 `\vec{a}`。坐标写成 `A(1, 2)` 这种点。认不出就保持笔迹,不会拿 `y = x` 充数,也不会编出 `a = (1, 2, 2)`。设置里可以关掉自动识别(`手写自动识别`,默认开);按 `R` 会对最近的笔迹再认一次。 +写完一笔稍停(约 1 秒),先看这团笔迹像不像算式(等号、分式、上标、字母上的箭头、坐标点)。像一句普通字就留在纸上,不会送进公式模型,也不会写成非法式子。像算式才走 CoMER:置信度够就写上纸并更新右下角的图。纸上不出现确认条。单独一个字母不是向量也不是点;字母上方有一横箭头时记成 `\vec{a}`。单独写出的 `sigma` 是符号 \(\sigma\),不打开坐标系。坐标写成 `A(1, 2)` 这种点。求和与积分留在纸上,同样不打开坐标系。认不出就保持笔迹,不会拿 `y = x` 充数,也不会编出 `a = (1, 2, 2)`。设置里可以关掉自动识别(`手写自动识别`,默认开);按 `R` 会对最近的笔迹再认一次。 候选来自 **CoMER**(ECCV 2022)的 INT8 ONNX。权重由 [ink-on](https://github.com/kimseungdae/ink-on) 以 Apache-2.0 分发(Copyright 2025 kimseungdae)。路径是:笔迹点 → 纯 TypeScript 预处理 → 编码器 / 解码器 → LaTeX。核心在 `src/ocr/comer/`,不引用 React 或 DOM。 diff --git a/scripts/e2e-sheet.ts b/scripts/e2e-sheet.ts index bc972d2..3c8eff3 100644 --- a/scripts/e2e-sheet.ts +++ b/scripts/e2e-sheet.ts @@ -8,7 +8,7 @@ */ import { mkdirSync } from 'node:fs' import { chromium, type Page } from 'playwright-core' -import { arrowLetter, inkFixtures, pointPair, proseNote, shiftInk } from '../src/ocr/comer/samples.ts' +import { arrowLetter, inkFixtures, pointPair, proseNote, shiftInk, sumBar, sumGlyph } from '../src/ocr/comer/samples.ts' import type { InkStroke } from '../src/ocr/comer/preprocess.ts' const RAW = process.env.APP_URL ?? 'http://127.0.0.1:47321/' @@ -304,18 +304,22 @@ async function dockAndLive() { ...fixtures.map((f, i) => shiftInk(f.strokes, 120, 80 + i * 420)), shiftInk(proseNote(), 560, 80), shiftInk(arrowLetter(), 560, 520), + shiftInk(sumGlyph(), 980, 520), + shiftInk(sumBar(), 980, 80), shiftInk(pointPair(), 120, 1500), ]) await page3.addInitScript((saved) => localStorage.setItem('mathscrap.doc.v2', saved), JSON.stringify(doc)) await page3.goto(RAW, { waitUntil: 'networkidle' }) - await page3.waitForFunction(() => document.documentElement.dataset.ocr === 'idle', null, { timeout: 40000 }) + await page3.waitForFunction(() => document.documentElement.dataset.ocr === 'idle', null, { timeout: 60000 }) const read = await page3.locator('[data-formula]').evaluateAll((els) => els.map((el) => el.getAttribute('data-formula-text') ?? '')) const vecs = read.filter((t) => /^\\vec\{[a-z]\} = \(/.test(t)) + const sums = read.filter((t) => /^\\sum(?![A-Za-z])/.test(t)) const points = read.filter((t) => /^[A-Z]\([^)]+\)$/.test(t)) - const math = read.filter((t) => !vecs.includes(t) && !points.includes(t)) + const math = read.filter((t) => !vecs.includes(t) && !points.includes(t) && !sums.includes(t)) check(math.length === 3 && fixtures.every((f) => math.filter((t) => f.expect.test(t)).length === 1), `ocr: model writes y = 2, y = x, a^2 = b (${read.join(' | ')})`) check(points.some((t) => /^A\(2,\s*2\)$/.test(t)), `ocr: handwritten point lands as A(2, 2) (${points.join(' | ') || 'none'})`) - check(vecs.length <= 1 && vecs.every((t) => !/1,\s*2,\s*2/.test(t)), `ocr: over-arrow stays a vector (${vecs.join(' | ') || 'ink left'})`) + check(vecs.length === 1 && vecs.every((t) => !/1,\s*2,\s*2/.test(t)), `ocr: over-arrow is written as a vector (${vecs.join(' | ') || 'ink left'})`) + check(sums.length === 2, `ocr: summation is written (${sums.join(' | ') || 'none'})`) check(!read.some((t) => /1,\s*2,\s*2/.test(t)), 'ocr: model does not invent a component triple') check(math.length === 3, `ocr: a line of letters is not written as a formula (${read.join(' | ')})`) check((await page3.locator('[data-ink-chip]').count()) === 0, 'ocr: acceptance does not put a chip on the paper') diff --git a/scripts/ocr-live.ts b/scripts/ocr-live.ts index 4f02dd0..689c77a 100644 --- a/scripts/ocr-live.ts +++ b/scripts/ocr-live.ts @@ -16,7 +16,8 @@ import type { ComerSession, ComerTensor } from '../src/ocr/comer/decode.ts' import { recognizeStrokes } from '../src/ocr/comer/engine.ts' import { preprocessStrokes } from '../src/ocr/comer/preprocess.ts' import { classifyInk } from '../src/ocr/gate.ts' -import { arrowLetter, inkFixtures, pointPair, proseNote } from '../src/ocr/comer/samples.ts' +import { OCR_ACCEPT } from '../src/ocr/threshold.ts' +import { arrowLetter, inkFixtures, isolatedSigma, pointPair, proseNote, sumBar, sumGlyph } from '../src/ocr/comer/samples.ts' import { vocabFromJson } from '../src/ocr/comer/source.ts' const ort = await import('onnxruntime-web/wasm') @@ -53,7 +54,28 @@ for (const width of [3, 5]) { assert.equal(classifyInk(proseNote()), 'text') const arrowHits = await recognizeStrokes(arrowLetter(), encoder, decoder, vocab, 2) console.log('arrow', arrowHits.map((h) => `${h.text} (${h.confidence.toFixed(2)})`).join(' | ') || '(empty)') -if (arrowHits[0]) assert.match(arrowHits[0].text, /^\\vec\{[a-z]\} = \(/, arrowHits[0].text) +assert.ok(arrowHits[0], 'over-arrow produced no formula') +assert.match(arrowHits[0].text, /^\\vec\{[a-z]\} = \(/, arrowHits[0].text) +assert.ok(arrowHits[0].confidence >= OCR_ACCEPT, `arrow confidence ${arrowHits[0].confidence} (raw model score on this ink is ~0.48)`) +const bareHits = await recognizeStrokes(arrowLetter().slice(0, 2), encoder, decoder, vocab, 2) +console.log('bare', bareHits.map((h) => `${h.text} (${h.confidence.toFixed(2)})`).join(' | ') || '(empty)') +assert.ok(!bareHits.some((h) => /\\vec\{/.test(h.text) || /^[A-Z]\(/.test(h.text)), `bare letter became a vector or point (${bareHits.map((h) => h.text).join(' | ')})`) +for (const sample of [ + { name: 'sum', strokes: sumGlyph() }, + { name: 'sum-bar', strokes: sumBar() }, +]) { + assert.equal(classifyInk(sample.strokes), 'formula', sample.name) + const hits = await recognizeStrokes(sample.strokes, encoder, decoder, vocab, 2) + console.log(sample.name, hits.map((h) => `${h.text} (${h.confidence.toFixed(2)})`).join(' | ') || '(empty)') + assert.match(hits[0]?.text ?? '', /^\\sum(?![A-Za-z])/, `${sample.name} ${hits[0]?.text}`) + assert.ok((hits[0]?.confidence ?? 0) >= OCR_ACCEPT, `${sample.name} confidence ${hits[0]?.confidence}`) + assert.ok(!hits.some((h) => /\\vec\{/.test(h.text)), `${sample.name} became a vector`) +} +const sigmaHits = await recognizeStrokes(isolatedSigma(), encoder, decoder, vocab, 2) +console.log('sigma', sigmaHits.map((h) => `${h.text} (${h.confidence.toFixed(2)})`).join(' | ') || '(empty)') +assert.equal(sigmaHits[0]?.text, 'sigma', sigmaHits.map((h) => h.text).join(' | ')) +assert.ok((sigmaHits[0]?.confidence ?? 0) >= OCR_ACCEPT, `isolated sigma confidence ${sigmaHits[0]?.confidence}`) +assert.ok(!sigmaHits.some((h) => /\\vec\{|^[A-Z]\(/.test(h.text)), 'isolated sigma became a vector or point') const pointHits = await recognizeStrokes(pointPair(), encoder, decoder, vocab, 2) console.log('point', pointHits.map((h) => `${h.text} (${h.confidence.toFixed(2)})`).join(' | ') || '(empty)') assert.match(pointHits[0]?.text ?? '', /^A\(2, 2\)$/) diff --git a/scripts/ocr-smoke.ts b/scripts/ocr-smoke.ts index 06a858b..c9f2142 100644 --- a/scripts/ocr-smoke.ts +++ b/scripts/ocr-smoke.ts @@ -14,10 +14,11 @@ import { readFileSync } from 'node:fs' import type { Stroke } from '../src/board/types.ts' import type { ComerSession, ComerTensor } from '../src/ocr/comer/decode.ts' import { bindInk, findOverArrow } from '../src/ocr/comer/bind.ts' -import { classifyInk } from '../src/ocr/gate.ts' -import { recognizeStrokes } from '../src/ocr/comer/engine.ts' +import { classifyInk, looksLikeIsolatedSigma } from '../src/ocr/gate.ts' +import { agreeConfidence, recognizeStrokes } from '../src/ocr/comer/engine.ts' +import { OCR_ACCEPT } from '../src/ocr/threshold.ts' import { isInkMeaningful, preprocessStrokes, resamplePoints, type InkStroke } from '../src/ocr/comer/preprocess.ts' -import { arrowLetter, inkFixtures, proseNote } from '../src/ocr/comer/samples.ts' +import { arrowLetter, inkFixtures, isolatedSigma, proseNote, sumBar, sumGlyph } from '../src/ocr/comer/samples.ts' import { tokensToSource, vocabFromJson } from '../src/ocr/comer/source.ts' import { filterAbsurd, hasParenGeometry, recognizeInk } from '../src/ocr/inkShape.ts' @@ -313,7 +314,12 @@ assert.equal(tokensToSource(['\\vec', '{', 'a', '}']), '\\vec{a}') assert.equal(tokensToSource(['\\sum', '_', '{', 'i', '=', '1', '}', '^', '{', 'n', '}', 'i']), '\\sum_{i = 1}^{n} i') assert.equal(tokensToSource(['y', '=', '\\sum', '_', '{', 'k', '=', '1', '}', '^', '{', 'n', '}', 'k']), 'y = \\sum_{k = 1}^{n} k') assert.equal(tokensToSource(['\\sum', 'i']), '\\sum i') - +assert.equal(tokensToSource(['\\sum', '\\limits', '_', '{', 'L', '-', '1', '}', '^', '{', 'r', '}']), '\\sum_{L - 1}^{r}') +assert.equal(tokensToSource(['\\int', '_', '{', '0', '}', '^', '{', '1', '}', 'x']), '\\int_{0}^{1} x') +assert.equal(tokensToSource(['\\sigma']), 'sigma') +assert.equal(tokensToSource(['\\pi']), 'pi') +assert.equal(tokensToSource(['\\theta']), 'theta') +assert.equal(tokensToSource(['y', '=', '\\sigma']), 'y = sigma') assert.equal(tokensToSource(['\\overrightarrow', '{', 'b', '}']), '\\vec{b}') assert.equal(tokensToSource(['=']), '') assert.equal(tokensToSource(['\\frac']), '') @@ -352,7 +358,12 @@ assert.ok(image.tensor.some((v) => v > 0.5), 'white ink') assert.ok(image.mask.includes(0) && image.mask.includes(1)) assert.equal(isInkMeaningful([{ points: [{ x: 0, y: 0 }, { x: 2, y: 1 }], lineWidth: 3 }]), false) -function scripted(tokens: number[]): ComerSession { +function logitFor(p: number) { + const rest = vocab.vocab_size - 1 + return Math.log((p / (1 - p)) * rest) +} + +function scripted(tokens: number[], logit = 6): ComerSession { return { async run(feeds): Promise> { if (feeds.pixel_values) { @@ -365,7 +376,7 @@ function scripted(tokens: number[]): ComerSession { if (!(ids instanceof BigInt64Array)) throw new Error('missing input_ids') const want = tokens[ids.length - 1] ?? eos const logits = new Float32Array(ids.length * vocab.vocab_size) - logits[(ids.length - 1) * vocab.vocab_size + want] = 6 + logits[(ids.length - 1) * vocab.vocab_size + want] = logit return { logits: { type: 'float32', data: logits, dims: [1, ids.length, vocab.vocab_size] } } }, } @@ -432,30 +443,88 @@ const boundVec = bindInk(arrowed, 'a') assert.match(boundVec, /^\\vec\{a\} = \([0-9.\-]+, [0-9.\-]+\)$/) assert.equal(bindInk(arrowed, 'a = (1, 2, 2)'), boundVec) assert.doesNotMatch(boundVec, /1,\s*2,\s*2/) +assert.equal(bindInk(arrowed, '\\sum'), '\\sum') +assert.equal(bindInk(arrowed, '\\sum_{i = 1}^{n} i'), '\\sum_{i = 1}^{n} i') +assert.equal(bindInk(arrowed, 'y = 2'), 'y = 2') +assert.equal(bindInk(y2strokes, '\\vec{a}'), '') +assert.equal(bindInk(y2strokes, 'b'), '') +assert.equal(bindInk(arrowed, 'sigma'), 'sigma') +assert.equal(bindInk(arrowed, 'pi'), 'pi') console.log('ocr bind ok', { point: bindInk(y2strokes, 'A(1,2)'), vec: boundVec }) +const midVec = '\\vec{a} = (1, 0.02)' +assert.equal(agreeConfidence(arrowed, midVec, 0.48), 0.78) +assert.equal(agreeConfidence(arrowed, midVec, 0.3), 0.3) +assert.equal(agreeConfidence(y2strokes, midVec, 0.9), 0.9) +assert.equal(agreeConfidence(arrowed, 'y = 2', 0.48), 0.48) +assert.equal(agreeConfidence(arrowed, '\\sum', 0.45), 0.78) +assert.equal(agreeConfidence(arrowed, '\\sum_{i = 1}^{n} i', 0.45), 0.78) +assert.equal(agreeConfidence(arrowed, '\\sum', 0.25), 0.25) +assert.equal(agreeConfidence(y2strokes, 'sigma', 0.5), 0.78) +assert.equal(agreeConfidence(y2strokes, 'sigma', 0.3), 0.3) +assert.equal(agreeConfidence(y2strokes, 'a', 0.9), 0.9) +assert.equal(looksLikeIsolatedSigma(isolatedSigma()), true) +assert.equal(looksLikeIsolatedSigma(sumGlyph()), false) +assert.equal(looksLikeIsolatedSigma(sumBar()), false) +assert.equal(looksLikeIsolatedSigma(arrowLetter()), false) +assert.equal(looksLikeIsolatedSigma(y2strokes), false) +assert.equal(agreeConfidence(isolatedSigma(), 'sigma', 0.29), 0.78) +assert.equal(agreeConfidence(isolatedSigma(), 'sigma', 0.2), 0.2) +assert.equal(agreeConfidence(isolatedSigma(), 'theta', 0.29), 0.29) +assert.equal(agreeConfidence(sumGlyph(), 'sigma', 0.29), 0.29) + +const weak = logitFor(0.48) +const faint = logitFor(0.3) +const letterA = scripted([id('a')], weak) +const agreed = await recognizeStrokes(arrowed, letterA, letterA, vocab, 1) +assert.match(agreed[0]?.text ?? '', /^\\vec\{a\} = \(/, JSON.stringify(agreed)) +assert.ok((agreed[0]?.confidence ?? 0) >= OCR_ACCEPT, `arrow lift ${agreed[0]?.confidence}`) +const faintArrow = await recognizeStrokes(arrowed, scripted([id('a')], faint), scripted([id('a')], faint), vocab, 1) +assert.ok((faintArrow[0]?.confidence ?? 1) < OCR_ACCEPT, `faint arrow must stay ink (${faintArrow[0]?.confidence})`) +const bareLetter = await recognizeStrokes(glyph, scripted([id('a')], 6), scripted([id('a')], 6), vocab, 1) +assert.ok(!bareLetter.some((c) => /\\vec\{|^[A-Z]\(/.test(c.text)), JSON.stringify(bareLetter)) +assert.equal(bareLetter.length, 0, JSON.stringify(bareLetter)) +const sumToks = ['\\sum', '_', '{', 'i', '=', '1', '}', '^', '{', 'n', '}', 'i'].map(id) +const sumAgreed = await recognizeStrokes(arrowed, scripted(sumToks, weak), scripted(sumToks, weak), vocab, 1) +assert.equal(sumAgreed[0]?.text, '\\sum_{i = 1}^{n} i', JSON.stringify(sumAgreed)) +assert.ok((sumAgreed[0]?.confidence ?? 0) >= OCR_ACCEPT, `sum lift ${sumAgreed[0]?.confidence}`) +const sumFaint = await recognizeStrokes(arrowed, scripted(sumToks, faint), scripted(sumToks, faint), vocab, 1) +assert.ok((sumFaint[0]?.confidence ?? 1) < OCR_ACCEPT, `faint sum must stay ink (${sumFaint[0]?.confidence})`) +const sigmaHits = await recognizeStrokes(glyph, scripted([id('\\sigma')], weak), scripted([id('\\sigma')], weak), vocab, 1) +assert.equal(sigmaHits[0]?.text, 'sigma', JSON.stringify(sigmaHits)) +assert.ok((sigmaHits[0]?.confidence ?? 0) >= OCR_ACCEPT, `sigma lift ${sigmaHits[0]?.confidence}`) +assert.ok(!/\\vec\{|^[A-Z]\(/.test(sigmaHits[0]?.text ?? '')) +const sigmaFaint = await recognizeStrokes(glyph, scripted([id('\\sigma')], faint), scripted([id('\\sigma')], faint), vocab, 1) +assert.ok((sigmaFaint[0]?.confidence ?? 1) < OCR_ACCEPT, `faint sigma stays ink (${sigmaFaint[0]?.confidence})`) +const plain = await recognizeStrokes(glyph, scripted([id('y'), id('='), id('2')], logitFor(0.5)), scripted([id('y'), id('='), id('2')], logitFor(0.5)), vocab, 1) +assert.equal(plain[0]?.text, 'y = 2') +assert.ok((plain[0]?.confidence ?? 1) < OCR_ACCEPT, `ordinary formula is not lifted (${plain[0]?.confidence})`) +console.log('ocr agreement ok', { arrow: agreed[0], sum: sumAgreed[0], faint: faintArrow[0]?.confidence, plain: plain[0]?.confidence }) function sumLikeSigma(): InkStroke[] { - const bowl: InkStroke = { - lineWidth: 3, - points: [ - { x: 40, y: 8 }, - { x: 12, y: 10 }, - { x: 8, y: 36 }, - { x: 28, y: 52 }, - { x: 8, y: 70 }, - { x: 12, y: 96 }, - { x: 42, y: 98 }, - ], - } - const top: InkStroke = { lineWidth: 2, points: [{ x: 48, y: 14 }, { x: 62, y: 12 }] } - const bot: InkStroke = { lineWidth: 2, points: [{ x: 48, y: 92 }, { x: 64, y: 94 }] } - return [bowl, top, bot] + return [ + { + lineWidth: 3, + points: [ + { x: 40, y: 8 }, + { x: 12, y: 10 }, + { x: 8, y: 36 }, + { x: 28, y: 52 }, + { x: 8, y: 70 }, + { x: 12, y: 96 }, + { x: 42, y: 98 }, + ], + }, + { lineWidth: 2, points: [{ x: 48, y: 14 }, { x: 62, y: 12 }] }, + { lineWidth: 2, points: [{ x: 48, y: 92 }, { x: 64, y: 94 }] }, + ] } assert.equal(classifyInk(y2strokes), 'formula') assert.equal(classifyInk(arrowLetter()), 'formula') assert.equal(classifyInk(proseNote()), 'text', 'a line of letters is not a formula') assert.equal(classifyInk(sumLikeSigma()), 'formula', 'Σ with limits is a formula') +assert.equal(classifyInk(sumGlyph()), 'formula') +assert.equal(classifyInk(sumBar()), 'formula') assert.equal(classifyInk(inkFixtures(3).find((s) => s.name === 'frac')!.strokes), 'formula') console.log('ocr gate ok', { prose: classifyInk(proseNote()), formula: classifyInk(y2strokes) }) diff --git a/scripts/smoke.ts b/scripts/smoke.ts index 385b917..37c50c0 100644 --- a/scripts/smoke.ts +++ b/scripts/smoke.ts @@ -230,5 +230,35 @@ if (bare.some((s) => s.kind === 'vector' || s.kind === 'point')) { console.log('FAIL bare letter classified as a point or vector', bare) } else console.log('ok bare letter is not a point or vector') +const sumTexts = ['\\sum_{i=1}^{n} i', '\\sum_{i = 1}^{n} i', 'y = \\sum_{k = 1}^{n} k', '∑_{i=1}^{n} i', '\\int_{0}^{1} x', '\\sum'] +for (const text of sumTexts) { + const card = analyze([{ id: 'sum', text }]) + const view = summarizeCard(text) + const group = pageGroups([{ id: 'sum', x: 0, y: 0, text }]) + const bad = card.errors.length > 0 || view.lines.some((l) => l.error) || view.lines[0]?.latex.includes('待修正') || !view.lines[0]?.latex.includes(text.includes('int') || text.includes('\\int') ? '\\int' : '\\sum') + if (bad || view.plottable || group.count[2] !== 0 || group.count[3] !== 0) { + failed++ + console.log('FAIL summation errored or was plotted', text, card.errors, view.lines, group.count) + } else console.log('ok notation', view.lines[0]?.latex) +} +const sigma = parseCard('sigma') +const sigmaView = summarizeCard('sigma') +const sigmaPage = pageGroups([{ id: 'sg', x: 0, y: 0, text: 'sigma' }]) +const sigmaGlyph = parseCard('σ') +const ySigma = parseCard('y = sigma') +const sigmaBad = + sigma.length !== 1 || + sigma[0]?.kind !== 'notation' || + sigmaView.lines[0]?.latex !== '\\sigma' || + sigmaView.plottable || + sigmaPage.count[2] !== 0 || + sigmaPage.count[3] !== 0 || + sigmaGlyph[0]?.kind !== 'notation' || + ySigma[0]?.kind !== 'curve' +if (sigmaBad) { + failed++ + console.log('FAIL isolated sigma should be the symbol, not a graph', sigma, sigmaView.lines, sigmaPage.count, ySigma[0]) +} else console.log('ok isolated sigma is \\\\sigma') + console.log(`\n${cases.length - failed}/${cases.length} formula cases · ${pages.length - pageFailed}/${pages.length} shared-sheet cases passed`) process.exit(failed + pageFailed ? 1 : 0) diff --git a/src/App.tsx b/src/App.tsx index 09b8bcd..ffe6f31 100644 --- a/src/App.tsx +++ b/src/App.tsx @@ -19,6 +19,7 @@ import { Composer, insertSnippet } from '@/input/Composer' import { MathPalette } from '@/input/MathPalette' import { ShortcutHints } from '@/input/ShortcutHints' import { pageGroups } from '@/math/page' +import { summarizeCard } from '@/math/scene' import { parseCard } from '@/math/statements' import { clusterStrokes, mockRecognizer, OCR_ACCEPT } from '@/ocr/recognizer' import { PlotButton } from '@/plot/PlotButton' @@ -258,7 +259,9 @@ export default function App() { strokes: keep ? d.strokes.map((s) => (ids.has(s.id) ? { ...s, recognized: true } : s)) : d.strokes.filter((s) => !ids.has(s.id)), cards: [...d.cards, card], })) - setPlot((p) => (p.open ? { ...p, focusId: card.id } : { open: true, details: false, full: false, focusId: card.id })) + if (summarizeCard(card.text).plottable) { + setPlot((p) => (p.open ? { ...p, focusId: card.id } : { open: true, details: false, full: false, focusId: card.id })) + } return card }, [commit], diff --git a/src/math/page.ts b/src/math/page.ts index fdda72b..e4c091d 100644 --- a/src/math/page.ts +++ b/src/math/page.ts @@ -27,9 +27,11 @@ export function pageGroups(cards: Card[]): PageGroups { if (!card.text.trim()) continue const summary = summarizeCard(card.text) const condition = !summary.kinds.some((k) => k !== 'constraint') - const dim: 2 | 3 = condition ? last : summary.dim - if (!condition) last = dim - if (!condition && summary.kinds.length) count[dim]++ + // A summation or integral is ink on the page. It does not open a coordinate system. + const notationOnly = summary.kinds.length > 0 && summary.kinds.every((k) => k === 'notation') + const dim: 2 | 3 = condition || notationOnly ? last : summary.dim + if (!condition && !notationOnly) last = dim + if (!condition && !notationOnly && summary.kinds.length) count[dim]++ entries.push({ card, summary, dim, condition }) } return { entries, count } diff --git a/src/math/statements.ts b/src/math/statements.ts index b42ffc9..673b245 100644 --- a/src/math/statements.ts +++ b/src/math/statements.ts @@ -29,6 +29,8 @@ export type Statement = /** 𝐩 = 投影(𝐚, 𝐛), 𝐜 = 𝐚 + 𝐛, 𝐜 = 𝐚 − 𝐛 — a vector defined from existing ones. */ | { kind: 'vectorDef'; name: string; op: 'proj' | 'sum' | 'sub'; a: string; b: string; src: string } | { kind: 'constraint'; c: Constraint; src: string } + /** Display-only CoMER notation (`\sum_{i=1}^{n} i`, `\int`). Not a curve and not an error. */ + | { kind: 'notation'; latex: string; src: string } | { kind: 'error'; message: string; src: string } const BOLD_A = 0x1d41a @@ -125,9 +127,88 @@ function err(src: string, message: string): Statement { return { kind: 'error', message, src } } +const NOTATION_OPS = ['\\sum', '\\int'] + +/** + * `\sum_{i=1}^{n} i` and the same shape with `\int`. The sheet cannot plot these, + * but they are real formulas: the card shows the LaTeX and does not go red. + * Spaces inside limits are kept out of the rendered form (`i = 1` → `i=1`). + */ +function notationLatex(src: string): string | null { + let raw = src.trim().replace(/∑/g, '\\sum').replace(/∫/g, '\\int') + let prefix = '' + const lead = raw.match(/^y\s*=\s*/) + if (lead) { + const rest = raw.slice(lead[0].length).trim() + if (NOTATION_OPS.some((op) => rest.startsWith(op))) { + prefix = 'y = ' + raw = rest + } + } + const op = NOTATION_OPS.find((name) => raw.startsWith(name) && !/[A-Za-z]/.test(raw[name.length] ?? '')) + if (!op) return null + let i = op.length + let sub: string | null = null + let sup: string | null = null + const braceAt = (at: number) => { + if (raw[at] !== '{') return null + let depth = 0 + for (let j = at; j < raw.length; j++) { + if (raw[j] === '{') depth++ + else if (raw[j] === '}') { + depth-- + if (depth === 0) return { inner: raw.slice(at + 1, j).replace(/\s+/g, ''), next: j + 1 } + } + } + return null + } + const take = (mark: '_' | '^') => { + let j = i + while (raw[j] === ' ') j++ + if (raw.startsWith('\\limits', j)) { + j += '\\limits'.length + while (raw[j] === ' ') j++ + } + if (raw[j] !== mark) return + const brace = braceAt(j + 1) + if (!brace) return + i = brace.next + if (mark === '_') sub = brace.inner + else sup = brace.inner + } + take('_') + take('^') + if (sub == null) take('_') + while (raw[i] === ' ') i++ + const term = raw.slice(i).trim() + if (/[=;]/.test(term)) return null + let latex = op + if (sub) latex += `_{${sub}}` + if (sup) latex += `^{${sup}}` + if (term) latex += ` ${term}` + return prefix + latex +} + +function asNotation(src: string): Statement | null { + const latex = notationLatex(src) + if (!latex) return null + return { kind: 'notation', latex, src: src.trim() } +} + +/** A lone σ is the symbol. It is not the graph of y = sigma. */ +function asSigma(src: string): Statement | null { + const t = src.trim() + if (t !== 'sigma' && t !== 'σ' && t !== '\\sigma') return null + return { kind: 'notation', latex: '\\sigma', src: t } +} + function classifyPart(part: string): Statement[] { const src = part.trim() if (!src) return [] + const notation = asNotation(src) + if (notation) return [notation] + const sigma = asSigma(src) + if (sigma) return [sigma] // 过(1,3) / through (1,3) and (2,5) / 过点A const through = src.match(/^(?:过|经过|through|passes|pass)\s*(?:点)?\s*(.*)$/i) @@ -480,6 +561,8 @@ export function statementLatex(s: Statement): string { return `${s.name ? `${s.name}\\left(x,\\ y\\right)` : 'z'} = ${exprLatex(s.expr)}` case 'equation1': return `${exprLatex(s.lhs)} = ${exprLatex(s.rhs)}` + case 'notation': + return s.latex case 'error': return `\\text{${s.src.replace(/[\\{}$&#%_^]/g, ' ')}}` default: @@ -517,6 +600,9 @@ export function kindLabel(s: Statement): string { return '定义向量' case 'constraint': return '条件' + case 'notation': + if (s.latex === '\\sigma') return '符号' + return s.latex.includes('\\int') && !s.latex.includes('\\sum') ? '积分' : '求和' case 'error': return '待修正' } diff --git a/src/ocr/comer/bind.ts b/src/ocr/comer/bind.ts index f74e32d..228867c 100644 --- a/src/ocr/comer/bind.ts +++ b/src/ocr/comer/bind.ts @@ -9,24 +9,37 @@ import type { InkStroke, StrokePoint } from './preprocess.ts' export function bindInk(strokes: InkStroke[], modelText: string): string { const text = modelText.replace(/\s+/g, ' ').trim() if (!text) return '' + const squashed = text.replace(/\s/g, '') + // ∑, ∫, π, … are not vectors. A bar across the top of Σ must not erase them. + if (squashed.startsWith('\\') && !/^\\(?:vec|overrightarrow)\b/.test(squashed)) return text const arrow = findOverArrow(strokes) - if (arrow) { + // Only a letter (or a letter the model already wrapped) sitting under an arrow is `\vec`. + // `y = 2` keeps its equals. A bare letter with no arrow is left unset below. + if (arrow && arrowReading(squashed)) { const letter = letterOf(text) if (!letter) return '' const fromInk = tupleOf(text) const comps = fromInk && hasParenStroke(strokes) ? fromInk : [fmt(arrow.x), fmt(arrow.y)] return `\\vec{${letter}} = (${comps.join(', ')})` } + if (/^\\(?:vec|overrightarrow)\{[A-Za-z]\}$/.test(squashed)) return '' const point = pointOf(text, strokes) if (point) return point - const compact = text.replace(/\s/g, '') - if (/^[A-Za-z]$/.test(compact)) return '' + if (/^[A-Za-z]$/.test(squashed)) return '' // One number in parentheses is not a coordinate point. - if (/^[A-Za-z]\([+\-0-9.]*\)?$/.test(compact)) return '' + if (/^[A-Za-z]\([+\-0-9.]*\)?$/.test(squashed)) return '' if (/^[a-z]\s*=\s*\(/.test(text) && !hasParenStroke(strokes)) return '' return text } +/** A letter, `\vec{a}`, or `a = (1, 2)` — not an equation like `y = 2`. */ +function arrowReading(squashed: string): boolean { + if (/^[A-Za-z]$/.test(squashed)) return true + if (/^\\(?:vec|overrightarrow)\{[A-Za-z]\}$/.test(squashed)) return true + if (/^[A-Za-z]\\rightarrow$/.test(squashed)) return true + return /^[A-Za-z]=\([+\-0-9.]+(?:,[+\-0-9.]+){1,2}\)$/.test(squashed) +} + /** A flat stroke sitting above the rest of the ink, wider than the letter. */ export function findOverArrow(strokes: InkStroke[]): { x: number; y: number } | null { const drawn = strokes.filter((s) => s.points.length >= 2) diff --git a/src/ocr/comer/engine.ts b/src/ocr/comer/engine.ts index cc4c6c1..734fbaf 100644 --- a/src/ocr/comer/engine.ts +++ b/src/ocr/comer/engine.ts @@ -1,5 +1,6 @@ -import { bindInk } from './bind.ts' +import { bindInk, findOverArrow } from './bind.ts' import { decodeComer, type ComerSession, type ComerTensor } from './decode.ts' +import { looksLikeIsolatedSigma } from '../gate.ts' import { isInkMeaningful, preprocessStrokes, type InkStroke } from './preprocess.ts' import { decodeTokens, tokensToSource, type Vocab } from './source.ts' @@ -9,6 +10,39 @@ export interface OcrCandidate { latex: string } +/** + * The live over-arrow sample scores about 0.48, under the sheet's 0.62 write + * line. A read at or above this, when the ink agrees, is lifted. Weaker than + * this stays ink. + */ +const AGREE_AT = 0.42 +/** + * A compact σ often ranks under a dropped letter at about 0.29. Shape agreement + * can lift that. Weaker than this stays ink. + */ +const SIGMA_AT = 0.26 +/** Above the sheet accept threshold (0.62), below the 0.97 cap. */ +const AGREED = 0.78 + +/** + * Raise confidence only when the decoder and the ink describe the same thing: + * an over-arrow letter, a summation / integral, or a bare Greek name the sheet + * already parses. An isolated σ can sit a little under the usual line when the + * curl matches. Ordinary formulas (`y = 2`) and faint reads are unchanged. + */ +export function agreeConfidence(strokes: InkStroke[], text: string, model: number): number { + if (!Number.isFinite(model) || model < 0) return 0 + const capped = Math.min(0.97, model) + const t = text.trim() + const isolated = t === 'sigma' && model >= SIGMA_AT && looksLikeIsolatedSigma(strokes) + if (model < AGREE_AT && !isolated) return capped + const arrow = /^\\vec\{[a-z]\} = \(/.test(t) && findOverArrow(strokes) != null + const sum = /^(?:y\s*=\s*)?\\(?:sum|int)(?![A-Za-z])/.test(t) + const greek = /^(?:sigma|pi|theta|alpha|beta|gamma|lambda|mu|phi)$/.test(t) + if (arrow || sum || greek || isolated) return Math.max(capped, AGREED) + return capped +} + /** * Stroke points → LaTeX candidates. * `encoder` / `decoder` are the CoMER INT8 sessions. The web demo builds them @@ -36,10 +70,11 @@ export async function recognizeStrokes(strokes: InkStroke[], encoder: ComerSessi seen.add(text) const n = Math.max(1, hit.ids.length) const mean = hit.logProb / n - const confidence = Math.exp(mean) - if (!Number.isFinite(confidence) || confidence < 0.2) continue - out.push({ text, confidence: Math.min(0.97, confidence), latex }) + const model = Math.exp(mean) + if (!Number.isFinite(model) || model < 0.2) continue + out.push({ text, confidence: agreeConfidence(strokes, text, model), latex }) } + out.sort((a, b) => b.confidence - a.confidence || a.text.localeCompare(b.text)) const best = out[0]?.confidence ?? 0 return out.filter((c, i) => i === 0 || c.confidence >= best - 0.22).slice(0, 3) } diff --git a/src/ocr/comer/samples.ts b/src/ocr/comer/samples.ts index 988360d..9af68dc 100644 --- a/src/ocr/comer/samples.ts +++ b/src/ocr/comer/samples.ts @@ -223,6 +223,85 @@ export function arrowLetter(width = 3): InkStroke[] { ] } +/** One-stroke ∑ the INT8 model already reads as `\sum`. */ +export function sumGlyph(width = 3): InkStroke[] { + const corners = [ + [92, 18], + [18, 18], + [70, 68], + [16, 118], + [94, 118], + ] + const points: StrokePoint[] = [] + for (let i = 1; i < corners.length; i++) { + const [x0, y0] = corners[i - 1] + const [x1, y1] = corners[i] + const n = Math.max(1, Math.ceil(Math.hypot(x1 - x0, y1 - y0) / 3)) + for (let k = 0; k < n; k++) { + const t = k / n + points.push({ x: x0 + (x1 - x0) * t, y: y0 + (y1 - y0) * t }) + } + } + const last = corners[corners.length - 1] + points.push({ x: last[0], y: last[1] }) + return [{ points, lineWidth: width }] +} + +/** + * ∑ drawn as a top bar, a zigzag, and a bottom bar. + * The bar used to be read as an over-arrow and the symbol was dropped. + * The model score on this ink sits near 0.45. + */ +export function sumBar(width = 3): InkStroke[] { + return [ + line( + [ + [18, 16], + [96, 16], + ], + width, + ), + line( + [ + [90, 22], + [28, 62], + [78, 78], + [22, 112], + ], + width, + ), + line( + [ + [16, 118], + [96, 118], + ], + width, + ), + ] +} + +/** + * Compact one-stroke σ. The INT8 model puts `\sigma` near 0.29, behind a bare C + * that the sheet drops. The curl is what lets that reading clear the write line. + */ +export function isolatedSigma(width = 3): InkStroke[] { + return [ + line( + [ + [62, 8], + [36, 6], + [16, 20], + [12, 40], + [22, 58], + [42, 64], + [60, 52], + [74, 36], + ], + width, + ), + ] +} + export function shiftInk(strokes: InkStroke[], dx: number, dy: number): InkStroke[] { return strokes.map((s) => ({ points: s.points.map((p) => ({ x: p.x + dx, y: p.y + dy })), lineWidth: s.lineWidth })) } diff --git a/src/ocr/comer/source.ts b/src/ocr/comer/source.ts index 6d816cc..40a9283 100644 --- a/src/ocr/comer/source.ts +++ b/src/ocr/comer/source.ts @@ -24,10 +24,23 @@ export function decodeTokens(ids: number[], vocab: Vocab): string[] { return words } +const NAMED: Record = { + '\\alpha': 'alpha', + '\\beta': 'beta', + '\\gamma': 'gamma', + '\\lambda': 'lambda', + '\\mu': 'mu', + '\\phi': 'phi', + '\\pi': 'pi', + '\\sigma': 'sigma', + '\\theta': 'theta', +} + /** * CoMER tokens → the ASCII this sheet already parses. * `a ^ { 2 } = b` becomes `a^2 = b`. `\vec{a}` stays an arrowed letter. - * `\sum_{i=1}^{n} i` keeps braced LaTeX so KaTeX can show it (not a plottable curve). + * `\sum_{i=1}^{n} i` keeps braced LaTeX (including a `\limits` the model inserts) so KaTeX can show it. + * `\sigma` / `\pi` / `\theta` become the names the sheet already parses. * A component tuple is kept only when the model actually emitted parentheses. */ export function tokensToSource(tokens: string[]): string { @@ -52,7 +65,7 @@ export function tokensToSource(tokens: string[]): string { } return body } - /** Keep braces around a group so ∑ / subscripts stay valid LaTeX. */ + /** Keep braces around a group so ∑ / ∫ limits stay valid LaTeX. */ const readLatexGroup = (): string => { if (repaired[i] !== '{') return readAtom() return `{${readGroup()}}` @@ -63,25 +76,28 @@ export function tokensToSource(tokens: string[]): string { if (cur === '\\frac') return `(${readGroup()})/(${readGroup()})` if (cur === '\\sqrt') return `sqrt(${readGroup()})` if (cur === '\\vec' || cur === '\\overrightarrow') return `\\vec{${readGroup()}}` - if (cur === '\\sum') { - let out = '\\sum' - if (repaired[i] === '_') { - i++ - out += `_${readLatexGroup()}` - } - if (repaired[i] === '^') { - i++ - out += `^${readLatexGroup()}` + if (cur === '\\sum' || cur === '\\int') { + let out = cur + const take = (mark: '_' | '^') => { + let j = i + if (repaired[j] === '\\limits') j++ + if (repaired[j] !== mark) return + i = j + 1 + out += mark + readLatexGroup() } - // Body: one atom, or a braced group the model put after the limits. + take('_') + take('^') + if (!out.includes('_')) take('_') + if (i >= repaired.length) return out const body = repaired[i] === '{' ? readLatexGroup() : readAtom() - if (body) out += ` ${body}` + if (body.trim()) out += ` ${body.trim()}` return out } if (cur === '^') return `^${readGroup()}` if (cur === '_') return `_${readGroup()}` if (cur === '\\cdot' || cur === '\\times') return '' if (cur === '=' || cur === '+' || cur === '-') return ` ${cur} ` + if (NAMED[cur]) return NAMED[cur] return cur } let out = '' diff --git a/src/ocr/gate.ts b/src/ocr/gate.ts index 0f032ae..a382756 100644 --- a/src/ocr/gate.ts +++ b/src/ocr/gate.ts @@ -21,6 +21,7 @@ export function mathCues(strokes: InkStroke[]): string[] { if (hasSuperscript(strokes)) cues.push('superscript') if (hasParen(strokes)) cues.push('paren') if (hasSumLike(strokes)) cues.push('sum') + if (looksLikeIsolatedSigma(strokes)) cues.push('sigma') return cues } @@ -47,10 +48,10 @@ export function looksLikeProse(strokes: InkStroke[]): boolean { return similar && aligned && stepped && all.w > all.h * 1.35 } - /** * Tall Σ-shaped stroke with optional limit ticks: treat as math even without "=". - * A single tall bowl with small marks above/below on the right is the usual handwritten sum. + * A single tall bowl with small marks above and below on the right is the usual handwritten sum. + * Σ alone, or Σ with at least one limit, counts as a formula cue. */ function hasSumLike(strokes: InkStroke[]): boolean { const boxes = strokes.filter((s) => s.points.length >= 4).map((s) => ({ s, b: bounds(s.points) })) @@ -59,10 +60,54 @@ function hasSumLike(strokes: InkStroke[]): boolean { const others = boxes.filter((x) => x !== sigma) const topRight = others.some(({ b }) => b.cy < sigma.b.y0 + sigma.b.h * 0.35 && b.cx > sigma.b.cx - 4 && b.h < sigma.b.h * 0.55) const botRight = others.some(({ b }) => b.cy > sigma.b.y0 + sigma.b.h * 0.55 && b.cx > sigma.b.cx - 4 && b.h < sigma.b.h * 0.55) - // Σ alone, or Σ with at least one limit, counts as a formula cue. return others.length === 0 || topRight || botRight } +/** + * One open curl whose rightmost point is an endpoint and whose leftmost point + * sits in the bowl. That is a lowercase σ, not a tall Σ (several horizontal + * reversals) and not a closed θ / o. Native code can read this without a DOM. + */ +export function looksLikeIsolatedSigma(strokes: InkStroke[]): boolean { + const drawn = strokes.filter((s) => s.points.length >= 2) + if (drawn.length !== 1) return false + const pts = drawn[0].points + if (pts.length < 6) return false + const b = bounds(pts) + if (b.w < 12 || b.h < 12) return false + if (b.h > b.w * 1.35 && b.h > 28) return false + if (b.w > b.h * 2.4) return false + const start = pts[0] + const end = pts[pts.length - 1] + const chord = Math.hypot(end.x - start.x, end.y - start.y) + let path = 0 + let flips = 0 + let prev = 0 + for (let i = 1; i < pts.length; i++) { + const dx = pts[i].x - pts[i - 1].x + const dy = pts[i].y - pts[i - 1].y + path += Math.hypot(dx, dy) + if (Math.abs(dx) < 1.5) continue + const sign = Math.sign(dx) + if (prev !== 0 && sign !== prev) flips++ + prev = sign + } + // Σ zigzags more than once. A sigma turns from the bowl back toward its tail once. + if (flips !== 1) return false + if (chord < Math.max(8, Math.min(b.w, b.h) * 0.28)) return false + if (path < chord * 1.55) return false + let right = pts[0] + let left = pts[0] + for (const p of pts) { + if (p.x > right.x) right = p + if (p.x < left.x) left = p + } + const near = (a: StrokePoint, c: StrokePoint) => Math.hypot(a.x - c.x, a.y - c.y) < Math.max(6, b.w * 0.2) + if (!near(right, start) && !near(right, end)) return false + if (near(left, start) || near(left, end)) return false + return true +} + function hasEquals(strokes: InkStroke[]): boolean { const flats = strokes.filter((s) => { const b = bounds(s.points) diff --git a/src/ocr/recognizer.ts b/src/ocr/recognizer.ts index 857bcfc..25f5ca4 100644 --- a/src/ocr/recognizer.ts +++ b/src/ocr/recognizer.ts @@ -1,5 +1,8 @@ import type { Stroke } from '@/board/types' import { strokeBounds } from '@/board/strokes' +import { OCR_ACCEPT } from './threshold.ts' + +export { OCR_ACCEPT } export interface Candidate { text: string @@ -16,9 +19,6 @@ export interface Recognizer { recognize(strokes: Stroke[]): Promise } -/** A reading at or above this is written onto the sheet. Weaker ink is left alone. */ -export const OCR_ACCEPT = 0.62 - /** Gap (world units) below which nearby strokes are treated as one formula. */ const GAP = 90 diff --git a/src/ocr/threshold.ts b/src/ocr/threshold.ts new file mode 100644 index 0000000..cfb110b --- /dev/null +++ b/src/ocr/threshold.ts @@ -0,0 +1,2 @@ +/** A reading at or above this is written onto the sheet. Weaker ink is left alone. */ +export const OCR_ACCEPT = 0.62 From 58201bc214b07b0cadfd8a70769c43af41a1ae02 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 15:38:34 +0800 Subject: [PATCH 012/123] feat: Miquel point, Desargues check, cyl/cone section eccentricity --- crates/mathcore/src/geometry.rs | 239 ++++++++++++++++++++++++++++++++ scripts/plot-cases.ts | 6 +- src/math/scene.ts | 75 +++++++++- src/wasm/pkg/mathcore_bg.wasm | Bin 564393 -> 569934 bytes 4 files changed, 318 insertions(+), 2 deletions(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 1928264..d0fc90f 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -1840,6 +1840,59 @@ pub fn points_analyze(points: &[NamedPoint]) -> Vec { } else { out.push(fact("形状判断", "\\text{类型}", format!("\\text{{{}{}边形}}", if convex { "凸" } else { "凹" }, n), None, "", "内角和 (n-2)·180°")); } + + // Desargues quick check: pts[0..3] vs pts[3..6] as △ABC, △A′B′C′. + if pts.len() >= 6 { + let (a, b, c) = (pts[0].1, pts[1].1, pts[2].1); + let (ap, bp, cp) = (pts[3].1, pts[4].1, pts[5].1); + let (na, nb, nc) = (&pts[0].0, &pts[1].0, &pts[2].0); + let (nap, nbp, ncp) = (&pts[3].0, &pts[4].0, &pts[5].0); + if let Some(s) = line_line_isect2(a, ap, b, bp) { + if collinear2(s, c, cp) { + out.push(fact( + "德萨格定理", + "\\text{Desargues}", + "\\text{透视}".into(), + None, + &format!("{na}{nap},{nb}{nbp},{nc}{ncp}\\ \\text{{共点}}"), + "两三角形对应顶点连线共点 ⇒ 对应边交点共线", + ).with(Shape::Point { + x: s[0], + y: s[1], + label: "S Desargues".into(), + })); + out.push(fact( + "德萨格定理", + "S", + pt(s[0], s[1]), + None, + "AA'\\cap BB'\\cap CC'", + "透视中心", + )); + let x = line_line_isect2(b, c, bp, cp); + let y = line_line_isect2(c, a, cp, ap); + let z = line_line_isect2(a, b, ap, bp); + if let (Some(x), Some(y), Some(z)) = (x, y, z) { + if collinear2(x, y, z) { + out.push(fact( + "德萨格定理", + "\\text{透视轴}", + "\\text{共线}".into(), + None, + "BC\\cap B'C',\\ CA\\cap C'A',\\ AB\\cap A'B'", + "对应边交点共线(德萨格透视轴)", + ).with(Shape::Segment { + x1: x[0], + y1: x[1], + x2: y[0], + y2: y[1], + label: "Desargues轴".into(), + })); + } + } + } + } + } out } @@ -2204,6 +2257,63 @@ fn line_isect(p: &NamedLine, q: &NamedLine) -> Option<[f64; 2]> { Some([(p.c * q.b - p.b * q.c) / det, (p.a * q.c - p.c * q.a) / det]) } + +/// Circumcenter and radius of △ABC; None if collinear. +fn circum2(a: [f64; 2], b: [f64; 2], c: [f64; 2]) -> Option<([f64; 2], f64)> { + let d = 2.0 * (a[0] * (b[1] - c[1]) + b[0] * (c[1] - a[1]) + c[0] * (a[1] - b[1])); + if d.abs() < 1e-14 { + return None; + } + let sq = |q: [f64; 2]| q[0] * q[0] + q[1] * q[1]; + let ux = (sq(a) * (b[1] - c[1]) + sq(b) * (c[1] - a[1]) + sq(c) * (a[1] - b[1])) / d; + let uy = (sq(a) * (c[0] - b[0]) + sq(b) * (a[0] - c[0]) + sq(c) * (b[0] - a[0])) / d; + let o = [ux, uy]; + let r = dist2(o, a); + if r < 1e-14 || !r.is_finite() { + return None; + } + Some((o, r)) +} + +fn collinear2(a: [f64; 2], b: [f64; 2], c: [f64; 2]) -> bool { + let cross = (b[0] - a[0]) * (c[1] - a[1]) - (b[1] - a[1]) * (c[0] - a[0]); + cross.abs() < 1e-8 * (1.0 + dist2(a, b) * dist2(a, c)) +} + +/// Second intersection of two circles, skipping `avoid` (the shared vertex). +fn circles_second_isect( + o1: [f64; 2], + r1: f64, + o2: [f64; 2], + r2: f64, + avoid: [f64; 2], +) -> Option<[f64; 2]> { + let dx = o2[0] - o1[0]; + let dy = o2[1] - o1[1]; + let d = dx.hypot(dy); + if d < 1e-12 || d > r1 + r2 + 1e-9 || d < (r1 - r2).abs() - 1e-9 { + return None; + } + let a = (r1 * r1 - r2 * r2 + d * d) / (2.0 * d); + let h2 = r1 * r1 - a * a; + if h2 < -1e-9 { + return None; + } + let h = h2.max(0.0).sqrt(); + let px = o1[0] + a * dx / d; + let py = o1[1] + a * dy / d; + let mx = -dy * h / d; + let my = dx * h / d; + let p_a = [px + mx, py + my]; + let p_b = [px - mx, py - my]; + let da = dist2(p_a, avoid); + let db = dist2(p_b, avoid); + if da < 1e-6 && db < 1e-6 { + return None; + } + Some(if da >= db { p_a } else { p_b }) +} + pub fn lines_analyze(ls: &[NamedLine], points: &[NamedPoint]) -> Vec { let mut out = Vec::new(); for l in ls { @@ -2379,6 +2489,94 @@ pub fn lines_analyze(ls: &[NamedLine], points: &[NamedPoint]) -> Vec { } } } + + // Miquel point of a complete quadrilateral (4 lines, 6 vertices). + if ls.len() >= 4 { + let n = ls.len().min(6); + 'miquel: for i0 in 0..n { + for i1 in (i0 + 1)..n { + for i2 in (i1 + 1)..n { + for i3 in (i2 + 1)..n { + let idx = [i0, i1, i2, i3]; + let mut ok_pairs = true; + for a in 0..4 { + for b in (a + 1)..4 { + if line_isect(&ls[idx[a]], &ls[idx[b]]).is_none() { + ok_pairs = false; + } + } + } + if !ok_pairs { + continue; + } + let tri = |a: usize, b: usize, c: usize| -> Option<[[f64; 2]; 3]> { + Some([ + line_isect(&ls[idx[a]], &ls[idx[b]])?, + line_isect(&ls[idx[b]], &ls[idx[c]])?, + line_isect(&ls[idx[c]], &ls[idx[a]])?, + ]) + }; + let (Some(t012), Some(t013), Some(t023), Some(t123)) = + (tri(0, 1, 2), tri(0, 1, 3), tri(0, 2, 3), tri(1, 2, 3)) + else { + continue; + }; + if collinear2(t012[0], t012[1], t012[2]) + || collinear2(t013[0], t013[1], t013[2]) + || collinear2(t023[0], t023[1], t023[2]) + || collinear2(t123[0], t123[1], t123[2]) + { + continue; + } + let (Some((o1, r1)), Some((o2, r2))) = + (circum2(t012[0], t012[1], t012[2]), circum2(t013[0], t013[1], t013[2])) + else { + continue; + }; + let shared = line_isect(&ls[idx[0]], &ls[idx[1]]).unwrap(); + let Some(m) = circles_second_isect(o1, r1, o2, r2, shared) else { + continue; + }; + let (Some((o3, r3)), Some((o4, r4))) = + (circum2(t023[0], t023[1], t023[2]), circum2(t123[0], t123[1], t123[2])) + else { + continue; + }; + if (dist2(m, o3) - r3).abs() > 1e-5 * (1.0 + r3) + || (dist2(m, o4) - r4).abs() > 1e-5 * (1.0 + r4) + { + continue; + } + let names = format!( + "{},{},{},{}", + ls[idx[0]].name, ls[idx[1]].name, ls[idx[2]].name, ls[idx[3]].name + ); + out.push(fact( + "米克尔点", + "\\text{Miquel}", + pt(m[0], m[1]), + None, + "\\odot(L_iL_jL_k)\\ \\text{共点}", + &format!("完全四线形 {{{names}}} 的四个三点形外接圆交于米克尔点"), + ).with(Shape::Point { + x: m[0], + y: m[1], + label: "Miquel".into(), + })); + out.push(fact( + "米克尔点", + "M", + pt(m[0], m[1]), + None, + "", + "米克尔点坐标", + )); + break 'miquel; + } + } + } + } + } out } @@ -3352,4 +3550,45 @@ mod tests { assert!(fs.iter().any(|f| f.group == "三线极线" && f.label.contains("l_"))); } + #[test] + fn miquel_complete_quadrilateral() { + // y=0, x=0, x+y=2, x-y=1 — four lines, six vertices, general position + let ls = vec![ + NamedLine { name: "l".into(), a: 0.0, b: 1.0, c: 0.0 }, + NamedLine { name: "m".into(), a: 1.0, b: 0.0, c: 0.0 }, + NamedLine { name: "n".into(), a: 1.0, b: 1.0, c: 2.0 }, + NamedLine { name: "p".into(), a: 1.0, b: -1.0, c: 1.0 }, + ]; + let out = lines_analyze(&ls, &[]); + assert!( + out.iter().any(|f| f.group == "米克尔点" && f.label.contains("Miquel")), + "Miquel missing: {:?}", + out.iter().map(|f| (&f.group, &f.label)).collect::>() + ); + assert!(out.iter().any(|f| f.group == "米克尔点" && f.label == "M")); + } + + #[test] + fn desargues_perspective_triangles() { + // S=O; A,B,C and scaled A',B',C' with distinct factors → perspective + axis + let pts = vec![ + NamedPoint { name: "A".into(), p: vec![2.0, 1.0] }, + NamedPoint { name: "B".into(), p: vec![-1.0, 2.0] }, + NamedPoint { name: "C".into(), p: vec![-2.0, -3.0] }, + NamedPoint { name: "A'".into(), p: vec![4.0, 2.0] }, + NamedPoint { name: "B'".into(), p: vec![-3.0, 6.0] }, + NamedPoint { name: "C'".into(), p: vec![-1.0, -1.5] }, + ]; + let out = points_analyze(&pts); + assert!( + out.iter().any(|f| f.group == "德萨格定理" && f.value.contains("透视")), + "Desargues perspective missing" + ); + assert!(out.iter().any(|f| f.group == "德萨格定理" && f.label == "S")); + assert!( + out.iter().any(|f| f.group == "德萨格定理" && f.label.contains("透视轴")), + "Desargues axis missing" + ); + } + } diff --git a/scripts/plot-cases.ts b/scripts/plot-cases.ts index e633d84..67980f3 100644 --- a/scripts/plot-cases.ts +++ b/scripts/plot-cases.ts @@ -97,7 +97,7 @@ export const cases: [string, string, Expect][] = [ ['二面角', 'x + 0*z = 0\ny + 0*z = 0', { dim: 3, facts: ['\\text{二面角}', '\\perp'] }], ['直线交球面', 'A(0,0,0)\nB(4,0,0)\nx^2 + y^2 + z^2 = 4', { dim: 3, facts: ['P_{AB\\cap', '|P_1P_2|'] }], ['笛卡尔圆', 'A(0,0)\nB(2,0)\nC(1,1.7320508075688772)\n⊙A: r = 1\n⊙B: r = 1\n⊙C: r = 1', { dim: 2, facts: ['\\text{Descartes}'], minFacts: 2 }], - ['圆柱截椭圆', 'x^2 + y^2 = 4\nx - z = 0', { dim: 3, facts: ['a_', 'b_', '\\text{椭圆}'] }], + ['圆柱截椭圆', 'x^2 + y^2 = 4\nx - z = 0', { dim: 3, facts: ['a_', 'b_', 'e_', '\\text{椭圆}'] }], ['英国国旗定理', 'A(0,0), B(4,0), C(4,3), D(0,3)', { dim: 2, facts: ['矩形', 'PA^2 + PC^2'], minFacts: 4 }], ['瓦里农平行四边形', 'A(0,0), B(4,0), C(5,3), D(1,3)', { dim: 2, facts: ['\\text{Varignon}', 'M_0'] }], ['三圆根心', 'A(0,0)\nB(2,0)\nC(1,1.7320508075688772)\n⊙A: r = 1\n⊙B: r = 1\n⊙C: r = 1', { dim: 2, facts: ['l_{', 'R_{\\odot', '\\text{幂}'], minFacts: 5 }], @@ -109,6 +109,10 @@ export const cases: [string, string, Expect][] = [ ['莫利定理', '△ABC: a = 3, b = 4, c = 5', { dim: 2, facts: ['\\text{Morley}', '|M_0M_1|'], minFacts: 3 }], ['西姆松与三线极线', '△ABC: a = 3, b = 4, c = 5', { dim: 2, facts: ['\\text{Simson}', 'l_{\\text{Simson}}', '\\tau(I)', 'OH\\text{ 九点圆直径}'], minFacts: 6 }], ['凯莱门杰四面体', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,0,1)', { dim: 3, facts: ['V_{\\text{四面体}}', 'V_{\\text{Cayley'] }], + ['米克尔完全四线形', 'y = 0\nx = 0\nx + y = 2\nx - y = 1', { dim: 2, facts: ['\\text{Miquel}', 'M'], minFacts: 2 }], + ['德萨格透视', 'A(2,1), B(-1,2), C(-2,-3), A\'(4,2), B\'(-3,6), C\'(-1,-1.5)', { dim: 2, facts: ['\\text{Desargues}', '\\text{透视轴}'], minFacts: 2 }], + ['圆柱截线离心率', 'x^2 + y^2 = 4\nx - z = 0', { dim: 3, facts: ['a_', 'b_', 'e_', '\\text{椭圆}'] }], + ['圆锥截线离心率', 'x^2 + y^2 - z^2 = 0\nx + 2z = 2', { dim: 3, facts: ['e_', '\\text{椭圆}'] }], ['空间螺旋线', 'r(t) = (cos(t), sin(t), t/3)', { dim: 3 }], ['空间三点', 'P(1,2,3), Q(0,1,-1), R(2,0,1)', { dim: 3 }], ] diff --git a/src/math/scene.ts b/src/math/scene.ts index 487074b..a0d5cf3 100644 --- a/src/math/scene.ts +++ b/src/math/scene.ts @@ -1029,10 +1029,83 @@ export function analyze(cards: CardInput[], solutionIndex = 0): Analysis { why: '圆柱被斜平面截得椭圆', shape: null, }) + const ecc = Math.sqrt(Math.max(0, 1 - (b * b) / (a * a))) + facts.push({ + group: '圆柱与平面', + label: `e_{${cyl.name}\\cap ${p.name}}`, + value: engine.nice(ecc), + num: ecc, + how: 'e = \\sqrt{1 - (b/a)^2} = \\cos\\psi', + why: '截线椭圆离心率(ψ 为轴与平面的线面角)', + shape: null, + }) } } } - if (facts.length) sections.push({ id: 'cyl-plane', title: '圆柱 ∩ 平面', subtitle: '椭圆半轴 · 线面角', tone: 'geo', facts }) + if (facts.length) sections.push({ id: 'cyl-plane', title: '圆柱 ∩ 平面', subtitle: '椭圆半轴 · 离心率 · 线面角', tone: 'geo', facts }) + } + + // Right circular cone x²+y² = z² (α = 45°) ∩ plane → conic eccentricity e = cosβ / cosα. + { + const coneItems = good.filter((i) => i.st.kind === 'implicit3') + const facts: RustFact[] = [] + for (const item of coneItems) { + const F = item.st.F.replace(/\s+/g, '') + // accept x^2+y^2-z^2(=0) or x^2+y^2=z^2 + const isUnitCone = + /^(?:\()?([+-]?x\^2\+y\^2-z\^2|-?z\^2\+x\^2\+y\^2)(?:\))?(?:-\(0\)|(=0)?)?$/.test(F) || + /^x\^2\+y\^2=z\^2$/.test(F) || + /^z\^2=x\^2\+y\^2$/.test(F) || + /^\(x\^2\+y\^2\)-\(z\^2\)$/.test(F) || + /^\(x\^2\)\+\(y\^2\)-\(z\^2\)$/.test(F) + if (!isUnitCone) continue + const coneName = item.st.name ?? '\\Gamma' + const alpha = Math.PI / 4 // semi-vertical angle + const cosA = Math.cos(alpha) + for (const p of planes) { + const ln = Math.hypot(p.n[0], p.n[1], p.n[2]) + if (ln < 1e-12) continue + const sinPsi = Math.abs(p.n[2]) / ln // ψ = angle between axis and plane + const cosPsi = Math.sqrt(Math.max(0, 1 - sinPsi * sinPsi)) + const label = `${coneName} \\cap ${p.name}` + if (sinPsi < 1e-9) { + facts.push({ + group: '圆锥与平面', + label, + value: '\\text{双曲线(平面 ∥ 轴)}', + num: null, + how: '\\beta = 0', + why: '平面平行于轴,截线为双曲线', + shape: null, + }) + continue + } + const e = cosPsi / cosA + let kind = '\\text{椭圆}' + if (Math.abs(e - 1) < 1e-6) kind = '\\text{抛物线}' + else if (e > 1) kind = '\\text{双曲线}' + else if (e < 1e-6) kind = '\\text{圆}' + facts.push({ + group: '圆锥与平面', + label, + value: kind, + num: e, + how: 'e = \\cos\\beta / \\cos\\alpha', + why: '直角圆锥(α=45°)被平面截得的圆锥曲线类型', + shape: null, + }) + facts.push({ + group: '圆锥与平面', + label: `e_{${coneName}\\cap ${p.name}}`, + value: engine.nice(e), + num: e, + how: 'e = \\cos\\beta / \\cos\\alpha,\ \\sin\\beta = |\\vec n\\cdot\\vec k|/|\\vec n|', + why: '圆锥截线离心率(β = 轴与平面的线面角)', + shape: null, + }) + } + } + if (facts.length) sections.push({ id: 'cone-plane', title: '圆锥 ∩ 平面', subtitle: '离心率 · 截线类型', tone: 'geo', facts }) } diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 59b90526d04a930a6f0ea7582fa40293ed77d1b2..19682d3d8b0d4952c34454aba1a8071f9b8b18b0 100644 GIT binary patch delta 130966 zcmdqK3w%_?*+0Iso88Sj#)_}8QvH3OXXczeyV*o|+rIzL=Z|gX zoH=u5o_X%iGjnDic{cL;o=EdlZ`$ptx2EQ1=BAoQdVeHx&28SBM7DXD?>=0=?z>n7 zw@gTRM9k~i)aJ>IdSoY+sXtGN1g@BW#iDC&@Ou1n=3h5=q33O1`n=1onYVEMoJE&- z-t`Cd&EiE1ubc1r+@GWF7tfh{<=llg{CK{n%bzuG(Uq6Yb1HV5GXq1*-|=T&yy%L# zmt8sM(z#bH_WatPI{*45*UZ0SuICkh>Sb3hzH0uwC7#dx)~A0;9UArQ^oK6Ha>@K_ z7Nd5~ylbzyZvJA=tA78&xl86>@A-#6YvE;A&YyeDoOz4pUvkM}&!1IA42JjonSfya zoGY)r;-dN2c$NmTuUa_w%K5Pdd;Hl~Ey4(~n*Z_puUWKc$zo5tKNwv+_lm19VIJ7? 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crates/mathcore/src/geometry.rs | 244 ++++++++++++++++++++++++++++++++ scripts/plot-cases.ts | 7 +- src/wasm/pkg/mathcore_bg.wasm | Bin 569934 -> 576895 bytes 3 files changed, 250 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index d0fc90f..f7e7e10 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -1893,6 +1893,102 @@ pub fn points_analyze(points: &[NamedPoint]) -> Vec { } } } + + // Pascal (cyclic hexagon) + Brianchon (opposite-vertex diagonals) for 6-gon in order. + if n == 6 { + let v: [[f64; 2]; 6] = std::array::from_fn(|i| pts[i].1); + let names: [&str; 6] = std::array::from_fn(|i| pts[i].0.as_str()); + // Cyclic? circumcircle of first three; others on it. + if let Some((o, r)) = circum2(v[0], v[1], v[2]) { + let cyclic = (3..6).all(|i| (dist2(v[i], o) - r).abs() < 1e-6 * (1.0 + r)); + if cyclic { + // Opposite sides: AB∩DE, BC∩EF, CD∩FA + let p01 = line_line_isect2(v[0], v[1], v[3], v[4]); + let p12 = line_line_isect2(v[1], v[2], v[4], v[5]); + let p23 = line_line_isect2(v[2], v[3], v[5], v[0]); + match (p01, p12, p23) { + (Some(x), Some(y), Some(z)) if collinear2(x, y, z) => { + out.push(fact( + "帕斯卡定理", + "\\text{Pascal}", + "\\text{共线}".into(), + None, + "AB\\cap DE,\\ BC\\cap EF,\\ CD\\cap FA", + "圆内接六边形:三组对边交点共线(帕斯卡线)", + ).with(Shape::Segment { + x1: x[0], + y1: x[1], + x2: y[0], + y2: y[1], + label: "Pascal".into(), + })); + out.push(fact( + "帕斯卡定理", + "\\text{Pascal线}", + line_eq_latex(y[1] - x[1], x[0] - y[0], (y[1] - x[1]) * x[0] + (x[0] - y[0]) * x[1]), + None, + "", + "帕斯卡线方程", + )); + } + (None, None, None) => { + out.push(fact( + "帕斯卡定理", + "\\text{Pascal}", + "\\text{无穷远直线}".into(), + None, + "AB\\parallel DE,\\ BC\\parallel EF,\\ CD\\parallel FA", + "对边皆平行:帕斯卡线为无穷远直线", + )); + } + _ => {} + } + } + } + // Brianchon: diagonals joining opposite vertices AD, BE, CF concur. + if let Some(s) = line_line_isect2(v[0], v[3], v[1], v[4]) { + if collinear2(s, v[2], v[5]) { + // also check tangential side condition a+c+e = b+d+f (sufficient for circle) + let side = |i: usize, j: usize| dist2(v[i], v[j]); + let ace = side(0, 1) + side(2, 3) + side(4, 5); + let bdf = side(1, 2) + side(3, 4) + side(5, 0); + out.push(fact( + "布利安雄定理", + "\\text{Brianchon}", + "\\text{共点}".into(), + None, + &format!( + "{}{}\\cap{}{}\\cap{}{}", + names[0], names[3], names[1], names[4], names[2], names[5] + ), + "六边形对顶点连线共点(布利安雄点)", + ).with(Shape::Point { + x: s[0], + y: s[1], + label: "Brianchon".into(), + })); + out.push(fact( + "布利安雄定理", + "B", + pt(s[0], s[1]), + None, + "AD\\cap BE\\cap CF", + "布利安雄点", + )); + if (ace - bdf).abs() < 1e-6 * (1.0 + ace) { + out.push(fact( + "布利安雄定理", + "a+c+e = b+d+f", + nice(ace), + Some(ace), + "a+c+e = b+d+f", + "对边和相等:存在内切圆(切线六边形)", + )); + } + } + } + } + out } @@ -1995,6 +2091,39 @@ fn points3_analyze(points: &[NamedPoint]) -> Vec { out.push(fact("距离", &format!("d({}, \\text{{平面}})", pts[3].0), nice(h), Some(h), "d = \\frac{3V}{S}", "等体积法")); } + + // Four face areas and altitudes from each vertex to the opposite face. + { + let verts = [pts[0].1, pts[1].1, pts[2].1, pts[3].1]; + let labels = [&pts[0].0, &pts[1].0, &pts[2].0, &pts[3].0]; + let faces = [[1usize, 2, 3], [0, 2, 3], [0, 1, 3], [0, 1, 2]]; + for (i, face) in faces.iter().enumerate() { + let (p, q, r) = (verts[face[0]], verts[face[1]], verts[face[2]]); + let nrm = cross3(sub3(q, p), sub3(r, p)); + let s_face = len3(nrm) / 2.0; + let fname = format!("{}{}{}", labels[face[0]], labels[face[1]], labels[face[2]]); + out.push(fact( + "四面体面", + &format!("S_{{\\triangle {}}}", fname), + nice(s_face), + Some(s_face), + "S = \\frac12|\\vec{u}\\times\\vec{v}|", + "四面体的一个面的面积", + )); + if s_face > 1e-12 && vol > 1e-12 { + let h_i = 3.0 * vol / s_face; + out.push(fact( + "四面体面", + &format!("h_{{{}}}", labels[i]), + nice(h_i), + Some(h_i), + "h = \\frac{3V}{S_{\\text{对面}}}", + &format!("从顶点 {} 到对面的高", labels[i]), + )); + } + } + } + // Viviani for regular tetrahedron: sum of distances from an interior point to the four faces = altitude. { let edges = [ @@ -2343,6 +2472,21 @@ pub fn lines_analyze(ls: &[NamedLine], points: &[NamedPoint]) -> Vec { out.push(fact("点与直线", &format!("{} \\in {}", p.name, nm), "\\checkmark".into(), None, "", "代入方程成立")); } else { out.push(fact("点与直线", &format!("d({}, {})", p.name, nm), nice(d), Some(d), "d = \\frac{|Ax_0 + By_0 + C|}{\\sqrt{A^2 + B^2}}", "点到直线距离").with(Shape::Segment { x1: x, y1: y, x2: foot[0], y2: foot[1], label: format!("{} 到 {}", p.name, nm) })); + + let rp = [2.0 * foot[0] - x, 2.0 * foot[1] - y]; + out.push(fact( + "反射", + &format!("{}^{{\\prime}}_{{{}}}", p.name, nm), + pt(rp[0], rp[1]), + None, + "P' = 2\\,\\mathrm{foot} - P", + &format!("点 {} 关于直线 {} 的反射", p.name, nm), + ).with(Shape::Point { + x: rp[0], + y: rp[1], + label: format!("{}′/{}", p.name, nm), + })); + } } } @@ -2621,6 +2765,22 @@ pub fn planes_analyze(ps: &[NamedPlane], points: &[NamedPoint]) -> Vec { "P + \\frac{d - \\vec n\\cdot P}{|\\vec n|^2}\\vec n", "点到平面的垂足", ).with(Shape::Point3 { x: foot[0], y: foot[1], z: foot[2], label: format!("foot {} {}", q.name, p.name) })); + + let rp = [2.0 * foot[0] - x[0], 2.0 * foot[1] - x[1], 2.0 * foot[2] - x[2]]; + out.push(fact( + "反射", + &format!("{}^{{\\prime}}_{{{}}}", q.name, p.name), + pt3(rp), + None, + "P' = 2\\,\\mathrm{foot} - P", + &format!("点 {} 关于平面 {} 的反射", q.name, p.name), + ).with(Shape::Point3 { + x: rp[0], + y: rp[1], + z: rp[2], + label: format!("{}′/{}", q.name, p.name), + })); + } } } @@ -3591,4 +3751,88 @@ mod tests { ); } + #[test] + fn pascal_cyclic_hexagon() { + let pts = vec![ + NamedPoint { name: "A".into(), p: vec![5.0, 0.0] }, + NamedPoint { name: "B".into(), p: vec![4.0, 3.0] }, + NamedPoint { name: "C".into(), p: vec![-3.0, 4.0] }, + NamedPoint { name: "D".into(), p: vec![-5.0, 0.0] }, + NamedPoint { name: "E".into(), p: vec![-3.0, -4.0] }, + NamedPoint { name: "F".into(), p: vec![4.0, -3.0] }, + ]; + let out = points_analyze(&pts); + assert!( + out.iter().any(|f| f.group == "帕斯卡定理" && f.value.contains("共线")), + "Pascal missing" + ); + assert!(out.iter().any(|f| f.group == "帕斯卡定理" && f.label.contains("Pascal线"))); + } + + #[test] + fn brianchon_regular_hexagon() { + let s3 = 3f64.sqrt(); + let pts = vec![ + NamedPoint { name: "A".into(), p: vec![1.0, 0.0] }, + NamedPoint { name: "B".into(), p: vec![0.5, s3 / 2.0] }, + NamedPoint { name: "C".into(), p: vec![-0.5, s3 / 2.0] }, + NamedPoint { name: "D".into(), p: vec![-1.0, 0.0] }, + NamedPoint { name: "E".into(), p: vec![-0.5, -s3 / 2.0] }, + NamedPoint { name: "F".into(), p: vec![0.5, -s3 / 2.0] }, + ]; + let out = points_analyze(&pts); + assert!( + out.iter().any(|f| f.group == "布利安雄定理" && f.value.contains("共点")), + "Brianchon missing" + ); + assert!(out.iter().any(|f| f.group == "布利安雄定理" && f.label.contains("a+c+e"))); + assert!( + out.iter().any(|f| f.group == "帕斯卡定理" && f.value.contains("无穷远")), + "Pascal at infinity for regular hex" + ); + } + + #[test] + fn tetra_face_areas_and_altitudes() { + let pts = vec![ + NamedPoint { name: "A".into(), p: vec![0.0, 0.0, 0.0] }, + NamedPoint { name: "B".into(), p: vec![1.0, 0.0, 0.0] }, + NamedPoint { name: "C".into(), p: vec![0.0, 1.0, 0.0] }, + NamedPoint { name: "D".into(), p: vec![0.0, 0.0, 1.0] }, + ]; + let out = points_analyze(&pts); + let faces = out.iter().filter(|f| f.group == "四面体面" && f.label.starts_with("S_")).count(); + assert_eq!(faces, 4, "four face areas"); + let hs = out.iter().filter(|f| f.group == "四面体面" && f.label.starts_with("h_")).count(); + assert_eq!(hs, 4, "four altitudes"); + let sabc = out.iter().find(|f| f.label.contains("ABC") && f.label.starts_with("S_")).unwrap(); + assert!((sabc.num.unwrap() - 0.5).abs() < 1e-9); + let hd = out.iter().find(|f| f.label == "h_{D}").unwrap(); + assert!((hd.num.unwrap() - 1.0).abs() < 1e-9); // V=1/6, S_ABC=1/2 → h=1 + } + + #[test] + fn reflect_point_over_line_and_plane() { + let ls = vec![NamedLine { name: "l".into(), a: 0.0, b: 1.0, c: 0.0 }]; // y=0 + let pts = vec![NamedPoint { name: "P".into(), p: vec![1.0, 2.0] }]; + let out = lines_analyze(&ls, &pts); + let rp = out.iter().find(|f| f.group == "反射").expect("line reflection"); + assert!(rp.value.contains("1") && rp.value.contains("-2") || rp.value.contains("1,\\ -2") || rp.value.contains("(1"), "got {}", rp.value); + if let Some(Shape::Point { x, y, .. }) = rp.shape.as_ref() { + assert!((*x - 1.0).abs() < 1e-9 && (*y + 2.0).abs() < 1e-9); + } else { + panic!("expected point shape"); + } + let planes = vec![NamedPlane { name: "α".into(), n: [0.0, 0.0, 1.0], d: 0.0 }]; // z=0 + let q = vec![NamedPoint { name: "Q".into(), p: vec![1.0, 2.0, 3.0] }]; + let out3 = planes_analyze(&planes, &q); + let rq = out3.iter().find(|f| f.group == "反射").expect("plane reflection"); + if let Some(Shape::Point3 { x, y, z, .. }) = rq.shape.as_ref() { + assert!((*x - 1.0).abs() < 1e-9 && (*y - 2.0).abs() < 1e-9 && (*z + 3.0).abs() < 1e-9); + } else { + panic!("expected Point3"); + } + } + + } diff --git a/scripts/plot-cases.ts b/scripts/plot-cases.ts index 67980f3..0a9e348 100644 --- a/scripts/plot-cases.ts +++ b/scripts/plot-cases.ts @@ -93,7 +93,7 @@ export const cases: [string, string, Expect][] = [ ['线面角', 'A(0,0,0)\nB(0,0,1)\nC(1,0,0)\nz = 0', { dim: 3, facts: ['\\theta(AB, α)', 'AB \\perp α', 'AC \\parallel α', '\\text{foot}(B, α)'] }], ['两圆根轴', 'x^2 + y^2 = 4\n(x-3)^2 + y^2 = 4', { dim: 2, facts: ['l_{', '相交', '公共弦'] }], ['两球根面', 'x^2 + y^2 + z^2 = 4\n(x-3)^2 + y^2 + z^2 = 4', { dim: 3, facts: ['\\pi_', '\\rho_', '公共弦'] }], - ['四面体体积', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,0,1)', { dim: 3, facts: ['V_{\\text{四面体}}', 'V_{\\text{Cayley'] }], + ['四面体体积', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,0,1)', { dim: 3, facts: ['V_{\\text{四面体}}', 'V_{\\text{Cayley', 'S_{\\triangle', 'h_{'] }], ['二面角', 'x + 0*z = 0\ny + 0*z = 0', { dim: 3, facts: ['\\text{二面角}', '\\perp'] }], ['直线交球面', 'A(0,0,0)\nB(4,0,0)\nx^2 + y^2 + z^2 = 4', { dim: 3, facts: ['P_{AB\\cap', '|P_1P_2|'] }], ['笛卡尔圆', 'A(0,0)\nB(2,0)\nC(1,1.7320508075688772)\n⊙A: r = 1\n⊙B: r = 1\n⊙C: r = 1', { dim: 2, facts: ['\\text{Descartes}'], minFacts: 2 }], @@ -113,6 +113,11 @@ export const cases: [string, string, Expect][] = [ ['德萨格透视', 'A(2,1), B(-1,2), C(-2,-3), A\'(4,2), B\'(-3,6), C\'(-1,-1.5)', { dim: 2, facts: ['\\text{Desargues}', '\\text{透视轴}'], minFacts: 2 }], ['圆柱截线离心率', 'x^2 + y^2 = 4\nx - z = 0', { dim: 3, facts: ['a_', 'b_', 'e_', '\\text{椭圆}'] }], ['圆锥截线离心率', 'x^2 + y^2 - z^2 = 0\nx + 2z = 2', { dim: 3, facts: ['e_', '\\text{椭圆}'] }], + ['帕斯卡圆内接六边形', 'A(5,0), B(4,3), C(-3,4), D(-5,0), E(-3,-4), F(4,-3)', { dim: 2, facts: ['\\text{Pascal}', '\\text{Pascal线}'], minFacts: 2 }], + ['布利安雄正六边形', 'A(1,0), B(0.5,0.8660254037844386), C(-0.5,0.8660254037844386), D(-1,0), E(-0.5,-0.8660254037844386), F(0.5,-0.8660254037844386)', { dim: 2, facts: ['\\text{Brianchon}', 'a+c+e'], minFacts: 2 }], + ['四面体面与高', 'A(0,0,0)\nB(1,0,0)\nC(0,1,0)\nD(0,0,1)', { dim: 3, facts: ['S_{\\triangle', 'h_{'], minFacts: 8 }], + ['点关于直线反射', 'P(1,2)\ny = 0', { dim: 2, facts: ['P^{\\prime}', 'd(P'], minFacts: 2 }], + ['点关于平面反射', 'Q(1,2,3)\nz = 0', { dim: 3, facts: ['Q^{\\prime}', '\\text{foot}'], minFacts: 2 }], ['空间螺旋线', 'r(t) = (cos(t), sin(t), t/3)', { dim: 3 }], ['空间三点', 'P(1,2,3), Q(0,1,-1), R(2,0,1)', { dim: 3 }], ] diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 19682d3d8b0d4952c34454aba1a8071f9b8b18b0..e2dd7c93f3ee3a88b049e11e0b94f6d71ca033f3 100644 GIT binary patch delta 73753 zcmd443w&HIZ&y^zutib_l21^RSL#YF_~chMIw7+e+CRd*Mi zpcSJ=H#n6OAV69QL4D$bef6sHyoJppo@L%`y zqRn$T&-HhIe$Qp@nMl5T@v5GOqb2RVgOSoyL^b#R=nv63+n)LLkDiR3@ge)0z3G!b zv4O!CK5;aIYd`UM1V37J*4CxvKe*qrD^g3&U4?oj=}(@w(;kVYZ#ZvB?PSz-wm0)X zYl}UOM58?xO+R?v>+I2Jy6UStQ{9EGqsBW2BAe|lM7P^p>|SPBo9(ff>$uU)_9#N8 zN0_!Z+xr7h;We zx08sv1#Bn%yRWW$E2^t~J$FP@p&NB=)JFT;Ew@UIJ%r4|)Yl$HP#yoFWp88c$!HRV z8ZoCgmZNDkj=tJaB>tUfDf1_y>2o`lzZ3JfRAW=Zj4S@NB0a$Pg@tZ`Td1t2WZ}+o 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zmQg`_dL>|fP<-k7vT!2Q*oyJu$;8U=0kFLS+XB+J2jCq6cxM3K6@Yge7{XI+zaBh6 zv{2>ebiLyw@uO3Y{cmbA6>|Fie^b^}(Jejps5!DvBSyDK7@jfX#-w;&!*!264}Ek)5 zb%)b*XAa!p!%tJ)xloaXrzvqR4E~F!DQm8Pw4I^-bHy@wr>IW@e}?Bkh_W$M0XA=_-^mt()NV7sbQ^vV9s}-E3-7=+Gg^3O z0N&-tl(tMH46^w4`RQi4F5Hl(Lo1zI$Ww!by9VGr{`?gBHe_z*m*hnpZt-9BH30Oi zw;@v&{b}el`+YD`SGdo_0DKd;zpWnkfcqMlLYL#d*_X(>9Fl=}iVtsH4%r93vmB57 z=&z~C3h|cf=GSh?gM7}*RIow}3h#c|)H#C@vu!uwGCj3YM76N!IllA_h`Apo_~K3| z1Whyk&R*7&R*FuJ@EzZnUgJE>U2NFx_=XBrLI1S6LSd_6i)3D*KC4CFZr884jb+$m zj2PQ{cFfBt3y*?Pz=Lez6@E-#puC9xx@t~~qYy(oOXCo;0-bS{8m+>;Uo?b5?Mp4YSbd89Nu=u2FZe!6h1L@qj(^u%s8f^D=1-&6K&oL~%U9ah(YsKHx z@Ybbn!!!6ih+Og3rR3OvQJ7n*w?^DV&JU%;GZ==8q4=FY(J8i8 Date: Sun, 1 Nov 2026 15:42:24 +0800 Subject: [PATCH 014/123] feat: Feuerbach distances, Spieker center, and Nagel point --- crates/mathcore/src/geometry.rs | 160 ++++++++++++++++++++++++++++++++ scripts/plot-cases.ts | 2 +- src/wasm/pkg/mathcore_bg.wasm | Bin 576895 -> 580750 bytes 3 files changed, 161 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index f7e7e10..5ef5e5b 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -817,6 +817,143 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "一般三角形 OH 不是九点圆直径(仅当直角时重合)", )); } + + // Feuerbach: nine-point circle tangent to incircle (internally) and excircles (externally). + { + let ni = (r9 - r).abs(); + out.push(fact( + "费尔巴哈定理", + "|NI|", + nice(ni), + Some(ni), + "|NI| = R/2 - r", + "九点圆与内切圆内切(费尔巴哈)", + ).with(Shape::Segment { + x1: n9[0], + y1: n9[1], + x2: inc[0], + y2: inc[1], + label: "NI".into(), + })); + // verify from coordinates + let ni_coord = dist2(n9, inc); + if (ni_coord - ni).abs() < 1e-5 * (1.0 + ni) { + out.push(fact( + "费尔巴哈定理", + "\\text{内切}", + "\\checkmark".into(), + None, + "d(N,I) = R_N - r", + "九点圆与内切圆相切", + )); + } + for i in 0..3 { + let ri = area / (p - s[i]); + // excenter I_i opposite vertex i: (-a_i V_i + a_j V_j + a_k V_k) / (-a_i + a_j + a_k) + let (ai, aj, ak) = (s[i], s[(i + 1) % 3], s[(i + 2) % 3]); + let den = -ai + aj + ak; + if den.abs() < 1e-12 { + continue; + } + let ia = [ + (-ai * v[i][0] + aj * v[(i + 1) % 3][0] + ak * v[(i + 2) % 3][0]) / den, + (-ai * v[i][1] + aj * v[(i + 1) % 3][1] + ak * v[(i + 2) % 3][1]) / den, + ]; + let nia = r9 + ri; + let nia_coord = dist2(n9, ia); + out.push(fact( + "费尔巴哈定理", + &format!("|NI_{}|", SIDE[i]), + nice(nia), + Some(nia), + &format!("|NI_{s}| = R/2 + r_{s}", s = SIDE[i]), + "九点圆与旁切圆外切(费尔巴哈)", + )); + if (nia_coord - nia).abs() < 1e-5 * (1.0 + nia) { + out.push(fact( + "费尔巴哈定理", + &format!("I_{}", SIDE[i]), + pt(ia[0], ia[1]), + None, + "", + "旁心(与九点圆外切)", + ).with(Shape::Point { + x: ia[0], + y: ia[1], + label: format!("I{}", SIDE[i]), + })); + } + } + } + } + + // Spieker center: incenter of the medial triangle = perimeter centroid. + { + let den = 2.0 * (a + b + c); + let sp = [ + ((b + c) * pa[0] + (c + a) * pb[0] + (a + b) * pc[0]) / den, + ((b + c) * pa[1] + (c + a) * pb[1] + (a + b) * pc[1]) / den, + ]; + out.push(fact( + "斯皮克中心", + "Sp", + pt(sp[0], sp[1]), + None, + "Sp = \\frac{(b+c)A+(c+a)B+(a+b)C}{2(a+b+c)}", + "斯皮克中心:周界重心(中点三角形的内心)", + ).with(Shape::Point { + x: sp[0], + y: sp[1], + label: "Sp 斯皮克".into(), + })); + } + + // Nagel point: concurrence of vertex-to-excircle-contact cevians; bary (s−a:s−b:s−c). + { + let sa = p - a; + let sb = p - b; + let sc = p - c; + if p > 1e-12 { + let na = [ + (sa * pa[0] + sb * pb[0] + sc * pc[0]) / p, + (sa * pa[1] + sb * pb[1] + sc * pc[1]) / p, + ]; + out.push(fact( + "奈格尔点", + "Na", + pt(na[0], na[1]), + None, + "Na = \\frac{(s-a)A+(s-b)B+(s-c)C}{s}", + "奈格尔点:顶点与对旁切圆切点的连线交点", + ).with(Shape::Point { + x: na[0], + y: na[1], + label: "Na 奈格尔".into(), + })); + // Nagel line: I, G, Na collinear with IG:GNa = 1:2 + let ig = dist2(inc, centroid); + let gna = dist2(centroid, na); + let cross = (centroid[0] - inc[0]) * (na[1] - inc[1]) - (centroid[1] - inc[1]) * (na[0] - inc[0]); + if cross.abs() < 1e-6 * (1.0 + ig) * (1.0 + gna) && ig > 1e-12 { + let ratio = gna / ig; + out.push(fact( + "奈格尔点", + "I,\\ G,\\ Na", + "\\text{共线}".into(), + None, + "\\vec{INa} = 3\\vec{IG}", + "奈格尔线:内心、重心、奈格尔点共线", + )); + out.push(fact( + "奈格尔点", + "IG:GNa", + format!("1:{}", nice(ratio)), + Some(ratio), + "IG:GNa = 1:2", + "重心按 1:2 分 INa", + )); + } + } } // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. @@ -3558,6 +3695,29 @@ mod tests { assert!((oh2on.num.unwrap() - 2.5).abs() < 1e-9); } + #[test] + fn feuerbach_spieker_nagel() { + // 3-4-5: R=2.5, r=1 → |NI|=R/2−r=0.25; r_a=2,r_b=3,r_c=6 → |NI_*|=R/2+r_*. + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let ni = fs.iter().find(|f| f.group == "费尔巴哈定理" && f.label == "|NI|").expect("|NI|"); + assert!((ni.num.unwrap() - 0.25).abs() < 1e-9, "|NI|={}", ni.value); + assert!(fs.iter().any(|f| f.group == "费尔巴哈定理" && f.label.contains("内切"))); + let nia = fs.iter().find(|f| f.label == "|NI_a|").expect("|NI_a|"); + let nib = fs.iter().find(|f| f.label == "|NI_b|").expect("|NI_b|"); + let nic = fs.iter().find(|f| f.label == "|NI_c|").expect("|NI_c|"); + assert!((nia.num.unwrap() - 3.25).abs() < 1e-9, "|NI_a|={}", nia.value); + assert!((nib.num.unwrap() - 4.25).abs() < 1e-9, "|NI_b|={}", nib.value); + assert!((nic.num.unwrap() - 7.25).abs() < 1e-9, "|NI_c|={}", nic.value); + assert!(fs.iter().any(|f| f.group == "斯皮克中心" && f.label == "Sp")); + assert!(fs.iter().any(|f| f.group == "奈格尔点" && f.label == "Na")); + let ig = fs.iter().find(|f| f.group == "奈格尔点" && f.label == "IG:GNa").expect("IG:GNa"); + assert!((ig.num.unwrap() - 2.0).abs() < 1e-6, "IG:GNa={}", ig.value); + assert!(fs.iter().any(|f| f.group == "奈格尔点" && f.value.contains("共线"))); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/scripts/plot-cases.ts b/scripts/plot-cases.ts index 0a9e348..5577885 100644 --- a/scripts/plot-cases.ts +++ b/scripts/plot-cases.ts @@ -47,7 +47,7 @@ export const cases: [string, string, Expect][] = [ ['直线过两点', 'y = kx + b, 过(1, 3), 过(2, 5)', { solve: { k: 2, b: 1 } }], // ---- triangles / coordinate geometry ---- ['解三角形 SAS', '△ABC: a = 5, b = 7, C = 60°', { dim: 2, facts: ['\\sqrt{39}'], minFacts: 10 }], - ['解三角形 SSS', '△ABC: a=3, b=4, c=5', { dim: 2, facts: ['90', 'S_{\\text{海伦}}', '|OI|', 'r_a=', 'AF_{c}', '\\Pi_{\\text{Ceva}}', '\\Pi_{\\text{Menelaus}}', '\\text{Stewart}_{m_', 'ID_{a}', '\\mathcal{A}_', 'OG:GH', 'R_{\\text{九点}}'], minFacts: 37 }], + ['解三角形 SSS', '△ABC: a=3, b=4, c=5', { dim: 2, facts: ['90', 'S_{\\text{海伦}}', '|OI|', 'r_a=', 'AF_{c}', '\\Pi_{\\text{Ceva}}', '\\Pi_{\\text{Menelaus}}', '\\text{Stewart}_{m_', 'ID_{a}', '\\mathcal{A}_', 'OG:GH', 'R_{\\text{九点}}', '|NI|', '|NI_a|', 'Sp', 'Na', 'IG:GNa'], minFacts: 45 }], ['解三角形 SSA 两解', '△ABC: a = 6, b = 8, A = 40°', 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z<(40`E6;*@47qu#w(xmibJTd!!;qV`%}S2~?kiy@FnjP;dJM2RY(4qs`Q%>%jJX4| zqlaNP`pcY5JoqhOS%5u0>BT=&M|X$ zLK^qHmG(kTHut~MA9QG+^5X0nInKH1^z?F3p`JTNEmlCNPRA*W;}ys0>gzxBHAx-=O^w`OFp6U)p*)c1rbe5wZIpWJ~8ZTM5HaZ^n_hGiSPx& zErg#D#7VmniqI9|A%p=4X$TnzFCeT&*oshs@Dai}gr5+)d~8?xBaB0sj*x}05MeFC zPK3P(6$qyhzCpP8vAv^WgJew++9LEq7=-XN!YqXO2+I-He?phnLh9-&y1y2WW&KZ4 z*LAR#6HigrIuRMP_>|qWP8g2#{5q_|Hk{N0)#6iBxem{^5>HcVJ{HPTPUE)F20Ia0 z$&j9(FA|3D0G%h3VF(;sn0-jrb_;Vpr-XS&xPydm;F{Zb$7!R*D*``MurfXaePQnx z370mB^ENf_A{7;gA&xID+Rf3Kfr*Tg^7($A^xH7uPFcik*vI3BZE^o=k5 z+-{nyMc`%YXW`?X{1#>pq_LS!Rhx0p0{QJEl5?%}1xSiY#y&V3n9ZbB z-aO#Z66RSlLBc${LZ0^C3@IQ)N(@bb-4z=5NetJLoL6v04h-A}+@=mb+8o2G-J9S$Fq1`tc~~`_+y!fNxtg4B!b$1+7yMdX3`$z{7Yu8pXQ9W~ z`;##*sw~VW7r2ux{Hhnzb(9zSE6U*&LeRJFrFK)qd^2sorJhA1Ir4E}Hla@;W_g}R z%#-Z`#3+jS3X4QUsKr+dIxk_`B1XR{nSY^6MIymb1Ka_ajRdQ2&9_GQZt<<=__D@s zZdeWmkp=& Date: Sun, 1 Nov 2026 15:45:21 +0800 Subject: [PATCH 015/123] feat: Gergonne point, Lemoine/symmedian K, and Brocard angle/points --- crates/mathcore/src/geometry.rs | 182 +++++++++++++++++++++++++++++++- src/wasm/pkg/mathcore_bg.wasm | Bin 580750 -> 584092 bytes 2 files changed, 181 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 5ef5e5b..9e1bae9 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -669,7 +669,14 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "", "内心的等角共轭是自身", )); - + out.push(fact( + "等角共轭", + "G \\leftrightarrow K", + "\\text{等角共轭}".into(), + None, + "\\text{重心} \\leftrightarrow \\text{勒莫恩点}", + "重心与勒莫恩(对称中线)点互为等角共轭", + )); // Carnot: signed distances from O to the three sides sum to R + r. { @@ -956,6 +963,145 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // Gergonne point: concurrence of vertex-to-incircle-contact cevians; bary a/(s−a):… + { + let sa = p - a; + let sb = p - b; + let sc = p - c; + if sa > 1e-12 && sb > 1e-12 && sc > 1e-12 { + let wa = a / sa; + let wb = b / sb; + let wc = c / sc; + let den = wa + wb + wc; + let ge = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "格尔巩点", + "Ge", + pt(ge[0], ge[1]), + None, + "Ge = \\frac{\\frac{a}{s-a}A+\\frac{b}{s-b}B+\\frac{c}{s-c}C}{\\sum}", + "格尔巩点:顶点与对边内切圆切点的连线交点", + ).with(Shape::Point { + x: ge[0], + y: ge[1], + label: "Ge 格尔巩".into(), + })); + out.push(fact( + "格尔巩点", + "Ge \\leftrightarrow Na", + "\\text{等截共轭}".into(), + None, + "\\text{isotomic}", + "格尔巩点与奈格尔点互为等截共轭", + )); + } + } + + // Lemoine / symmedian point K: concurrence of symmedians; bary (a²:b²:c²). + { + let wa = a * a; + let wb = b * b; + let wc = c * c; + let den = wa + wb + wc; + if den > 1e-18 { + let kpt = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "勒莫恩点", + "K", + pt(kpt[0], kpt[1]), + None, + "K = \\frac{a^2 A + b^2 B + c^2 C}{a^2 + b^2 + c^2}", + "勒莫恩点(对称中线点):三对称中线交点", + ).with(Shape::Point { + x: kpt[0], + y: kpt[1], + label: "K 勒莫恩".into(), + })); + } + } + + // Brocard angle ω and Brocard points Ω, Ω′. + // cot ω = (a²+b²+c²)/(4S); Ω trilinear (c/b : a/c : b/a), Ω′ (b/c : c/a : a/b). + if area > 1e-12 { + let sum_sq = a * a + b * b + c * c; + let cot_w = sum_sq / (4.0 * area); + let tan_w = 1.0 / cot_w; + let omega = tan_w.atan(); + out.push(fact( + "布罗卡", + "\\omega", + deg(omega), + Some(omega), + "\\cot\\omega = \\frac{a^2+b^2+c^2}{4S}", + "布罗卡角", + )); + out.push(fact( + "布罗卡", + "\\tan\\omega", + nice(tan_w), + Some(tan_w), + "\\tan\\omega = \\frac{4S}{a^2+b^2+c^2}", + "布罗卡角的正切", + )); + out.push(fact( + "布罗卡", + "\\cot\\omega", + nice(cot_w), + Some(cot_w), + "\\cot\\omega = \\frac{a^2+b^2+c^2}{4S}", + "与 tan ω 互为倒数", + )); + if a > 1e-12 && b > 1e-12 && c > 1e-12 { + let wa = a * c / b; + let wb = b * a / c; + let wc = c * b / a; + let den = wa + wb + wc; + let om = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "布罗卡", + "\\Omega", + pt(om[0], om[1]), + None, + "\\text{trilinear }(c/b:a/c:b/a)", + "第一布罗卡点", + ).with(Shape::Point { + x: om[0], + y: om[1], + label: "Ω 布罗卡".into(), + })); + let wa2 = a * b / c; + let wb2 = b * c / a; + let wc2 = c * a / b; + let den2 = wa2 + wb2 + wc2; + let omp = [ + (wa2 * pa[0] + wb2 * pb[0] + wc2 * pc[0]) / den2, + (wa2 * pa[1] + wb2 * pb[1] + wc2 * pc[1]) / den2, + ]; + out.push(fact( + "布罗卡", + "\\Omega'", + pt(omp[0], omp[1]), + None, + "\\text{trilinear }(b/c:c/a:a/b)", + "第二布罗卡点(与 Ω 互为等角共轭)", + ).with(Shape::Point { + x: omp[0], + y: omp[1], + label: "Ω′ 布罗卡".into(), + })); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -3718,6 +3864,40 @@ mod tests { assert!(fs.iter().any(|f| f.group == "奈格尔点" && f.value.contains("共线"))); } + #[test] + fn gergonne_lemoine_brocard() { + // 3-4-5: Ge → (3.25, 1.5); K → (3.2, 1.2); tan ω = 12/25 = 0.48; cot ω = 25/12. + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let ge = fs.iter().find(|f| f.group == "格尔巩点" && f.label == "Ge").expect("Ge"); + // nice() prefers exact forms: (13/4, 3/2) == (3.25, 1.5) + assert!( + (ge.value.contains("3.25") || ge.value.contains("13/4") || ge.value.contains("\\frac{13}{4}")) + && (ge.value.contains("1.5") || ge.value.contains("3/2") || ge.value.contains("\\frac{3}{2}")), + "Ge={}", + ge.value + ); + assert!(fs.iter().any(|f| f.group == "格尔巩点" && f.value.contains("等截"))); + let kp = fs.iter().find(|f| f.group == "勒莫恩点" && f.label == "K").expect("K"); + // (3.2, 1.2) == (16/5, 6/5) + assert!( + (kp.value.contains("3.2") || kp.value.contains("16/5") || kp.value.contains("\\frac{16}{5}")) + && (kp.value.contains("1.2") || kp.value.contains("6/5") || kp.value.contains("\\frac{6}{5}")), + "K={}", + kp.value + ); + assert!(fs.iter().any(|f| f.group == "等角共轭" && f.label.contains("G") && f.label.contains("K"))); + let tan_w = fs.iter().find(|f| f.group == "布罗卡" && f.label == "\\tan\\omega").expect("tan ω"); + assert!((tan_w.num.unwrap() - 0.48).abs() < 1e-9, "tan ω={}", tan_w.value); + let cot_w = fs.iter().find(|f| f.group == "布罗卡" && f.label == "\\cot\\omega").expect("cot ω"); + assert!((cot_w.num.unwrap() - 25.0 / 12.0).abs() < 1e-9, "cot ω={}", cot_w.value); + assert!(fs.iter().any(|f| f.group == "布罗卡" && f.label == "\\omega")); + assert!(fs.iter().any(|f| f.group == "布罗卡" && f.label == "\\Omega")); + assert!(fs.iter().any(|f| f.group == "布罗卡" && f.label == "\\Omega'")); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 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z-%%c7tJMFCzXOmr9>SuN@+V*@)p}CEYCTQ^e-ECcwBsi*+X|FxKa6@8U8cOlSSpCO z`uWUZ>=$sz5txZ5uTaJjvBCV#6^mv=zAvxP#Umoi+Uu%ryoMrX*E01gr5qJ;iBg{H zPj@2b_NB@gg`jJ`e|1+oHXjwKLDuT;^-J!3X5Fu>{+=$j!DeY)lz0qY(Sj~2Jtk&2 z+PYwMkky5eV|PdI(AZ-(4wGG5M>>mByD#Z~;rr<)ev?d5C;xg$Y0DfR?rW!BA(IfzG^*5mKoT*0*L??Y#< zh*W!bpJ?9*+(#UT4E!m$#8y(i%(kL@S;=Z!Lf>d#kM8%O_^UALv%uWKqP`tDS4CZj QY5U2S?sN;f(;eFKzh0WB0{{R3 From e2c5c60a9437da31a0d6c727fa5bff4212f48bd8 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 15:48:03 +0800 Subject: [PATCH 016/123] feat: de Longchamps, Mittenpunkt, and Schiffler point --- crates/mathcore/src/geometry.rs | 144 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 584092 -> 586652 bytes 2 files changed, 144 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 9e1bae9..1d23163 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -1102,6 +1102,108 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // de Longchamps point L: reflection of H over O (so O midpoint of LH); on Euler line. + { + let longch = [2.0 * circ[0] - orth[0], 2.0 * circ[1] - orth[1]]; + out.push(fact( + "德龙尚点", + "L", + pt(longch[0], longch[1]), + None, + "L = 2O - H", + "德龙尚点:垂心关于外心的对称点", + ).with(Shape::Point { + x: longch[0], + y: longch[1], + label: "L 德龙尚".into(), + })); + let mid = [(longch[0] + orth[0]) / 2.0, (longch[1] + orth[1]) / 2.0]; + if dist2(mid, circ) < 1e-6 * (1.0 + dist2(circ, orth)) { + out.push(fact( + "德龙尚点", + "O = \\text{中点}(L,H)", + "\\checkmark".into(), + None, + "\\overrightarrow{OL} = -\\overrightarrow{OH}", + "外心是 LH 的中点(欧拉线上)", + )); + } + } + + // Mittenpunkt Mi: perspector of medial and excentral triangles; bary a(s-a):b(s-b):c(s-c). + { + let sa = p - a; + let sb = p - b; + let sc = p - c; + let wa = a * sa; + let wb = b * sb; + let wc = c * sc; + let den = wa + wb + wc; + if den > 1e-12 { + let mi = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "米滕点", + "Mi", + pt(mi[0], mi[1]), + None, + "Mi = \\frac{a(s-a)A+b(s-b)B+c(s-c)C}{\\sum}", + "米滕点(Mittenpunkt):旁心三角形与中点三角形的透视中心", + ).with(Shape::Point { + x: mi[0], + y: mi[1], + label: "Mi 米滕".into(), + })); + } + } + + // Schiffler point: concurrence of Euler lines of ABC, IBC, ICA, IAB. + // Construct as Euler(ABC) ∩ Euler(IBC); cross-check with Euler(ICA). + if let Some((o_ibc, _)) = circum2(inc, pb, pc) { + let g_ibc = [ + (inc[0] + pb[0] + pc[0]) / 3.0, + (inc[1] + pb[1] + pc[1]) / 3.0, + ]; + if let Some(sf) = line_line_isect2(circ, orth, o_ibc, g_ibc) { + let cross = (orth[0] - circ[0]) * (sf[1] - circ[1]) - (orth[1] - circ[1]) * (sf[0] - circ[0]); + let scale = (1.0 + dist2(circ, orth)) * (1.0 + dist2(circ, sf)); + if cross.abs() < 1e-5 * scale { + out.push(fact( + "席弗勒点", + "Sc", + pt(sf[0], sf[1]), + None, + "\\text{Euler}(\\triangle ABC)\\cap\\text{Euler}(\\triangle IBC)", + "席弗勒点:内心三角形与原三角形欧拉线的交点", + ).with(Shape::Point { + x: sf[0], + y: sf[1], + label: "Sc 席弗勒".into(), + })); + if let Some((o_ica, _)) = circum2(inc, pc, pa) { + let g_ica = [ + (inc[0] + pc[0] + pa[0]) / 3.0, + (inc[1] + pc[1] + pa[1]) / 3.0, + ]; + if let Some(sf2) = line_line_isect2(circ, orth, o_ica, g_ica) { + if dist2(sf, sf2) < 1e-5 * (1.0 + dist2(circ, orth)) { + out.push(fact( + "席弗勒点", + "\\text{Euler}(ICA)", + "\\checkmark".into(), + None, + "\\text{Euler}(ICA)\\ni Sc", + "与 △ICA 的欧拉线亦交于同一点", + )); + } + } + } + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -3898,6 +4000,48 @@ mod tests { assert!(fs.iter().any(|f| f.group == "布罗卡" && f.label == "\\Omega'")); } + + #[test] + fn longchamps_mittenpunkt_schiffler() { + // 3-4-5: H=C=(3.2,2.4), O=(2.5,0) → L=2O−H=(1.8,−2.4); + // Mi bary a(s−a):… → (28/11, 6/11); Sc on Euler line, matches Euler(ICA). + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let l = fs.iter().find(|f| f.group == "德龙尚点" && f.label == "L").expect("L"); + assert!( + (l.value.contains("1.8") || l.value.contains("9/5") || l.value.contains("\\frac{9}{5}")) + && (l.value.contains("-2.4") || l.value.contains("-\\frac{12}{5}") || l.value.contains("-12/5")), + "L={}", + l.value + ); + assert!(fs.iter().any(|f| f.group == "德龙尚点" && f.label.contains("中点"))); + let mi = fs.iter().find(|f| f.group == "米滕点" && f.label == "Mi").expect("Mi"); + assert!( + mi.value.contains("28/11") + || mi.value.contains("\\frac{28}{11}") + || mi.value.contains("2.54"), + "Mi={}", + mi.value + ); + assert!(fs.iter().any(|f| f.group == "席弗勒点" && f.label == "Sc"), "Sc missing"); + assert!( + fs.iter().any(|f| f.group == "席弗勒点" && f.label.contains("ICA")), + "Schiffler ICA concurrence missing" + ); + let sc = fs.iter().find(|f| f.group == "席弗勒点" && f.label == "Sc").unwrap(); + // Sc ≈ (2.68421, 0.63158) = (51/19, 12/19) + assert!( + sc.value.contains("2.68") + || sc.value.contains("51/19") + || sc.value.contains("\\frac{51}{19}") + || sc.value.contains("0.63"), + "Sc={}", + sc.value + ); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 7575ee8f995b8eac6307c5be7bed7dda8e3f8fc2..51e10e5de835bae5296689578c546c7677a1f72f 100644 GIT binary patch delta 66348 zcmcG%3qVy>7B_y+K9`rgu84}Fc)%Av@SV?mY|`G(X_{&Jnx?*KX3Cl#GtD&5E>2Wb zSk$357ENfBRFs(5r6NNmMMTAj#DIeBwVqhNhj(w=@NvXZHgMI-)Z3y8pJHr?fA+sddw8Sy zb#(gZWFsOwhyK&%usDNF(tW<1sPr^?@}!S4B6vxZIX`CjkRp9K?>JQB;fee^N;K=$ z@|XpuC1*q$5t%IRw0IAIam#t>H#HvL%7|Da%}6UjTX^X+B6)#!?Q#^LmI^fA`NNF} z0JY__8E~L(I%1}}yQxGge4zDe`hXGsUfp!q-HbHS9!np8g54}PGJOA3Xs7`lrJmwt zPs_74BZJ@B4L}UPpOQ%5QyN=hL@dl?y)Y<30Xfj)j?j#W{iRV7wcHr*bYAxvS|7~c 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zRf&0z%(BpP>{`m0cWfpei{+IE*~BY6n0`TiA^$=?y#4UMW9;MWBId?~-J#gSA}+i) zFx%Yc5l0}NikMgG>4=dP%k4NULR*+}+d$|2Q5a&3ny! zKSWIA(MEx;9=L!w90{^hCr?Ooq)i^@m^gV{+BAo6NT91l7aCE-UD)&Hz+A(a5IyOx TSgR?O$KI;?MNri*e%t;J?7OOW From 25742510c28de2138983f3c608c1d92f9ecb738e Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 15:49:41 +0800 Subject: [PATCH 017/123] feat: Bevan point, orthic triangle feet, and Euler reflection point --- crates/mathcore/src/geometry.rs | 198 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 586652 -> 591189 bytes 2 files changed, 198 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 1d23163..b7a9ca0 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -1204,6 +1204,164 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // Bevan point: circumcenter of the excentral triangle = reflection of I over O. + { + let bevan = [2.0 * circ[0] - inc[0], 2.0 * circ[1] - inc[1]]; + out.push(fact( + "贝万点", + "Be", + pt(bevan[0], bevan[1]), + None, + "Be = 2O - I", + "贝万点:旁心三角形的外心(内心关于外心的对称点)", + ).with(Shape::Point { + x: bevan[0], + y: bevan[1], + label: "Be 贝万".into(), + })); + let mut ex = [[0.0f64; 2]; 3]; + let mut ex_ok = true; + for i in 0..3 { + let (ai, aj, ak) = (s[i], s[(i + 1) % 3], s[(i + 2) % 3]); + let den = -ai + aj + ak; + if den.abs() < 1e-12 { + ex_ok = false; + break; + } + ex[i] = [ + (-ai * v[i][0] + aj * v[(i + 1) % 3][0] + ak * v[(i + 2) % 3][0]) / den, + (-ai * v[i][1] + aj * v[(i + 1) % 3][1] + ak * v[(i + 2) % 3][1]) / den, + ]; + } + if ex_ok { + if let Some((o_ex, _)) = circum2(ex[0], ex[1], ex[2]) { + if dist2(o_ex, bevan) < 1e-5 * (1.0 + dist2(circ, inc)) { + out.push(fact( + "贝万点", + "O(I_a I_b I_c)", + "\\checkmark".into(), + None, + "Be = O(I_a I_b I_c)", + "旁心三角形的外心与 2O−I 重合", + )); + } + } + } + } + + // Orthic triangle: feet of the altitudes (on the nine-point circle). + { + let n9loc = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; + let r9loc = rr / 2.0; + let mut feet = [[0.0f64; 2]; 3]; + let mut ok = true; + for i in 0..3 { + let p0 = v[i]; + let q1 = v[(i + 1) % 3]; + let q2 = v[(i + 2) % 3]; + let dx = q2[0] - q1[0]; + let dy = q2[1] - q1[1]; + let den = dx * dx + dy * dy; + if den < 1e-18 { + ok = false; + break; + } + let t = ((p0[0] - q1[0]) * dx + (p0[1] - q1[1]) * dy) / den; + feet[i] = [q1[0] + t * dx, q1[1] + t * dy]; + } + if ok { + for i in 0..3 { + let f = feet[i]; + out.push(fact( + "垂足三角形", + &format!("H_{}", SIDE[i]), + pt(f[0], f[1]), + None, + &format!("H_{s} = \\text{{足}}_{{{s}}}", s = SIDE[i]), + "垂足三角形的顶点(高线足)", + ).with(Shape::Point { + x: f[0], + y: f[1], + label: format!("H{} 垂足", SIDE[i]), + })); + } + let on_n9 = (0..3).all(|i| (dist2(feet[i], n9loc) - r9loc).abs() < 1e-5 * (1.0 + r9loc)); + if on_n9 { + out.push(fact( + "垂足三角形", + "H_a, H_b, H_c \\in \\text{九点圆}", + "\\checkmark".into(), + None, + "d(N, H_*) = R/2", + "垂足三角形内接于九点圆", + )); + } + } + } + + // Euler reflection point X(110): reflections of Euler line over the sides concur on (O). + // May fail to concur for some right triangles — emit only when found. + { + let reflect = |pt: [f64; 2], s1: [f64; 2], s2: [f64; 2]| -> [f64; 2] { + let dx = s2[0] - s1[0]; + let dy = s2[1] - s1[1]; + let den = dx * dx + dy * dy; + if den < 1e-18 { + return pt; + } + let t = ((pt[0] - s1[0]) * dx + (pt[1] - s1[1]) * dy) / den; + let foot = [s1[0] + t * dx, s1[1] + t * dy]; + [2.0 * foot[0] - pt[0], 2.0 * foot[1] - pt[1]] + }; + let mirrors = [(pb, pc), (pc, pa), (pa, pb)]; + let mut segs: [([f64; 2], [f64; 2]); 3] = [([0.0; 2], [0.0; 2]); 3]; + let mut ok = true; + for (i, (s1, s2)) in mirrors.into_iter().enumerate() { + let p = reflect(circ, s1, s2); + let mut q = reflect(orth, s1, s2); + if dist2(p, q) < 1e-9 { + q = reflect(centroid, s1, s2); + if dist2(p, q) < 1e-9 { + ok = false; + break; + } + } + segs[i] = (p, q); + } + if ok { + if let (Some(e1), Some(e2)) = ( + line_line_isect2(segs[0].0, segs[0].1, segs[1].0, segs[1].1), + line_line_isect2(segs[0].0, segs[0].1, segs[2].0, segs[2].1), + ) { + if dist2(e1, e2) < 1e-5 * (1.0 + rr) { + let er = e1; + out.push(fact( + "欧拉反射点", + "E_r", + pt(er[0], er[1]), + None, + "\\mathrm{refl}_{BC}(OH)\\cap\\mathrm{refl}_{CA}(OH)", + "欧拉反射点:欧拉线关于三边的反射线交点", + ).with(Shape::Point { + x: er[0], + y: er[1], + label: "Er 欧拉反射".into(), + })); + if (dist2(er, circ) - rr).abs() < 1e-5 * (1.0 + rr) { + out.push(fact( + "欧拉反射点", + "E_r \\in (O)", + "\\checkmark".into(), + None, + "d(O, E_r) = R", + "欧拉反射点在外接圆上", + )); + } + } + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -4042,6 +4200,46 @@ mod tests { ); } + + #[test] + fn bevan_orthic_euler_reflection() { + // 3-4-5: Be = 2O−I = (2,−1); orthic feet; Euler reflection skipped (right). + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let be = fs.iter().find(|f| f.group == "贝万点" && f.label == "Be").expect("Be"); + assert!( + (be.value.contains("2") || be.value.contains("2.0")) + && (be.value.contains("-1")), + "Be={}", + be.value + ); + assert!(fs.iter().any(|f| f.group == "贝万点" && f.label.contains("I_a"))); + assert!(["H_a", "H_b", "H_c"].iter().all(|lab| fs.iter().any(|f| f.group == "垂足三角形" && f.label == *lab))); + assert!(fs.iter().any(|f| f.group == "垂足三角形" && f.label.contains("九点圆"))); + let hc = fs.iter().find(|f| f.group == "垂足三角形" && f.label == "H_c").expect("Hc"); + assert!( + hc.value.contains("3.2") || hc.value.contains("16/5") || hc.value.contains("\\frac{16}{5}"), + "Hc={}", + hc.value + ); + + // Acute 6-7-8: Euler reflection point on circumcircle. + let k2 = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().any(|f| f.group == "欧拉反射点" && f.label == "E_r"), "E_r missing on 6-7-8"); + assert!(fs2.iter().any(|f| f.group == "欧拉反射点" && f.label.contains("(O)"))); + let er = fs2.iter().find(|f| f.group == "欧拉反射点" && f.label == "E_r").unwrap(); + assert!( + er.value.contains("1.7") || er.value.contains("4.4") || er.value.contains("\\frac"), + "Er={}", + er.value + ); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 51e10e5de835bae5296689578c546c7677a1f72f..ec70a56cbbd579c1a82720698e4c8497253eddda 100644 GIT binary patch delta 77165 zcmce<3qV}ewKqOz4@@B8F+B1lkTa8zK;BV89vaP#Bx=>FecbkX@6~(%ecU$ft+n;G zz3puWD=Mwgq6a-h(F}wtDp6t*L5)fj6_qGjRMgm_QbmiFC@L!I_gic4bLPx2VC?7j zk1hM0efDGRwbyH}z4o5^*XBR{`vt9kNuAo$-RYYa@yYh?J+G&ZiO7|=6kIgrvM%AD 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z?H|*sRib{&mtFD3BkgK<3_J$!EG`T@)$LC=SBW9gw0P>U8rxIldL4~k4MU5;zYqM} zHDAuAJ*&kR()pb<=}oA$&2w#*0id_T0+G9#8Hbs0gxjBBW*Q{UeMLu4hylfIj#t`lv-4SGjmac&bE_zpWkV-^nrU9>2ME5dE?%KEfnsS zw?s_9n7uZqS-T;^bGCrhFzF#z!?B{9u zez8XS z{HIdHHJelF%%blPi(1tuCeEB;?__7WWcbWxpAesElXahnYgGHN=+x5iP64Z8Vn2d+ zPQdVIRim;K)7ryW^&|YZa8nKcx$rZG_eBZJnCDe9uIz!6fLTl$@y!MvYQj7nwlQIz zMv}yYa2blcF}w zJ0XHzGXm}LVDdrgEX56fE-qK6fxCF%T^`|cxwUGN*GUl|W!$2mlcHsS5%!v^WS|c} ziQZ_?TR|q8)5N*X3TaOEz&C;WoAPuYxVID2O{6E~{769sSU|(=S)k*T0%#7vhYKJw zmfoRf1!A#}SDDRXN4Pp=wCa=?955P~W!4P1tm~~Tqx+{sc%(tkb@?BJ%XPBS<+it% z+gHlUw9cnRduza{pLCNlZz9zP^QoU`)fvdIfp_W78K@~)cd2%v=pFU!uFbhDn}()j z{m+bfS!LkSm^!)j4g8iH)6PQCCV1x0`s}#`E~L93SZ;c|X{ zg3Gh;zu+P&@aaO{K5>S9>da*O)N%GvQ)ecQ0UE~=-w1ENXLBxY4E|ep>HV|VVIB#3 zJ;cLv7x(v(_q3a5#XppQK@V+Cb74Oaxj=&+(zoZ)I-4G9qEtjSl8Qs9?H_2KMXU_LOH1o-+N5bT?Pd3p6oEv?$0B14sKoLIg~_NHBOrJVl- DYp>uS From c3e9efe055880013bf0cfb0d1c8ec076a4dae71f Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 15:52:01 +0800 Subject: [PATCH 018/123] feat: contact triangle, Spieker circle radius, stable Kosnita; fix Gergonne bary --- crates/mathcore/src/geometry.rs | 175 ++++++++++++++++++++++++++++++-- src/wasm/pkg/mathcore_bg.wasm | Bin 591189 -> 594553 bytes 2 files changed, 167 insertions(+), 8 deletions(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index b7a9ca0..ee7b470 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -964,15 +964,16 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } - // Gergonne point: concurrence of vertex-to-incircle-contact cevians; bary a/(s−a):… + // Gergonne point: concurrence of vertex-to-incircle-contact cevians; bary 1/(s−a):… { let sa = p - a; let sb = p - b; let sc = p - c; if sa > 1e-12 && sb > 1e-12 && sc > 1e-12 { - let wa = a / sa; - let wb = b / sb; - let wc = c / sc; + // bary 1/(s−a):1/(s−b):1/(s−c) = isotomic conjugate of Nagel (s−a:s−b:s−c) + let wa = 1.0 / sa; + let wb = 1.0 / sb; + let wc = 1.0 / sc; let den = wa + wb + wc; let ge = [ (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, @@ -983,7 +984,7 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "Ge", pt(ge[0], ge[1]), None, - "Ge = \\frac{\\frac{a}{s-a}A+\\frac{b}{s-b}B+\\frac{c}{s-c}C}{\\sum}", + "Ge = \\frac{\\frac{1}{s-a}A+\\frac{1}{s-b}B+\\frac{1}{s-c}C}{\\sum}", "格尔巩点:顶点与对边内切圆切点的连线交点", ).with(Shape::Point { x: ge[0], @@ -1362,6 +1363,127 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // Contact (intouch) triangle: incircle tangency points on the sides. + // On BC: BD = s-b, DC = s-c; perspector is the Gergonne point. + { + let sa = p - a; + let sb = p - b; + let sc = p - c; + if sa > 1e-12 && sb > 1e-12 && sc > 1e-12 { + let xa = section_point(pb, pc, sb, sc); + let xb = section_point(pc, pa, sc, sa); + let xc = section_point(pa, pb, sa, sb); + let pts = [(xa, "a"), (xb, "b"), (xc, "c")]; + for (q, lab) in pts { + out.push(fact( + "接触三角形", + &format!("X_{}", lab), + pt(q[0], q[1]), + None, + &format!("X_{s}\\text{{ on side }}{s}", s = lab), + "内切圆与边的切点(接触三角形顶点)", + ).with(Shape::Point { + x: q[0], + y: q[1], + label: format!("X{} 切点", lab), + })); + } + if (dist2(inc, xa) - r).abs() < 1e-5 * (1.0 + r) + && (dist2(inc, xb) - r).abs() < 1e-5 * (1.0 + r) + && (dist2(inc, xc) - r).abs() < 1e-5 * (1.0 + r) + { + out.push(fact( + "接触三角形", + "|IX_*|", + nice(r), + Some(r), + "|IX_a| = |IX_b| = |IX_c| = r", + "切点到内心的距离等于内切圆半径", + )); + } + let wa = 1.0 / sa; + let wb = 1.0 / sb; + let wc = 1.0 / sc; + let den = wa + wb + wc; + let ge = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + let cross = (xa[0] - pa[0]) * (ge[1] - pa[1]) - (xa[1] - pa[1]) * (ge[0] - pa[0]); + if cross.abs() < 1e-5 * (1.0 + dist2(pa, xa)) * (1.0 + dist2(pa, ge)) { + out.push(fact( + "接触三角形", + "A, X_a, Ge", + "\\text{共线}".into(), + None, + "A X_a \\ni Ge", + "接触三角形与原三角形的透视中心为格尔巩点", + )); + } + } + } + + // Spieker circle: incircle of the medial triangle; center Sp, radius r/2. + { + let den = 2.0 * (a + b + c); + let sp = [ + ((b + c) * pa[0] + (c + a) * pb[0] + (a + b) * pc[0]) / den, + ((b + c) * pa[1] + (c + a) * pb[1] + (a + b) * pc[1]) / den, + ]; + let r_sp = r / 2.0; + out.push(fact( + "斯皮克圆", + "r_{\\text{Sp}}", + nice(r_sp), + Some(r_sp), + "r_{\\text{Sp}} = r/2", + "斯皮克圆:中点三角形的内切圆,半径为 r/2", + ).with(Shape::Circle { + cx: sp[0], + cy: sp[1], + r: r_sp, + label: "斯皮克圆".into(), + })); + out.push(fact( + "斯皮克圆", + "S_{\\text{中点}}/(s/2)", + nice(r_sp), + Some(r_sp), + "\\frac{S/4}{s/2} = \\frac{r}{2}", + "由中点三角形的面积与半周长推出", + )); + } + + // Kosnita point: A O_a ∩ B O_b ∩ C O_c with O_a = circumcenter of △OBC. + // Skip when △OAB / OBC / OCA is degenerate (e.g. right △ with O on a side). + { + let oa = circum2(circ, pb, pc); + let ob = circum2(circ, pc, pa); + let oc = circum2(circ, pa, pb); + if let (Some((oa, _)), Some((ob, _)), Some((oc, _))) = (oa, ob, oc) { + if let (Some(k1), Some(k2)) = ( + line_line_isect2(pa, oa, pb, ob), + line_line_isect2(pa, oa, pc, oc), + ) { + if dist2(k1, k2) < 1e-5 * (1.0 + rr) { + let ko = k1; + out.push(fact( + "科斯尼塔点", + "Ko", + pt(ko[0], ko[1]), + None, + "AO_a \\cap BO_b \\cap CO_c", + "科斯尼塔点:A 与 △OBC 外心等连线的交点", + ).with(Shape::Point { + x: ko[0], + y: ko[1], + label: "Ko 科斯尼塔".into(), + })); + } + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -4132,10 +4254,14 @@ mod tests { assert!(r.error.is_none(), "{:?}", r.error); let fs = &r.cases[0].facts; let ge = fs.iter().find(|f| f.group == "格尔巩点" && f.label == "Ge").expect("Ge"); - // nice() prefers exact forms: (13/4, 3/2) == (3.25, 1.5) + // bary 1/(s−a):… on 3-4-5 → (3.109…, 1.309…) = (171/55, 72/55) assert!( - (ge.value.contains("3.25") || ge.value.contains("13/4") || ge.value.contains("\\frac{13}{4}")) - && (ge.value.contains("1.5") || ge.value.contains("3/2") || ge.value.contains("\\frac{3}{2}")), + ge.value.contains("3.10") + || ge.value.contains("1.30") + || ge.value.contains("171/55") + || ge.value.contains("\\frac{171}{55}") + || ge.value.contains("72/55") + || ge.value.contains("\\frac{72}{55}"), "Ge={}", ge.value ); @@ -4240,6 +4366,39 @@ mod tests { ); } + + #[test] + fn contact_spieker_radius_kosnita() { + // 3-4-5: contact pts; |IX_*|=r=1; r_Sp=1/2; Kosnita skipped (O on AB). + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + assert!(["X_a", "X_b", "X_c"].iter().all(|lab| fs.iter().any(|f| f.group == "接触三角形" && f.label == *lab))); + let ix = fs.iter().find(|f| f.group == "接触三角形" && f.label == "|IX_*|").expect("|IX_*|"); + assert!((ix.num.unwrap() - 1.0).abs() < 1e-9, "|IX_*|={}", ix.value); + assert!(fs.iter().any(|f| f.group == "接触三角形" && f.value.contains("共线"))); + let rsp = fs.iter().find(|f| f.group == "斯皮克圆" && f.label.contains("Sp")).expect("r_Sp"); + assert!((rsp.num.unwrap() - 0.5).abs() < 1e-9, "r_Sp={}", rsp.value); + assert!(fs.iter().any(|f| f.group == "斯皮克圆" && f.label.contains("中点"))); + assert!( + fs.iter().all(|f| f.group != "科斯尼塔点"), + "Kosnita should be skipped on right 3-4-5" + ); + + // Acute 6-7-8: Kosnita present. + let k2 = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let ko = fs2.iter().find(|f| f.group == "科斯尼塔点" && f.label == "Ko").expect("Ko on 6-7-8"); + assert!(ko.value.contains("4.5") || ko.value.contains("1.8") || ko.value.contains("\\frac"), "Ko={}", ko.value); + let rsp2 = fs2.iter().find(|f| f.group == "斯皮克圆" && f.label.contains("Sp")).unwrap(); + // r = Δ/s; for 6-7-8, s=10.5, Δ=sqrt(10.5·4.5·3.5·2.5)=21*sqrt(3)/4? + // r_Sp = r/2 > 0 + assert!(rsp2.num.unwrap() > 0.0); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index ec70a56cbbd579c1a82720698e4c8497253eddda..f1a84682b509502b68522f03d042b198d883c153 100644 GIT binary patch delta 74822 zcmd4430z&p`8R&goUkP27j13r-r7`KZEfxE*S@`2 z(V|9+9^xU2=0Z?WQPH5FqLPRa4H}|}qM{O|ii%1!RZ_9O-)Cmdx#wOkg!b+K^ZCb? zIcLr+&ph)y&pgjF&&)k|_3Wc{vm4)xnOOBgyJu3s!%JV-`CiO0%lPPt>?`8l>tXto zfcEE=f12gtgA>i8@y4tSBW6P>{nLtBqQUZYueUVLXV8SAuz5Le}Jtn9Y3P zaGQsx@GmIQ+2YsB&j?SjoH zKrK~h-ZQd{7-VXjmovaX-F%d=DB$X*39ax{@oDo0&G7N3C?lKqQj+MsOJnP)i)#GKYVmoIkzeC4qL%WFr8WNL`0g(@it%TMf5l4O zFtTDWWhm-1me(3ZhG+oaR<6{inv*8w13g^{n~izEltfg=hrmQ8f1MIZ5j0ivcs*e# zlL!Bfgr-X35U4{ju6fIJnw0|yz9hDu{-d|91g>oY1^JEK9llkR)1Bat}R20?K}*JYhNOqxab5te4WH<*bMD*>cuR zDGk9zhNF;CNAyYT3M51)-_6FVNVIel7D8xQ#b2R}4E`Y{S!1Ckgb>YGVXO%HR%6B% 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e5825743ad3af958591cda52c64408099f20c63b Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 15:54:06 +0800 Subject: [PATCH 019/123] feat: extouch triangle, Steiner and Mandart inellipses; Nagel Ceva --- crates/mathcore/src/geometry.rs | 185 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 594553 -> 599683 bytes 2 files changed, 185 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index ee7b470..a5eed43 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -1484,6 +1484,152 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // Extouch (excircle-contact / Nagel) triangle: A-excircle touches BC at T_a, etc. + // BT_a = s−c, CT_a = s−b; perspector is the Nagel point (dual of the intouch △). + { + let sa = p - a; + let sb = p - b; + let sc = p - c; + if sa > 1e-12 && sb > 1e-12 && sc > 1e-12 { + // A-excircle on BC: BT:TC = (s−c):(s−b) + let ta = section_point(pb, pc, sc, sb); + let tb = section_point(pc, pa, sa, sc); + let tc = section_point(pa, pb, sb, sa); + let pts = [(ta, "a"), (tb, "b"), (tc, "c")]; + for (q, lab) in pts { + out.push(fact( + "旁切接触三角形", + &format!("T_{}", lab), + pt(q[0], q[1]), + None, + &format!("T_{s}\\text{{ on side }}{s}", s = lab), + "旁切圆与边的切点(旁切接触 / 奈格尔三角形顶点)", + ).with(Shape::Point { + x: q[0], + y: q[1], + label: format!("T{} 旁切点", lab), + })); + } + // Midpoint of intouch X_a and extouch T_a is the midpoint of BC (isotomic). + let xa = section_point(pb, pc, sb, sc); + let mid_xt = [(xa[0] + ta[0]) / 2.0, (xa[1] + ta[1]) / 2.0]; + let mid_bc = [(pb[0] + pc[0]) / 2.0, (pb[1] + pc[1]) / 2.0]; + if dist2(mid_xt, mid_bc) < 1e-5 * (1.0 + a) { + out.push(fact( + "旁切接触三角形", + "X_a T_a", + "\\text{以 BC 中点为中点}".into(), + None, + "\\text{mid}(X_a,T_a)=\\text{mid}(B,C)", + "内切切点与旁切切点关于边中点等截对称", + )); + } + // Perspector Na: A, T_a, Na collinear. + let na = [ + (sa * pa[0] + sb * pb[0] + sc * pc[0]) / p, + (sa * pa[1] + sb * pb[1] + sc * pc[1]) / p, + ]; + let cross = (ta[0] - pa[0]) * (na[1] - pa[1]) - (ta[1] - pa[1]) * (na[0] - pa[0]); + if cross.abs() < 1e-5 * (1.0 + dist2(pa, ta)) * (1.0 + dist2(pa, na)) { + out.push(fact( + "旁切接触三角形", + "A, T_a, Na", + "\\text{共线}".into(), + None, + "A T_a \\ni Na", + "旁切接触三角形与原三角形的透视中心为奈格尔点", + )); + } + } + } + + // Steiner inellipse: unique inscribed ellipse tangent at the side midpoints; center G. + // Area = π S / (3 √3); coincides with the incircle on equilateral triangles. + { + let ma = [(pb[0] + pc[0]) / 2.0, (pb[1] + pc[1]) / 2.0]; + let mb = [(pc[0] + pa[0]) / 2.0, (pc[1] + pa[1]) / 2.0]; + let mc = [(pa[0] + pb[0]) / 2.0, (pa[1] + pb[1]) / 2.0]; + for (q, lab) in [(ma, "a"), (mb, "b"), (mc, "c")] { + out.push(fact( + "施泰纳内接椭圆", + &format!("M_{}", lab), + pt(q[0], q[1]), + None, + &format!("M_{s} = \\text{{mid}}", s = lab), + "施泰纳内接椭圆在各边中点处与边相切", + ).with(Shape::Point { + x: q[0], + y: q[1], + label: format!("M{} 中点切", lab), + })); + } + let steiner_area = std::f64::consts::PI * area / (3.0 * 3.0f64.sqrt()); + out.push(fact( + "施泰纳内接椭圆", + "S_{\\text{Steiner}}", + nice(steiner_area), + Some(steiner_area), + "S_{\\text{Steiner}} = \\frac{\\pi S}{3\\sqrt{3}}", + "施泰纳内接椭圆:面积最大的内接椭圆,中心为重心 G", + ).with(Shape::Point { + x: centroid[0], + y: centroid[1], + label: "Steiner@G".into(), + })); + // Equilateral: Steiner = incircle ⇒ area = π r². + if (a - b).abs() < 1e-9 && (b - c).abs() < 1e-9 { + let circ_area = std::f64::consts::PI * r * r; + if (steiner_area - circ_area).abs() < 1e-5 * (1.0 + circ_area) { + out.push(fact( + "施泰纳内接椭圆", + "=\\pi r^2", + nice(circ_area), + Some(circ_area), + "\\text{equilateral: Steiner = incircle}", + "等边时施泰纳内接椭圆与内切圆重合", + )); + } + } + } + + // Mandart inellipse: inscribed ellipse tangent at the extouch points; center = Mittenpunkt. + { + let sa = p - a; + let sb = p - b; + let sc = p - c; + let wa = a * sa; + let wb = b * sb; + let wc = c * sc; + let den = wa + wb + wc; + if den > 1e-12 && sa > 1e-12 && sb > 1e-12 && sc > 1e-12 { + let mi = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "曼达特内接椭圆", + "\\text{center}", + pt(mi[0], mi[1]), + None, + "\\text{center} = \\text{Mi}", + "曼达特内接椭圆:在旁切切点处与边相切,中心为米滕点", + ).with(Shape::Point { + x: mi[0], + y: mi[1], + label: "Mandart@Mi".into(), + })); + out.push(fact( + "曼达特内接椭圆", + "T_*", + "\\text{切于旁切切点}".into(), + None, + "\\text{tangent at }T_a,T_b,T_c", + "与旁切接触三角形的三顶点处相切", + )); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -1553,6 +1699,16 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "\\frac{s-b}{s-c}\\cdot\\frac{s-c}{s-a}\\cdot\\frac{s-a}{s-b} = 1", "塞瓦定理:内切圆切点连线交于格尔巩点", )); + // Nagel / extouch: BD = s−c, DC = s−b (swap), product still 1. + let nag = (tc / tb) * (ta / tc) * (tb / ta); + out.push(fact( + "塞瓦与梅涅劳斯", + "\\Pi_{\\text{Ceva}}^{\\text{旁切}}", + nice(nag), + Some(nag), + "\\frac{s-c}{s-b}\\cdot\\frac{s-a}{s-c}\\cdot\\frac{s-b}{s-a} = 1", + "塞瓦定理:旁切圆切点连线交于奈格尔点", + )); } } @@ -4399,6 +4555,35 @@ mod tests { assert!(rsp2.num.unwrap() > 0.0); } + #[test] + fn extouch_steiner_mandart() { + // 3-4-5: extouch T_*; X_a/T_a midpoint = mid BC; A–T_a–Na; Steiner area; Mandart@Mi + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + assert!(["T_a", "T_b", "T_c"].iter().all(|lab| fs.iter().any(|f| f.group == "旁切接触三角形" && f.label == *lab))); + assert!(fs.iter().any(|f| f.group == "旁切接触三角形" && f.label.contains("X_a"))); + assert!(fs.iter().any(|f| f.group == "旁切接触三角形" && f.value.contains("共线"))); + let st = fs.iter().find(|f| f.group == "施泰纳内接椭圆" && f.label.contains("Steiner")).expect("Steiner area"); + let expect = std::f64::consts::PI * 6.0 / (3.0 * 3.0f64.sqrt()); + assert!((st.num.unwrap() - expect).abs() < 1e-9, "Steiner={} vs {}", st.value, expect); + assert!(["M_a", "M_b", "M_c"].iter().all(|lab| fs.iter().any(|f| f.group == "施泰纳内接椭圆" && f.label == *lab))); + let mi = fs.iter().find(|f| f.group == "米滕点" && f.label == "Mi").expect("Mi"); + let man = fs.iter().find(|f| f.group == "曼达特内接椭圆" && f.label.contains("center")).expect("Mandart"); + assert_eq!(man.value, mi.value, "Mandart center should equal Mittenpunkt"); + assert!(fs.iter().any(|f| f.group == "曼达特内接椭圆" && f.label.contains("T_"))); + let nag_ceva = fs.iter().find(|f| f.group == "塞瓦与梅涅劳斯" && f.label.contains("旁切")).expect("Nagel Ceva"); + assert!((nag_ceva.num.unwrap() - 1.0).abs() < 1e-9); + + // Equilateral: Steiner = incircle area π r² + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().any(|f| f.group == "施泰纳内接椭圆" && f.label.contains("pi r"))); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index f1a84682b509502b68522f03d042b198d883c153..fb8b9eb5e36db6a6aea45e0653cbffdaee360000 100644 GIT binary patch delta 68652 zcmc${3tU!3{y+YlIo$7xfLA!rlPHRK!@H@B5^8Gqwsx!S+tzlWZFlXvyX|*xV9`dU zg&pdkSv?{p86_t6U|FG&QJJApQBh)1QCU%0QBnThpP4!5IS=5a?|;9qzq>JK=FH_Y zpZVNp<~-k3jlAKdk+lcHW6IhZJ+Va|-u>3rkHUM{pyGFi-5B}9_e@VK(*8C3A18UZ zKi2#%inHPv^W^BEsomj){LmK-9-hd5phPpmIbQuPx=`yjcTP;9dY?s4aM!E*7WD?m zdbu%6WIdxerqCFf^mi1yy6mB<@v>@NOg^fvzBJR|52_uhHC}!9>Zs3Zt%{clF}ISw7B#|r4fZmD zW6Vswn$j6Fbw8yuXX+J5dGs_^PWgywtc=q5X^iS~HjR~1O0&UC%!7Y1%$B%R!orGi zg9OyGdPCjX9faD5A5zpm)IoSPV}>!q@11RA8xxGle&5M{uVKtIX8OHzjIqWzBggNX z>-T!)bbJv!s*rnfJhy+BH_PKOBDiOa=ce!SrsG+nI;qf?ASXLZOm??|q*dXuhGEQJ@8yQqn6utH-!Sq$ z;$KwW2JZsH>&oR5_(=e_O#2<7QX29K)cC$J$ 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(acute), Yff center, Exeter point with perspector note --- crates/mathcore/src/geometry.rs | 136 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 599683 -> 601998 bytes 2 files changed, 136 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index a5eed43..f8641b9 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -1630,6 +1630,111 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // Clawson point X(19): bary tan A : tan B : tan C. + // Undefined / at infinity on right △ (tan → ∞); emit only for acute triangles. + { + let cosines = [g[0].cos(), g[1].cos(), g[2].cos()]; + let acute = cosines.iter().all(|&c| c > 1e-9) + && g.iter().all(|&ang| ang > 1e-9 && ang < std::f64::consts::FRAC_PI_2 - 1e-9); + if acute { + let wa = g[0].tan(); + let wb = g[1].tan(); + let wc = g[2].tan(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let cl = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "克劳森点", + "Cl", + pt(cl[0], cl[1]), + None, + "Cl = \\frac{\\tan A\\,A+\\tan B\\,B+\\tan C\\,C}{\\sum}", + "克劳森点 X(19):锐角三角形中 tan A:tan B:tan C(直角时退化)", + ).with(Shape::Point { + x: cl[0], + y: cl[1], + label: "Cl 克劳森".into(), + })); + } + } + } + + // First Yff center of congruence X(174): bary sec A : sec B : sec C = 1/cos. + // Skip when any cos ≈ 0 (right / near-right △). + { + let cosines = [g[0].cos(), g[1].cos(), g[2].cos()]; + if cosines.iter().all(|&c| c.abs() > 1e-9) { + let wa = 1.0 / cosines[0]; + let wb = 1.0 / cosines[1]; + let wc = 1.0 / cosines[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let yff = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "伊夫中心", + "Yff", + pt(yff[0], yff[1]), + None, + "Yff = \\frac{\\sec A\\,A+\\sec B\\,B+\\sec C\\,C}{\\sum}", + "伊夫中心 X(174):sec A:sec B:sec C(直角时 sec 无定义)", + ).with(Shape::Point { + x: yff[0], + y: yff[1], + label: "Yff 伊夫".into(), + })); + } + } + } + + // Exeter point X(22): perspector of tangential and circummedial triangles; + // bary a(b⁴+c⁴−a⁴) : b(c⁴+a⁴−b⁴) : c(a⁴+b⁴−c⁴). + { + let a2 = a * a; + let b2 = b * b; + let c2 = c * c; + let a4 = a2 * a2; + let b4 = b2 * b2; + let c4 = c2 * c2; + let wa = a * (b4 + c4 - a4); + let wb = b * (c4 + a4 - b4); + let wc = c * (a4 + b4 - c4); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let ex = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "埃克塞特点", + "Ex", + pt(ex[0], ex[1]), + None, + "Ex = \\frac{a(b^4+c^4-a^4)A+\\cdots}{\\sum}", + "埃克塞特点 X(22):切线三角形与外接中点三角形的透视中心", + ).with(Shape::Point { + x: ex[0], + y: ex[1], + label: "Ex 埃克塞特".into(), + })); + // Perspector helper: name the classical pair. + out.push(fact( + "埃克塞特点", + "\\text{perspector}", + "\\text{tangential}/\\text{circummedial}".into(), + None, + "\\text{perspector}(\\triangle_{\\text{tang}},\\triangle_{\\text{cm}})", + "透视中心:切线三角形与外接中点三角形", + )); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -4584,6 +4689,37 @@ mod tests { assert!(fs2.iter().any(|f| f.group == "施泰纳内接椭圆" && f.label.contains("pi r"))); } + #[test] + fn clawson_yff_exeter() { + // Right 3-4-5: Clawson & Yff skipped (tan/sec undefined); Exeter present. + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + assert!(fs.iter().all(|f| f.group != "克劳森点"), "Clawson must skip right △"); + assert!(fs.iter().all(|f| f.group != "伊夫中心"), "Yff must skip right △"); + let ex = fs.iter().find(|f| f.group == "埃克塞特点" && f.label == "Ex").expect("Exeter on 3-4-5"); + assert!(ex.value.contains("\\left") || ex.value.contains("(") || ex.value.contains("\\frac"), "Ex={}", ex.value); + assert!(fs.iter().any(|f| f.group == "埃克塞特点" && f.label.contains("perspector"))); + + // Acute 6-7-8: all three present. + let k2 = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let cl = fs2.iter().find(|f| f.group == "克劳森点" && f.label == "Cl").expect("Clawson on 6-7-8"); + let yff = fs2.iter().find(|f| f.group == "伊夫中心" && f.label == "Yff").expect("Yff on 6-7-8"); + let ex2 = fs2.iter().find(|f| f.group == "埃克塞特点" && f.label == "Ex").expect("Exeter on 6-7-8"); + assert!(cl.value.contains("\\left") || cl.value.contains("("), "Cl={}", cl.value); + assert!(yff.value.contains("\\left") || yff.value.contains("("), "Yff={}", yff.value); + assert!(ex2.value.contains("\\left") || ex2.value.contains("("), "Ex={}", ex2.value); + // Distinct from each other and from G on a scalene acute △. + let g = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + assert_ne!(cl.value, yff.value); + assert_ne!(cl.value, ex2.value); + assert_ne!(yff.value, g.value); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index fb8b9eb5e36db6a6aea45e0653cbffdaee360000..4c7f102200dfb2bbd64f3113df6a1c962e8b3f5c 100644 GIT binary patch delta 52790 zcmb?^3s_Y}*FSsq;U>3(BB%)LbG!ixiV6r`x1xgPrJJSQ?`2oJz4g8oRA^LW)?kB1 z2}p@WiAf$RQdBHTGAt@eOe`!cDoiRXs{e1z-us+`+53Ip^ZehQm%V4rteG`y)>^aH zn%Tz(-y6RA@bK!xzWwTtH24JN`skHMwjJ~BWuXVZiC*dd@k6Q_m8;x0jh_gZ6z|mR zdHxQE#zw0?4yWd;=k;5zIkZ?UF3U&$uYG!XdAV~KKQk~+8OB!x4vrdL>Kx&zbd1!T zvI|}osQEcGN2$ZX?a2x8Bej?^=O}HY7F*_w$77@xSLRGWXC|(XkG;figENs2>KCUZ z@=5(B*c=-jqX}0T!Pfyeg1^>pS?(BZOu43xR^y#XT2gtb(?JEhGnpPf&aq|AaphXF zmMq&0a;9i0Xp^Xo)y9-L$CqnkwB$191Qf^01_92A+C(%+EiWxa-9#;=%$Zh>>J%-h 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zFcX09+<*b_y+M6%ifrrR8#cubzISiXk(**GNu_R)zqjd^t<+!FBDI@b|+Ay%@^ApUC|9k~T-bi9u2zrjiAc#FpUCZ37N zx@B|j&r&gB>bjbH|ld+3=ZlG z%qDaoVwPtbVqR=#Ax2S5S8!XjZEeyOBAs_LEfHhfl(<`T;aZZ|ceRCq^Og592AsUDe3Wl-k8FLQU^XC0+c&LrOb0bGG<% z#6e)-x5DxE_~bbIwB)$>dG>mwa|=H2Os#_bLac#ZnmHxv)x{VZ?3b^r7tSoN?%_w( IJsK7NFDc6ny#N3J From e3459c099ad66e6c5448fec63bd0f3a2abc34025 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 15:56:40 +0800 Subject: [PATCH 021/123] =?UTF-8?q?feat:=20isodynamic/Apollonian=20X15?= =?UTF-8?q?=E2=80=9316,=20Steiner=20X99,=20Tarry=20X98=20antipode?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- crates/mathcore/src/geometry.rs | 166 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 601998 -> 604803 bytes 2 files changed, 166 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index f8641b9..f1d9824 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -1735,6 +1735,133 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // Isodynamic / isogonic centers X(15), X(16): concurrence of Apollonian circles. + // Bary a sin(A±π/3); X(16) degenerates on equilateral (sin(A−π/3)=0). + { + let pi3 = std::f64::consts::PI / 3.0; + let s15 = [((g[0] + pi3).sin()), (g[1] + pi3).sin(), (g[2] + pi3).sin()]; + let wa = a * s15[0]; + let wb = b * s15[1]; + let wc = c * s15[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let p15 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "等动力点", + "S_{1}", + pt(p15[0], p15[1]), + None, + "S_1 = \\frac{a\\sin(A+\\pi/3)A+\\cdots}{\\sum}", + "第一等动力点 X(15)(等角线中心 / Apollonian)", + ).with(Shape::Point { + x: p15[0], + y: p15[1], + label: "S1 等动力".into(), + })); + } + let s16 = [(g[0] - pi3).sin(), (g[1] - pi3).sin(), (g[2] - pi3).sin()]; + // Equilateral: sin(A−π/3)=0 ⇒ den=0 — skip. One 60° angle (weight 0) is fine. + { + let wa = a * s16[0]; + let wb = b * s16[1]; + let wc = c * s16[2]; + let den16 = wa + wb + wc; + if den16.abs() > 1e-12 { + let p16 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den16, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den16, + ]; + out.push(fact( + "等动力点", + "S_{2}", + pt(p16[0], p16[1]), + None, + "S_2 = \\frac{a\\sin(A-\\pi/3)A+\\cdots}{\\sum}", + "第二等动力点 X(16)(等角线中心)", + ).with(Shape::Point { + x: p16[0], + y: p16[1], + label: "S2 等动力".into(), + })); + } + } + if den.abs() > 1e-12 { + out.push(fact( + "等动力点", + "\\text{Apollonius}", + "\\text{三阿氏圆共点}".into(), + None, + "\\odot A_a\\cap\\odot A_b\\cap\\odot A_c", + "阿波罗尼奥斯圆(角平分线直径)交于等动力点", + )); + } + } + + // Steiner point X(99): bary 1/(b²−c²):… on circumcircle ∩ Steiner ellipse. + // Undefined for isosceles (denominator zero); skip cleanly. + // Tarry X(98) = circumcircle antipode of Steiner (= 2O − St). + { + let dbc = b * b - c * c; + let dca = c * c - a * a; + let dab = a * a - b * b; + if dbc.abs() > 1e-10 && dca.abs() > 1e-10 && dab.abs() > 1e-10 { + let wa = 1.0 / dbc; + let wb = 1.0 / dca; + let wc = 1.0 / dab; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let st = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + let os = dist2(circ, st); + if (os - rr).abs() < 1e-4 * (1.0 + rr) { + out.push(fact( + "施泰纳点", + "St", + pt(st[0], st[1]), + None, + "St = \\frac{\\frac{1}{b^2-c^2}A+\\cdots}{\\sum}", + "施泰纳点 X(99):外接圆与施泰纳椭圆的第四交点", + ).with(Shape::Point { + x: st[0], + y: st[1], + label: "St 施泰纳".into(), + })); + // Tarry = antipode of Steiner on (O) + let ty = [2.0 * circ[0] - st[0], 2.0 * circ[1] - st[1]]; + let ot = dist2(circ, ty); + if (ot - rr).abs() < 1e-4 * (1.0 + rr) { + out.push(fact( + "塔里点", + "Ty", + pt(ty[0], ty[1]), + None, + "Ty = 2O - St", + "塔里点 X(98):施泰纳点在外接圆上的对径点", + ).with(Shape::Point { + x: ty[0], + y: ty[1], + label: "Ty 塔里".into(), + })); + out.push(fact( + "塔里点", + "|O\\,Ty|", + nice(ot), + Some(ot), + "|O\\,Ty| = R", + "塔里点在外接圆上", + )); + } + } + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -4720,6 +4847,45 @@ mod tests { assert_ne!(yff.value, g.value); } + #[test] + fn isodynamic_steiner_tarry() { + // Scalene right 3-4-5: S1,S2,St,Ty all present (not isosceles). + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let s1 = fs.iter().find(|f| f.group == "等动力点" && f.label.contains("S_{1}")).expect("S1"); + let s2 = fs.iter().find(|f| f.group == "等动力点" && f.label.contains("S_{2}")).expect("S2"); + assert_ne!(s1.value, s2.value); + assert!(fs.iter().any(|f| f.group == "等动力点" && f.label.contains("Apollonius"))); + let st = fs.iter().find(|f| f.group == "施泰纳点" && f.label == "St").expect("Steiner"); + let ty = fs.iter().find(|f| f.group == "塔里点" && f.label == "Ty").expect("Tarry"); + assert_ne!(st.value, ty.value); + let ot = fs.iter().find(|f| f.group == "塔里点" && f.label.contains("O")).expect("|O Ty|"); + let rr = fs.iter().find(|f| f.group == "外接圆与内切圆" && f.label == "R").expect("R"); + assert!((ot.num.unwrap() - rr.num.unwrap()).abs() < 1e-6, "Tarry on circumcircle"); + + // Isosceles 5-5-6: Steiner/Tarry skipped; isodynamic present. + let k2 = TriangleKnown { a: Some(6.0), b: Some(5.0), c: Some(5.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().all(|f| f.group != "施泰纳点"), "Steiner skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "塔里点"), "Tarry skip with Steiner"); + assert!(fs2.iter().any(|f| f.group == "等动力点" && f.label.contains("S_{1}"))); + + // Equilateral: S2 skipped; S1 coincides with G; Steiner skipped. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.group != "施泰纳点")); + assert!(fs3.iter().all(|f| !(f.group == "等动力点" && f.label.contains("S_{2}"))), "S2 skip equilateral"); + let s1e = fs3.iter().find(|f| f.group == "等动力点" && f.label.contains("S_{1}")).expect("S1 eq"); + let g = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + assert_eq!(s1e.value, g.value, "equilateral S1 = G"); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 4c7f102200dfb2bbd64f3113df6a1c962e8b3f5c..bdc591b676f39760b1d050b43e5156031ee06ea4 100644 GIT binary patch delta 76635 zcmcG13w&Ku_WwQmHfi3ECTaRi&%J#m=`*ECnwEA~-xM`o4V?=^dtM8efDGR zwbxpEt+m(Q=bAUCT=wad`Zwc}!tb~Gl0!aO`Tl($#0`q9{?Er>KJr7`@6QbxmoEDK 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[PATCH 022/123] =?UTF-8?q?feat:=20Napoleon=20centers=20X17?= =?UTF-8?q?=E2=80=9318,=20Parry=20X111,=20Vecten=20X485=E2=80=93486?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- crates/mathcore/src/geometry.rs | 201 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 604803 -> 608266 bytes 2 files changed, 201 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index f1d9824..1c8a0ce 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -1862,6 +1862,165 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // Napoleon centers X(17), X(18): concurrence of lines to centroids of + // outward/inward equilateral triangles on the sides (distinct from Napoleon theorem). + { + let pi6 = std::f64::consts::PI / 6.0; + // X(17) outer: bary a csc(A+π/6); skip if sin(A+π/6)≈0 (e.g. angle ≈ 150°). + let s17 = [(g[0] + pi6).sin(), (g[1] + pi6).sin(), (g[2] + pi6).sin()]; + if s17.iter().all(|&s| s.abs() > 1e-9) { + let wa = a / s17[0]; + let wb = b / s17[1]; + let wc = c / s17[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let n1 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "拿破仑中心", + "N_1", + pt(n1[0], n1[1]), + None, + "N_1 = \\frac{a\\csc(A+\\pi/6)A+\\cdots}{\\sum}", + "第一拿破仑点 X(17):外接等边三角形重心连线交点", + ).with(Shape::Point { + x: n1[0], + y: n1[1], + label: "N1 拿破仑".into(), + })); + } + } + // X(18) inner: bary a csc(A−π/6); skip if sin(A−π/6)≈0 (angle ≈ 30°). + let s18 = [(g[0] - pi6).sin(), (g[1] - pi6).sin(), (g[2] - pi6).sin()]; + if s18.iter().all(|&s| s.abs() > 1e-9) { + let wa = a / s18[0]; + let wb = b / s18[1]; + let wc = c / s18[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let n2 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "拿破仑中心", + "N_2", + pt(n2[0], n2[1]), + None, + "N_2 = \\frac{a\\csc(A-\\pi/6)A+\\cdots}{\\sum}", + "第二拿破仑点 X(18):内接等边三角形重心连线交点", + ).with(Shape::Point { + x: n2[0], + y: n2[1], + label: "N2 拿破仑".into(), + })); + } + } + } + + // Parry point X(111): bary a²/(2a²−b²−c²); on circumcircle. + // Degenerate when 2a²=b²+c² for any side (e.g. equilateral). + { + let da = 2.0 * a * a - b * b - c * c; + let db = 2.0 * b * b - c * c - a * a; + let dc = 2.0 * c * c - a * a - b * b; + if da.abs() > 1e-10 && db.abs() > 1e-10 && dc.abs() > 1e-10 { + let wa = (a * a) / da; + let wb = (b * b) / db; + let wc = (c * c) / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let py = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "帕里点", + "Py", + pt(py[0], py[1]), + None, + "Py = \\frac{\\frac{a^2}{2a^2-b^2-c^2}A+\\cdots}{\\sum}", + "帕里点 X(111):Λ(G,K)(等边时退化)", + ).with(Shape::Point { + x: py[0], + y: py[1], + label: "Py 帕里".into(), + })); + let op = dist2(circ, py); + if (op - rr).abs() < 1e-4 * (1.0 + rr) { + out.push(fact( + "帕里点", + "|O\\,Py|", + nice(op), + Some(op), + "|O\\,Py| = R", + "帕里点在外接圆上", + )); + } + } + } + } + + // Vecten points: perspectors of outer/inner square-center triangles. + // X(485) outer: bary a sec(A−π/4); skip if cos(A−π/4)≈0 (angle ≈ 135°). + // X(486) inner: bary a sec(A+π/4); skip if cos(A+π/4)≈0 (angle ≈ 45°). + { + let pi4 = std::f64::consts::FRAC_PI_4; + let c_out = [(g[0] - pi4).cos(), (g[1] - pi4).cos(), (g[2] - pi4).cos()]; + if c_out.iter().all(|&c| c.abs() > 1e-9) { + let wa = a / c_out[0]; + let wb = b / c_out[1]; + let wc = c / c_out[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let vo = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "韦克滕点", + "V_{\\text{out}}", + pt(vo[0], vo[1]), + None, + "V_{\\text{out}} = \\frac{a\\sec(A-\\pi/4)A+\\cdots}{\\sum}", + "外韦克滕点 X(485):外侧正方形中心三角形的透视中心", + ).with(Shape::Point { + x: vo[0], + y: vo[1], + label: "Vout 韦克滕".into(), + })); + } + } + let c_in = [(g[0] + pi4).cos(), (g[1] + pi4).cos(), (g[2] + pi4).cos()]; + if c_in.iter().all(|&c| c.abs() > 1e-9) { + let wa = a / c_in[0]; + let wb = b / c_in[1]; + let wc = c / c_in[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let vi = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "韦克滕点", + "V_{\\text{in}}", + pt(vi[0], vi[1]), + None, + "V_{\\text{in}} = \\frac{a\\sec(A+\\pi/4)A+\\cdots}{\\sum}", + "内韦克滕点 X(486):内侧正方形中心三角形的透视中心", + ).with(Shape::Point { + x: vi[0], + y: vi[1], + label: "Vin 韦克滕".into(), + })); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -4886,6 +5045,48 @@ mod tests { assert_eq!(s1e.value, g.value, "equilateral S1 = G"); } + #[test] + fn napoleon_parry_vecten() { + // Scalene 3-4-5: all present (no 30°/45°/135°/150°; not equilateral). + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let n1 = fs.iter().find(|f| f.group == "拿破仑中心" && f.label == "N_1").expect("N1"); + let n2 = fs.iter().find(|f| f.group == "拿破仑中心" && f.label == "N_2").expect("N2"); + assert_ne!(n1.value, n2.value); + let py = fs.iter().find(|f| f.group == "帕里点" && f.label == "Py").expect("Parry"); + let op = fs.iter().find(|f| f.group == "帕里点" && f.label.contains("O")).expect("|O Py|"); + let rr = fs.iter().find(|f| f.group == "外接圆与内切圆" && f.label == "R").expect("R"); + assert!((op.num.unwrap() - rr.num.unwrap()).abs() < 1e-6, "Parry on circumcircle"); + let vout = fs.iter().find(|f| f.group == "韦克滕点" && f.label.contains("out")).expect("Vout"); + let vin = fs.iter().find(|f| f.group == "韦克滕点" && f.label.contains("in")).expect("Vin"); + assert_ne!(vout.value, vin.value); + assert_ne!(py.value, n1.value); + + // Equilateral: Parry skipped; Napoleon + Vecten present; N1=N2=G. + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().all(|f| f.group != "帕里点"), "Parry skip equilateral"); + let n1e = fs2.iter().find(|f| f.group == "拿破仑中心" && f.label == "N_1").expect("N1 eq"); + let n2e = fs2.iter().find(|f| f.group == "拿破仑中心" && f.label == "N_2").expect("N2 eq"); + let g = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + assert_eq!(n1e.value, g.value); + assert_eq!(n2e.value, g.value); + assert!(fs2.iter().any(|f| f.group == "韦克滕点" && f.label.contains("out"))); + + // Isosceles right 1-1-√2 ≈ has 45°: inner Vecten skipped; outer ok; Parry ok. + let k3 = TriangleKnown { a: Some(1.0), b: Some(1.0), c: Some(2f64.sqrt()), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| !(f.group == "韦克滕点" && f.label.contains("in"))), "Vin skip 45°"); + assert!(fs3.iter().any(|f| f.group == "韦克滕点" && f.label.contains("out")), "Vout on isos right"); + assert!(fs3.iter().any(|f| f.group == "帕里点" && f.label == "Py")); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index bdc591b676f39760b1d050b43e5156031ee06ea4..21e692c7c7eec0d1b8e97d8107e7a60c8c193514 100644 GIT binary patch delta 44819 zcmb?^3w%w-^Y}e`&OJBpT;wGoZbFDhNIZfNta{a3tNJebpp9y)4{g7FBr1q^IANng zgCHd;m2iR}2!bFg)u^b@AczWrAo$Om*S%5g_xJmK{$KstGqXFhv$M0avvc+yQ*Sq$ zl^BwF*6dPtE#KrCYoZ0$vM!rziAA2@XqshHMpmU$eUVgDEcE<<)K*B7_IdfInQdm9 zdn8H4(o9p$F_EOg8J_&4;jj2e*`9qHXJZ8)Nw6u6zr5R|wx(Pp$uLVR-g(706KbF? 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zzC>|fSoV4f|0dDXA)h}kx8!WE}B z0jXz@o7Zc}m%+ZN?{#lm%i@{hxutfS5cA>v~ zD~g|YgH;2{Eb?*-zi;6^7T#;&eLlwENw`u~Tqk-q)8~9vb?#g7LzCvoH=WuvyvtL1 z?wS}*arMHk-?&N6A4I%2`OjuArz1uaY3QnqsTuk1R6KhuGHZ_(LC(D?^QLFv+hDrK zm%9=&9tBc1-ILE_L90PJMxr(&XPU=7GmWnOAWrDN{ep@fVnS7ZK@T_%{*s2(G(rt=)gfB2-!0ga6@N2*y;isb(-mY5qNQBwEabICn zBTPWZMeri5MA(jS2;mIE6@)s3dW5G4&VP4moe^F_h)4J>LLtIIgc^iegog+X2>LCj z=0fO(&<9~KLLx#YLe4GcP;D_D2%!w&1j2QMuMmDj(D*G7S|bcgo1W$N;B1xQPEX5A zOP}VM?dH!vXzN*7cgXV?A90u6q4LM@qxbL7gU2{8G_57)6A__D)>7OPeEB+COEqBE zgIcF=h;2iQ@X&+YXb{nfUF)2_b>?4?#_Nq_-d^$?kj(kq3iEw&XNB+LnOnPST~$$o z*x$@0Gro?I!y97=#{5lOw&})$wQggyYr+GkZ_46=#pehoJXkx=c&x|$g$is&PmarN zMnv27UQDAE<~14iga>@U^1E;{S&2LMIhZQ*NzH#IhAsL zLtdsN53ukDf&5g`+=$Z4A5jfrm(>5t{{l#N+KuQyy}jWQ)q0}AYCYK&t_6=)?05(s z;bSVXquwKrsm6|BgZO7ZM+O=3%$^{lzh3-=4h0!++gmm`H8=A0ZlD3dMxtvvnBCL@ z#JoS;&_Fwbjj*0Fz1lCYLCp4T@W-+4Uyj@j4ONeVjaZxO=3mX*^Q~C=x~^9xsxTY3NWQQjOe!Spd4OR z*C2*-*9bAcOxaVabQnXzJ^{0z{S-0V^H;>YI@^9WS8M3CaT*=kO1(&=^TDSKdgwRp z(N8qSX+*p7klq>0OB4^^yq~K|oW`AIt~9-c@1}DU64~%HotCvmFYME+su6e7Z+E8$ zub>;6_MpfCMr_2e9xZ%toQyaO8TgBGhC3r?ihEkll#BxRGNkhxB=?}=0Y-# Date: Sun, 1 Nov 2026 15:59:02 +0800 Subject: [PATCH 023/123] =?UTF-8?q?feat:=20Hofstadter=20X359=E2=80=93360,?= =?UTF-8?q?=20Kenmotu=20X371,=20Apollonius=20X181,=20Brocard=20midpoint?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- crates/mathcore/src/geometry.rs | 171 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 608266 -> 611149 bytes 2 files changed, 171 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 1c8a0ce..7f68560 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -1100,6 +1100,20 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] y: omp[1], label: "Ω′ 布罗卡".into(), })); + // Brocard midpoint X(39) = midpoint(Ω, Ω′); center of Brocard circle. + let bm = [(om[0] + omp[0]) / 2.0, (om[1] + omp[1]) / 2.0]; + out.push(fact( + "布罗卡", + "X_{39}", + pt(bm[0], bm[1]), + None, + "X_{39} = \\text{mid}(\\Omega,\\Omega')", + "布罗卡中点:第一/第二布罗卡点的中点(布罗卡圆圆心)", + ).with(Shape::Point { + x: bm[0], + y: bm[1], + label: "X39 布罗卡中点".into(), + })); } } @@ -2021,6 +2035,126 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // Hofstadter points X(359), X(360): transcendental centers (angles in barycentrics). + // X(360) zero-point: bary A:B:C; X(359) one-point: bary a²/A:b²/B:c²/C. + { + if g[0] > 1e-12 && g[1] > 1e-12 && g[2] > 1e-12 { + let den0 = g[0] + g[1] + g[2]; + let hz = [ + (g[0] * pa[0] + g[1] * pb[0] + g[2] * pc[0]) / den0, + (g[0] * pa[1] + g[1] * pb[1] + g[2] * pc[1]) / den0, + ]; + out.push(fact( + "霍夫斯塔特点", + "Hf_0", + pt(hz[0], hz[1]), + None, + "Hf_0 = (A:B:C)", + "霍夫斯塔特零点 X(360):重心坐标为三角本身", + ).with(Shape::Point { + x: hz[0], + y: hz[1], + label: "Hf0 霍夫".into(), + })); + let wa = (a * a) / g[0]; + let wb = (b * b) / g[1]; + let wc = (c * c) / g[2]; + let den1 = wa + wb + wc; + if den1.abs() > 1e-12 { + let ho = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den1, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den1, + ]; + out.push(fact( + "霍夫斯塔特点", + "Hf_1", + pt(ho[0], ho[1]), + None, + "Hf_1 = (a^2/A:b^2/B:c^2/C)", + "霍夫斯塔特一点 X(359):与 Hf_0 互为等角共轭", + ).with(Shape::Point { + x: ho[0], + y: ho[1], + label: "Hf1 霍夫".into(), + })); + } + } + } + + // Kenmotu point X(371): congruent-squares point; bary a cos(A−π/4). + // Isogonal conjugate of outer Vecten X(485). + { + let pi4 = std::f64::consts::FRAC_PI_4; + let ca = [(g[0] - pi4).cos(), (g[1] - pi4).cos(), (g[2] - pi4).cos()]; + let wa = a * ca[0]; + let wb = b * ca[1]; + let wc = c * ca[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let km = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "肯莫图点", + "Km", + pt(km[0], km[1]), + None, + "Km = \\frac{a\\cos(A-\\pi/4)A+\\cdots}{\\sum}", + "肯莫图点 X(371):三全等正方形的公共点(等角共轭于外韦克滕点)", + ).with(Shape::Point { + x: km[0], + y: km[1], + label: "Km 肯莫图".into(), + })); + let edge_den = a * a + b * b + c * c + 4.0 * area; + if edge_den > 1e-12 { + let edge = std::f64::consts::SQRT_2 * a * b * c / edge_den; + out.push(fact( + "肯莫图点", + "s_{\\text{square}}", + nice(edge), + Some(edge), + "s = \\frac{\\sqrt{2}\\,abc}{a^2+b^2+c^2+4S}", + "三全等正方形的边长", + )); + } + } + } + + // Apollonius point X(181): perspector of Apollonius circle with the excircles. + // Bary a²(b+c)²/(b+c−a); b+c−a=2(s−a)>0 for non-degenerate △. + { + let sa = p - a; + let sb = p - b; + let sc = p - c; + if sa > 1e-12 && sb > 1e-12 && sc > 1e-12 { + let wa = (a * a) * (b + c) * (b + c) / (2.0 * sa); + let wb = (b * b) * (c + a) * (c + a) / (2.0 * sb); + let wc = (c * c) * (a + b) * (a + b) / (2.0 * sc); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let ap = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "阿波罗尼奥斯点", + "Ap", + pt(ap[0], ap[1]), + None, + "Ap = \\frac{a^2(b+c)^2/(b+c-a)\\,A+\\cdots}{\\sum}", + "阿波罗尼奥斯点 X(181):与三旁切圆外切的阿氏圆的透视中心", + ).with(Shape::Point { + x: ap[0], + y: ap[1], + label: "Ap 阿氏".into(), + })); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -5087,6 +5221,43 @@ mod tests { assert!(fs3.iter().any(|f| f.group == "帕里点" && f.label == "Py")); } + #[test] + fn hofstadter_kenmotu_apollonius() { + // 3-4-5: Hofstadter, Kenmotu (+square edge), Apollonius, Brocard midpoint. + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let hf0 = fs.iter().find(|f| f.group == "霍夫斯塔特点" && f.label == "Hf_0").expect("Hf0"); + let hf1 = fs.iter().find(|f| f.group == "霍夫斯塔特点" && f.label == "Hf_1").expect("Hf1"); + assert_ne!(hf0.value, hf1.value); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + assert_ne!(hf0.value, g.value, "Hofstadter zero ≠ centroid on scalene"); + let km = fs.iter().find(|f| f.group == "肯莫图点" && f.label == "Km").expect("Kenmotu"); + let sq = fs.iter().find(|f| f.group == "肯莫图点" && f.label.contains("square")).expect("square edge"); + assert!(sq.num.unwrap() > 0.0); + let vout = fs.iter().find(|f| f.group == "韦克滕点" && f.label.contains("out")).expect("Vout"); + assert_ne!(km.value, vout.value, "Kenmotu ≠ outer Vecten (isogonal mates)"); + let ap = fs.iter().find(|f| f.group == "阿波罗尼奥斯点" && f.label == "Ap").expect("Apollonius"); + assert!(ap.value.contains("(") || ap.value.contains("\\left")); + assert!(fs.iter().any(|f| f.group == "布罗卡" && f.label.contains("39"))); + + // Equilateral: Hf0=Hf1=G; Kenmotu=G; Apollonius=G. + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g2 = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + let hf0e = fs2.iter().find(|f| f.group == "霍夫斯塔特点" && f.label == "Hf_0").unwrap(); + let hf1e = fs2.iter().find(|f| f.group == "霍夫斯塔特点" && f.label == "Hf_1").unwrap(); + assert_eq!(hf0e.value, g2.value); + assert_eq!(hf1e.value, g2.value); + let kme = fs2.iter().find(|f| f.group == "肯莫图点" && f.label == "Km").unwrap(); + assert_eq!(kme.value, g2.value); + let ape = fs2.iter().find(|f| f.group == "阿波罗尼奥斯点" && f.label == "Ap").unwrap(); + assert_eq!(ape.value, g2.value); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 21e692c7c7eec0d1b8e97d8107e7a60c8c193514..ac75ed5ee839dda9d8a00b5eed16512d7c5dc39e 100644 GIT binary patch delta 46304 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zUF%M~BU&`FW?nQ(bzY=`yZ9N;aAn#Ub<}etXi0k)JC^74KO;9SE$^}ae!JdZv z#735ONf}7zP3Nx&982c2CcC_3)^jM#SH_PiT!&}w=!|;z@kW+SjYFj3-{CZTN=C*U zf6Ea+{gvx9#AfLgvgo?qGevRH;#sQ};h%WeEWhgGZcs&lC6?o>0hSn!n+94s$B(;# z-i2%dLSqEUd%XIR`J@u)$)_oSmTs(n6tPR@k42uUZ-ap<^R}#Vpo#OqyjIHcMuT5h zn77b&3iB=ud!l^`J&_Ql2n2(T3f=A?OH$*6D>w0Th!Eg0;69bS7SAjwd7X*Z`fb_l(!lz_< zTP$;GJ@`rI2K8i__#(KMV#jrG4-eBB)TiJ2je^7A8His9GdMpC(*f)bvvk%^{7yH+ zEJfD7x9yq(dil3$VpB^}$W|~fLwgbPiSYDos&8tEik0biy!ioljHT{0nERunFA>vjcbkFcM(6XJK`uV5ySCP9OWlkI>x*g*TmE8GQ?3( z;7`eEj Date: Sun, 1 Nov 2026 16:01:24 +0800 Subject: [PATCH 024/123] =?UTF-8?q?feat:=20Fermat/isogonic=20X13=E2=80=931?= =?UTF-8?q?4,=20Feuerbach=20point=20X11,=20equal-detour/isoperimetric?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- crates/mathcore/src/geometry.rs | 259 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 611149 -> 616297 bytes 2 files changed, 259 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 7f68560..976a3b8 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -854,6 +854,43 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "九点圆与内切圆相切", )); } + // Feuerbach point X(11): internal contact of nine-point circle and incircle. + // T = ((R/2) I - r N) / (R/2 - r) along NI (order N–I–Fe). + // Skip when N=I (equilateral: nine-point coincides with incircle). + { + let den_f = r9 - r; + let ni_len = dist2(n9, inc); + if den_f.abs() > 1e-9 && ni_len > 1e-9 { + let fe = [ + (r9 * inc[0] - r * n9[0]) / den_f, + (r9 * inc[1] - r * n9[1]) / den_f, + ]; + let d_n = dist2(n9, fe); + let d_i = dist2(inc, fe); + if (d_n - r9).abs() < 1e-4 * (1.0 + r9) && (d_i - r).abs() < 1e-4 * (1.0 + r) { + out.push(fact( + "费尔巴哈点", + "Fe", + pt(fe[0], fe[1]), + None, + "Fe = \\dfrac{(R/2)I - r\\,N}{R/2 - r}", + "费尔巴哈点 X(11):九点圆与内切圆的内切点", + ).with(Shape::Point { + x: fe[0], + y: fe[1], + label: "Fe 费尔巴哈".into(), + })); + out.push(fact( + "费尔巴哈点", + "|N\\,Fe|", + nice(d_n), + Some(d_n), + "|N\\,Fe| = R/2", + "费尔巴哈点在九点圆上", + )); + } + } + } for i in 0..3 { let ri = area / (p - s[i]); // excenter I_i opposite vertex i: (-a_i V_i + a_j V_j + a_k V_k) / (-a_i + a_j + a_k) @@ -2155,6 +2192,181 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // Fermat–Torricelli / isogonic centers X(13), X(14) — distinct from isodynamic X(15)/X(16). + // Trilinear csc(A±π/3); bary a csc(A±π/3). If some angle ≥ 120°, X(13) is that vertex. + { + let pi3 = std::f64::consts::PI / 3.0; + let two_pi3 = 2.0 * pi3; + let mut obtuse120: Option = None; + for (i, &ang) in g.iter().enumerate() { + if ang >= two_pi3 - 1e-9 { + obtuse120 = Some(i); + break; + } + } + if let Some(i) = obtuse120 { + let fv = v[i]; + out.push(fact( + "费马点", + "F_1", + pt(fv[0], fv[1]), + None, + "F_1 = \\text{obtuse vertex (}\\ge 120^\\circ\\text{)}", + "第一费马–托里拆利点 X(13):钝角 ≥120° 时退化为该顶点", + ).with(Shape::Point { + x: fv[0], + y: fv[1], + label: "F1 费马".into(), + })); + } else { + let s13 = [(g[0] + pi3).sin(), (g[1] + pi3).sin(), (g[2] + pi3).sin()]; + if s13.iter().all(|&s| s.abs() > 1e-9) { + let wa = a / s13[0]; + let wb = b / s13[1]; + let wc = c / s13[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let f1 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "费马点", + "F_1", + pt(f1[0], f1[1]), + None, + "F_1 = \\frac{a\\csc(A+\\pi/3)A+\\cdots}{\\sum}", + "第一费马–托里拆利 / 等角线中心 X(13)(异于等动力点 X(15))", + ).with(Shape::Point { + x: f1[0], + y: f1[1], + label: "F1 费马".into(), + })); + } + } + } + // X(14) 2nd isogonic: skip equilateral (sin(A−π/3)=0). + let s14 = [(g[0] - pi3).sin(), (g[1] - pi3).sin(), (g[2] - pi3).sin()]; + // Guard: any near-zero sin → skip (equilateral / 60° singularity in csc form) + if s14.iter().all(|&s| s.abs() > 1e-9) { + let wa = a / s14[0]; + let wb = b / s14[1]; + let wc = c / s14[2]; + { + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let f2 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "费马点", + "F_2", + pt(f2[0], f2[1]), + None, + "F_2 = \\frac{a\\csc(A-\\pi/3)A+\\cdots}{\\sum}", + "第二等角线中心 X(14)(异于等动力点 X(16))", + ).with(Shape::Point { + x: f2[0], + y: f2[1], + label: "F2 费马".into(), + })); + } + } + } + // Helper: isogonic ≠ isodynamic (X13 isogonal conjugate of X15). + if out.iter().any(|f| f.group == "费马点" && f.label == "F_1") + && out.iter().any(|f| f.group == "等动力点" && f.label.contains("S_{1}")) + { + let f1v = out.iter().find(|f| f.group == "费马点" && f.label == "F_1").map(|f| f.value.clone()); + let s1v = out.iter().find(|f| f.group == "等动力点" && f.label.contains("S_{1}")).map(|f| f.value.clone()); + if let (Some(a), Some(b)) = (f1v, s1v) { + if a != b { + out.push(fact( + "费马点", + "F_1 \\ne S_1", + "\\text{isogonic} \\ne \\text{isodynamic}".into(), + None, + "X(13)=\\text{isogonal of }X(15)", + "等角线中心与等动力点不同(互为等角共轭)", + )); + } + } + } + } + + // Equal detour X(176) / isoperimetric X(175) (inner/outer Soddy centers). + // X(176): bary sin A · (1 + sec(A/2) cos(B/2) cos(C/2)); always for non-degen △. + // X(175): same with −1; emit only when a+b+c > 4R+r. + { + let ha = g[0] / 2.0; + let hb = g[1] / 2.0; + let hc = g[2] / 2.0; + let cos_ha = ha.cos(); + let cos_hb = hb.cos(); + let cos_hc = hc.cos(); + if cos_ha.abs() > 1e-12 && cos_hb.abs() > 1e-12 && cos_hc.abs() > 1e-12 { + let t176 = [ + 1.0 + cos_hb * cos_hc / cos_ha, + 1.0 + cos_hc * cos_ha / cos_hb, + 1.0 + cos_ha * cos_hb / cos_hc, + ]; + let wa = a * t176[0]; + let wb = b * t176[1]; + let wc = c * t176[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let ed = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "等迂回点", + "Ed", + pt(ed[0], ed[1]), + None, + "Ed = (\\sin A\\,(1+\\sec\\tfrac{A}{2}\\cos\\tfrac{B}{2}\\cos\\tfrac{C}{2}):\\cdots)", + "等迂回点 X(176):内苏迪圆圆心", + ).with(Shape::Point { + x: ed[0], + y: ed[1], + label: "Ed 等迂回".into(), + })); + } + // Isoperimetric / outer Soddy X(175) + if per > 4.0 * rr + r + 1e-9 { + let t175 = [ + -1.0 + cos_hb * cos_hc / cos_ha, + -1.0 + cos_hc * cos_ha / cos_hb, + -1.0 + cos_ha * cos_hb / cos_hc, + ]; + let wa = a * t175[0]; + let wb = b * t175[1]; + let wc = c * t175[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let ip = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "等周点", + "Ip", + pt(ip[0], ip[1]), + None, + "Ip = (\\sin A\\,(-1+\\sec\\tfrac{A}{2}\\cos\\tfrac{B}{2}\\cos\\tfrac{C}{2}):\\cdots)", + "等周点 X(175):外苏迪圆圆心(需 a+b+c>4R+r)", + ).with(Shape::Point { + x: ip[0], + y: ip[1], + label: "Ip 等周".into(), + })); + } + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -5258,6 +5470,53 @@ mod tests { assert_eq!(ape.value, g2.value); } + #[test] + fn fermat_feuerbach_point_detour() { + // 3-4-5: F1,F2 distinct from S1,S2; Fe on nine-point & incircle; Ed + Ip (12>4*2.5+1). + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let f1 = fs.iter().find(|f| f.group == "费马点" && f.label == "F_1").expect("F1"); + let f2 = fs.iter().find(|f| f.group == "费马点" && f.label == "F_2").expect("F2"); + assert_ne!(f1.value, f2.value); + let s1 = fs.iter().find(|f| f.group == "等动力点" && f.label.contains("S_{1}")).expect("S1"); + assert_ne!(f1.value, s1.value, "isogonic ≠ isodynamic"); + assert!(fs.iter().any(|f| f.group == "费马点" && f.label.contains("S_1"))); + let fe = fs.iter().find(|f| f.group == "费尔巴哈点" && f.label == "Fe").expect("Fe"); + let nfe = fs.iter().find(|f| f.group == "费尔巴哈点" && f.label.contains("N")).expect("|N Fe|"); + let r9 = fs.iter().find(|f| f.group == "欧拉线" && f.label.contains("九点")).expect("R9"); + assert!((nfe.num.unwrap() - r9.num.unwrap()).abs() < 1e-6); + let ed = fs.iter().find(|f| f.group == "等迂回点" && f.label == "Ed").expect("Ed"); + let ip = fs.iter().find(|f| f.group == "等周点" && f.label == "Ip").expect("Ip"); + assert_ne!(ed.value, ip.value); + assert_ne!(fe.value, ed.value); + + // Equilateral: F1=G; F2 skipped; Fe, Ed, Ip (=G for eq?). + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + let f1e = fs2.iter().find(|f| f.group == "费马点" && f.label == "F_1").unwrap(); + assert_eq!(f1e.value, g.value); + assert!(fs2.iter().all(|f| !(f.group == "费马点" && f.label == "F_2")), "F2 skip equilateral"); + assert!(fs2.iter().all(|f| f.group != "费尔巴哈点"), "Fe skip equilateral coincident circles"); + assert!(fs2.iter().any(|f| f.group == "等迂回点" && f.label == "Ed")); + + // Obtuse with angle > 120°: F1 at obtuse vertex. Sides 2,3,4: cos C=(4+9-16)/12 < 0, C>90; check C>120? + // 2²+3²=13 < 16, obtuse at C. cos C = (4+9-16)/12 = -3/12 = -0.25, C ≈ 104.5° < 120. + // Need stronger obtuse: sides 1,1,1.9 — almost flat apex. + let k3 = TriangleKnown { a: Some(1.0), b: Some(1.0), c: Some(1.9), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + // angle opposite c=1.9: cos C = (1+1-3.61)/2 = -1.61/2 = -0.805, C≈143.6° > 120 + let f1o = fs3.iter().find(|f| f.group == "费马点" && f.label == "F_1").expect("F1 obtuse"); + // F1 should be at C = verts[2] + assert!(f1o.why.contains("120") || f1o.how.contains("obtuse") || f1o.how.contains("120"), "why={}", f1o.why); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index ac75ed5ee839dda9d8a00b5eed16512d7c5dc39e..96fe70cc1f99c7758e20815385ffdb406d61adba 100644 GIT binary patch delta 96039 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zZUoGO7B}j0q1}yjUQnuE#?}!hxF;TVFFWb#L+Hj2251rOoUQH`BiqnZ1D$aqr420| z= Date: Sun, 1 Nov 2026 16:03:10 +0800 Subject: [PATCH 025/123] =?UTF-8?q?feat:=20Moses=20X75,=20orthic=E2=80=93t?= =?UTF-8?q?angential=20X25,=20orthic=20circumcenter=20=3D=20N?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- crates/mathcore/src/geometry.rs | 131 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 616297 -> 618600 bytes 2 files changed, 131 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 976a3b8..8fce584 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -1348,6 +1348,31 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "垂足三角形内接于九点圆", )); } + // Circumcenter of the orthic triangle is the nine-point center N. + if let Some((o_h, _)) = circum2(feet[0], feet[1], feet[2]) { + out.push(fact( + "垂足三角形", + "O(H_a H_b H_c)", + pt(o_h[0], o_h[1]), + None, + "O_{\\text{orthic}} = N", + "垂足三角形的外心(等于九点圆心)", + ).with(Shape::Point { + x: o_h[0], + y: o_h[1], + label: "O_H 垂足外心".into(), + })); + if dist2(o_h, n9loc) < 1e-5 * (1.0 + rr) { + out.push(fact( + "垂足三角形", + "O(H_a H_b H_c) = N", + "\\checkmark".into(), + None, + "O_{\\text{orthic}} = N = \\tfrac{O+H}{2}", + "垂足外心与九点圆心重合", + )); + } + } } } @@ -2367,6 +2392,72 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // Moses point X(75): isotomic conjugate of the incenter; bary (bc : ca : ab). + { + let wa = b * c; + let wb = c * a; + let wc = a * b; + let den = wa + wb + wc; + if den > 1e-18 { + let mo = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "摩西点", + "Mo", + pt(mo[0], mo[1]), + None, + "Mo = \\frac{bc\\,A + ca\\,B + ab\\,C}{\\sum}", + "摩西点 X(75):内心的等截共轭", + ).with(Shape::Point { + x: mo[0], + y: mo[1], + label: "Mo 摩西".into(), + })); + out.push(fact( + "摩西点", + "Mo \\leftrightarrow I", + "\\text{等截共轭}".into(), + None, + "\\text{isotomic of }I", + "摩西点与内心互为等截共轭(bary I=a:b:c ↔ 1/a:1/b:1/c)", + )); + } + } + + // X(25): homothetic center of orthic and tangential triangles; bary a²/(b²+c²−a²). + // Denominator vanishes at a right angle — skip then. + { + let da = b * b + c * c - a * a; + let db = c * c + a * a - b * b; + let dc = a * a + b * b - c * c; + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + let wa = (a * a) / da; + let wb = (b * b) / db; + let wc = (c * c) / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x25 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "垂足切线同调中心", + "X_{25}", + pt(x25[0], x25[1]), + None, + "X(25) = \\bigl(a^2/(b^2+c^2-a^2):\\cdots\\bigr)", + "X(25):垂足三角形与切线三角形的同调中心", + ).with(Shape::Point { + x: x25[0], + y: x25[1], + label: "X25 同调".into(), + })); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -5517,6 +5608,46 @@ mod tests { assert!(f1o.why.contains("120") || f1o.how.contains("obtuse") || f1o.how.contains("120"), "why={}", f1o.why); } + #[test] + fn moses_x25_orthic_circumcenter() { + // Scalene acute 6-7-8: Moses, X(25), orthic circumcenter = N. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let mo = fs.iter().find(|f| f.group == "摩西点" && f.label == "Mo").expect("Mo"); + let i = fs.iter().find(|f| f.group == "特殊点" && f.label == "I").expect("I"); + assert_ne!(mo.value, i.value, "Moses ≠ I on scalene"); + assert!(fs.iter().any(|f| f.group == "摩西点" && f.value.contains("等截"))); + let x25 = fs.iter().find(|f| f.group == "垂足切线同调中心" && f.label.contains("25")).expect("X25"); + assert_ne!(x25.value, mo.value); + assert!(fs.iter().any(|f| f.group == "垂足三角形" && f.label.contains("O(H_a"))); + assert!(fs.iter().any(|f| f.group == "垂足三角形" && f.label.contains("= N"))); + let oh = fs.iter().find(|f| f.group == "垂足三角形" && f.label == "O(H_a H_b H_c)").expect("Oh"); + let n = fs.iter().find(|f| f.group == "欧拉线" && f.label == "N").expect("N"); + assert_eq!(oh.value, n.value, "orthic circumcenter = N"); + + // Right 3-4-5: Moses still; X(25) skipped (right angle); orthic degenerates (two feet = right vertex). + let k2 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().any(|f| f.group == "摩西点" && f.label == "Mo")); + assert!(fs2.iter().all(|f| f.group != "垂足切线同调中心"), "X25 skip right"); + assert!(fs2.iter().all(|f| !(f.group == "垂足三角形" && f.label.contains("O(H_a"))), "orthic O skip right"); + + // Equilateral: Moses = I = G; X(25) = G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + let moe = fs3.iter().find(|f| f.group == "摩西点" && f.label == "Mo").unwrap(); + assert_eq!(moe.value, g.value); + let x25e = fs3.iter().find(|f| f.group == "垂足切线同调中心" && f.label.contains("25")).unwrap(); + assert_eq!(x25e.value, g.value); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 96fe70cc1f99c7758e20815385ffdb406d61adba..e759b7409f5d80409164f6cc3cb38874732e8804 100644 GIT binary patch delta 86472 zcmc${34C5t{y(03o+fR!=IN5|O>drVNz-(tJ9?_M)H1fgSUQZ^WH8M5&OY;`1VL1| z(UY3sX&a;jK}Zm!oghP0N)RR`Mi8W=BSEAIlZ%edeyt}$@y137ndB2p%rW&pA5%N{uD#Og-&r!xi-cCu1|2~7Qq?RLkw=PIZ4-TTY 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zBdfqK<6+mrJQwB8VPTf@*f1MJYuoT?__@q0U)C>qTbOYk+cAD%@cU|k*85BRk2 z22HB#dLg3gUv8r_v*uwf+Vw9wS=V(VsQyj2q2~C zr;Vqv#rhsKc?_&O9&-g#?^suOYb#(p;)SwvSa`QDEerFkC)5@$A+ybCWD{3aa@TVO z;rA_Fm8AMN>3poKV}d0#4g&T_%R$JFdEB?-&;T3<%xc?;Z!GYCZJ3Aa<~Gd3JTh6+ zFYr7FF*b(sz-EH_p?a=v>T`?lyAfL@?RH2GZT@f;5s9sZ7lZPzf6TUa&fZR*?-W|z+|^TkNey>APa{393bf>L z5kl2lxE>141d-7X5h;$T=m-B2fYU9BT(-=nYCkHBU-pG#&vEg7XHAGX=e*p z^T^RK9`evW6)r{<#|*gq-lS1jOIOF3Ex@eV_rT@Mo`cI%gsX5774wa0>57W9_&hK^ z@`{WQj!JeEtF*4At9is*pw|ZGagsa1TSC9l()F7f@p5RmVZ7`LB4_;NP&(fR6_y^V zM?URp_^4FSoH`Fgjg>a1xdUCTVq3NdH{Q52+!zSN^%?d~e^38m{XBz)_3QthX9DQ_ m2Ax~bwSgEl(t$ZgU$oHc400{jrU From 57ed49300c03171a3223933e0b14039c044864e7 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 16:04:44 +0800 Subject: [PATCH 026/123] feat: OI similitude centers X55/X56, Euler infinity X30 --- crates/mathcore/src/geometry.rs | 202 +++++++++++++++++++++++++++++++- src/wasm/pkg/mathcore_bg.wasm | Bin 618600 -> 622065 bytes 2 files changed, 201 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 8fce584..d46cf77 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -2458,7 +2458,175 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } - // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. + // X(55)/X(56): internal/external centers of similitude of circumcircle (O) and incircle (I). + // X(55) = (r O + R I)/(R+r) divides OI internally in R:r; bary a²(b+c−a). + // X(56) = (R I − r O)/(R−r) divides OI externally in R:r; bary a²/(b+c−a). + { + let sa = b + c - a; + let sb = c + a - b; + let sc = a + b - c; + if sa > 1e-12 && sb > 1e-12 && sc > 1e-12 { + let sum_rr = rr + r; + if sum_rr > 1e-12 { + let s55 = [ + (r * circ[0] + rr * inc[0]) / sum_rr, + (r * circ[1] + rr * inc[1]) / sum_rr, + ]; + // Cross-check bary a²(b+c−a) + let wa = a * a * sa; + let wb = b * b * sb; + let wc = c * c * sc; + let den = wa + wb + wc; + if den > 1e-12 { + let s55b = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + let s55u = if dist2(s55, s55b) < 1e-5 * (1.0 + dist2(circ, inc)) { + s55 + } else { + s55b + }; + out.push(fact( + "相似中心", + "S_{+}", + pt(s55u[0], s55u[1]), + None, + "S_{+} = \\dfrac{r\\,O + R\\,I}{R+r}", + "内相似中心 X(55):外接圆与内切圆的内相似中心", + ).with(Shape::Point { + x: s55u[0], + y: s55u[1], + label: "S+ X55".into(), + })); + let d_o = dist2(s55u, circ); + let d_i = dist2(s55u, inc); + if d_i > 1e-12 { + let ratio = d_o / d_i; + let expect = rr / r; + if (ratio - expect).abs() < 1e-4 * (1.0 + expect) { + out.push(fact( + "相似中心", + "OS_{+}:S_{+}I", + format!("{}:{}", nice(rr), nice(r)), + Some(expect), + "OS_{+}:S_{+}I = R:r", + "内相似中心按 R:r 内分 OI", + )); + } + } + } + } + let diff_rr = rr - r; + if diff_rr > 1e-12 { + let s56 = [ + (-r * circ[0] + rr * inc[0]) / diff_rr, + (-r * circ[1] + rr * inc[1]) / diff_rr, + ]; + let wa = (a * a) / sa; + let wb = (b * b) / sb; + let wc = (c * c) / sc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let s56b = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + let s56u = if dist2(s56, s56b) < 1e-5 * (1.0 + dist2(circ, inc)) { + s56 + } else { + s56b + }; + out.push(fact( + "相似中心", + "S_{-}", + pt(s56u[0], s56u[1]), + None, + "S_{-} = \\dfrac{R\\,I - r\\,O}{R-r}", + "外相似中心 X(56):外接圆与内切圆的外相似中心", + ).with(Shape::Point { + x: s56u[0], + y: s56u[1], + label: "S- X56".into(), + })); + // O, I, S+, S− collinear on the OI line + let cross = (inc[0] - circ[0]) * (s56u[1] - circ[1]) + - (inc[1] - circ[1]) * (s56u[0] - circ[0]); + let scale = (1.0 + dist2(circ, inc)) * (1.0 + dist2(circ, s56u)); + if cross.abs() < 1e-5 * scale { + out.push(fact( + "相似中心", + "O,\\ I,\\ S_{+},\\ S_{-}", + "\\text{共线}".into(), + None, + "S_{\\pm}\\in OI", + "内/外相似中心均在 OI 线上(互为关于 O,I 的调和共轭)", + )); + } + } + } + } + } + + // X(30) Euler infinity point: Euler line ∩ line at infinity (direction of OH). + // Emit unit direction when |OH| is non-degenerate; bary sum of g(a,b,c) is 0. + { + let ohx = orth[0] - circ[0]; + let ohy = orth[1] - circ[1]; + let oh_len = (ohx * ohx + ohy * ohy).sqrt(); + if oh_len > 1e-9 { + let ux = ohx / oh_len; + let uy = ohy / oh_len; + out.push(fact( + "欧拉无穷远点", + "X_{30}", + format!("({}, {})", nice(ux), nice(uy)), + None, + "X(30) = \\text{Euler}\\cap\\ell_{\\infty}", + "欧拉无穷远点:欧拉线与无穷远直线的交点(方向向量)", + )); + out.push(fact( + "欧拉无穷远点", + "\\overrightarrow{OH}/|OH|", + format!("({}, {})", nice(ux), nice(uy)), + None, + "\\parallel\\overrightarrow{OH}", + "欧拉线方向单位向量(X(30) 的仿射代表)", + )); + // Bary g = 2a⁴ − (b²−c²)² − a²(b²+c²); homogeneous sum ≈ 0 at infinity. + let g_a = { + let a2 = a * a; + let b2 = b * b; + let c2 = c * c; + 2.0 * a2 * a2 - (b2 - c2) * (b2 - c2) - a2 * (b2 + c2) + }; + let g_b = { + let a2 = b * b; + let b2 = c * c; + let c2 = a * a; + 2.0 * a2 * a2 - (b2 - c2) * (b2 - c2) - a2 * (b2 + c2) + }; + let g_c = { + let a2 = c * c; + let b2 = a * a; + let c2 = b * b; + 2.0 * a2 * a2 - (b2 - c2) * (b2 - c2) - a2 * (b2 + c2) + }; + let gsum = g_a + g_b + g_c; + if gsum.abs() < 1e-6 * (1.0 + g_a.abs() + g_b.abs() + g_c.abs()) { + out.push(fact( + "欧拉无穷远点", + "\\sum g(a,b,c)", + "0".into(), + Some(0.0), + "g=2a^4-(b^2-c^2)^2-a^2(b^2+c^2)", + "X(30) 重心坐标之和为 0(无穷远点判据)", + )); + } + } + } + + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { // Medians: each ratio = 1. @@ -5648,6 +5816,38 @@ mod tests { assert_eq!(x25e.value, g.value); } + #[test] + fn similitude_centers_euler_infinity() { + // 3-4-5: R=2.5, r=1; S+ divides OI in 2.5:1; S− on OI; X30 direction || OH. + let k = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let sp = fs.iter().find(|f| f.group == "相似中心" && f.label == "S_{+}").expect("S+"); + let sm = fs.iter().find(|f| f.group == "相似中心" && f.label == "S_{-}").expect("S-"); + assert_ne!(sp.value, sm.value); + let ratio = fs.iter().find(|f| f.group == "相似中心" && f.label.contains("OS")).expect("ratio"); + assert!((ratio.num.unwrap() - 2.5).abs() < 1e-6, "R/r={}", ratio.num.unwrap()); + assert!(fs.iter().any(|f| f.group == "相似中心" && f.value.contains("共线"))); + let x30 = fs.iter().find(|f| f.group == "欧拉无穷远点" && f.label.contains("30")).expect("X30"); + assert!(fs.iter().any(|f| f.group == "欧拉无穷远点" && f.label.contains("OH"))); + assert!(fs.iter().any(|f| f.group == "欧拉无穷远点" && f.label.contains("g") && f.value == "0")); + // Direction nonzero + assert!(x30.value.contains("(")); + + // Equilateral: S+=S−=O=I=G; X30 skipped (|OH|=0). + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + let spe = fs2.iter().find(|f| f.group == "相似中心" && f.label == "S_{+}").expect("S+ eq"); + let sme = fs2.iter().find(|f| f.group == "相似中心" && f.label == "S_{-}").expect("S- eq"); + assert_eq!(spe.value, g.value); + assert_eq!(sme.value, g.value); + assert!(fs2.iter().all(|f| f.group != "欧拉无穷远点"), "X30 skip equilateral"); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index e759b7409f5d80409164f6cc3cb38874732e8804..4c1cabc8a8df74cba2f76340325543c1ad42a6ac 100644 GIT binary patch delta 43597 zcmb?^34Bh+_xCgRK1=pQWRpd19zh}!yV$uZ_NAo@s#I00L5td2OM)N>!o>tZL{zj? zH0mlr5UsXR(Wa_uNh^q=mPV^+z29^1^E`Qy`u+az|MR|8&&)Y<&Y3ea=bTyY+^eFj z{@q9Q^U6%Fi;f%IlMHf2YW{W8W5Mg6OQG{Ee?1n(z$9UI*ZkjIJj_DMQH6QGP02*> 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z=snj(_GSG7_#Tx$9cj9LJycL<-Y<22#=`kvUjI~n)4(G%=6x0rAVjz| zfiSRHU~yWK92Sx)4X5{$bshumQ^o5MWZu<&NTK6$#s@T5US@Lfv&M_&UFU)vovrQ$nbP1DOs1ncEwTlf-quvU+1@BlB9 zrw7V?HkgWfz%t-p@^N@i?EK)go>&j=2Gf$Ba+bXy#A%Cy-iIO7CRGk|odWY3bO}Bm z)gFb={8Z_VSMkm2n(1-yxqgoz$9{6u(`)j`y2a;GWpa=!39r{|&&#nz#lTMz)TXx_ zCHEnoO_@IEE}GMt-m)RS^n!NxmIG3ArPF)C%ERFC>04*MASuqoF397p_ya#vzdkat zX$A7(jqnb9EY!AI_}nfLO4LX8b+-+5dQVuL;B(bpgU=gk27F}2a!>lm$fine5#sqe zBH&{PZNHb)xvxxgodmZA^LE3Qd@{7y(^p;$aqSOtdfyOVK_pjve;5@E!hqCw6t9He z&ghXur{2PdWF=AfRGA#RF3IU_aS41k6!-(y@loS*vZ5yEWQ~72>N?`N1tm#TI90~l c>nEEvawivWohm=YKOdRXe}<&~GeXz>AM-29y8r+H From be36be884f143a8c0132dbfdec885f1cdfbec802 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 16:05:58 +0800 Subject: [PATCH 027/123] feat: isogonals X57 (Mitten), X58 (Spieker), X84 (Bevan/hexyl) --- crates/mathcore/src/geometry.rs | 181 +++++++++++++++++++++++++++++++- src/wasm/pkg/mathcore_bg.wasm | Bin 622065 -> 624918 bytes 2 files changed, 180 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index d46cf77..80ddc16 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -2626,7 +2626,148 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } - // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. + // X(57): isogonal conjugate of Mittenpunkt X(9); perspector of intouch & excentral. + // Bary a/(b+c−a) = a/(2(s−a)). + { + let sa = b + c - a; + let sb = c + a - b; + let sc = a + b - c; + if sa > 1e-12 && sb > 1e-12 && sc > 1e-12 { + let wa = a / sa; + let wb = b / sb; + let wc = c / sc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x57 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "米滕等角共轭点", + "X_{57}", + pt(x57[0], x57[1]), + None, + "X(57) = \\bigl(a/(b+c-a):\\cdots\\bigr)", + "X(57):米滕点的等角共轭(接触△与旁心△的透视中心)", + ).with(Shape::Point { + x: x57[0], + y: x57[1], + label: "X57".into(), + })); + out.push(fact( + "米滕等角共轭点", + "X_{57} \\leftrightarrow Mi", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(9)", + "X(57) 与米滕点 X(9) 互为等角共轭", + )); + } + } + } + + // X(58): isogonal conjugate of Spieker X(10); bary a²/(b+c). + { + let wa = (a * a) / (b + c); + let wb = (b * b) / (c + a); + let wc = (c * c) / (a + b); + let den = wa + wb + wc; + if den > 1e-12 { + let x58 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "斯皮克等角共轭点", + "X_{58}", + pt(x58[0], x58[1]), + None, + "X(58) = \\bigl(a^2/(b+c):\\cdots\\bigr)", + "X(58):斯皮克中心的等角共轭", + ).with(Shape::Point { + x: x58[0], + y: x58[1], + label: "X58".into(), + })); + out.push(fact( + "斯皮克等角共轭点", + "X_{58} \\leftrightarrow Sp", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(10)", + "X(58) 与斯皮克中心 X(10) 互为等角共轭", + )); + } + } + + // X(84): isogonal conjugate of Bevan X(40); perspector of hexyl triangle. + // Bary a / (cos B + cos C − cos A − 1); skip when any denominator ≈ 0. + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + let da = cb + cc - ca - 1.0; + let db = cc + ca - cb - 1.0; + let dc = ca + cb - cc - 1.0; + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + let wa = a / da; + let wb = b / db; + let wc = c / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x84 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "己基透视中心", + "X_{84}", + pt(x84[0], x84[1]), + None, + "X(84) = \\bigl(a/(\\cos B+\\cos C-\\cos A-1):\\cdots\\bigr)", + "X(84):贝万点的等角共轭(己基三角形透视中心)", + ).with(Shape::Point { + x: x84[0], + y: x84[1], + label: "X84".into(), + })); + // Cross-check: isogonal of Be=2O−I via bary of Be then a²/x. + let be = [2.0 * circ[0] - inc[0], 2.0 * circ[1] - inc[1]]; + // signed areas for bary of Be + let area2 = |p: [f64; 2], q: [f64; 2], r: [f64; 2]| { + (q[0] - p[0]) * (r[1] - p[1]) - (q[1] - p[1]) * (r[0] - p[0]) + }; + let aa = area2(be, pb, pc); + let bb = area2(pa, be, pc); + let cc_ = area2(pa, pb, be); + let ssum = aa + bb + cc_; + if ssum.abs() > 1e-12 && aa.abs() > 1e-14 && bb.abs() > 1e-14 && cc_.abs() > 1e-14 { + let wa = (a * a) / aa; + let wb = (b * b) / bb; + let wc = (c * c) / cc_; + let den2 = wa + wb + wc; + if den2.abs() > 1e-12 { + let iso = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den2, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den2, + ]; + if dist2(iso, x84) < 1e-4 * (1.0 + dist2(circ, orth)) { + out.push(fact( + "己基透视中心", + "X_{84} \\leftrightarrow Be", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(40)", + "X(84) 与贝万点 X(40) 互为等角共轭", + )); + } + } + } + } + } + } + + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { // Medians: each ratio = 1. @@ -5848,6 +5989,44 @@ mod tests { assert!(fs2.iter().all(|f| f.group != "欧拉无穷远点"), "X30 skip equilateral"); } + #[test] + fn x57_x58_x84_isogonals() { + // Scalene 6-7-8: X57≠Mi, X58≠Sp, X84≠Be; isogonal notes present. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x57 = fs.iter().find(|f| f.group == "米滕等角共轭点" && f.label == "X_{57}").expect("X57"); + let mi = fs.iter().find(|f| f.group == "米滕点" && f.label == "Mi").expect("Mi"); + assert_ne!(x57.value, mi.value); + assert!(fs.iter().any(|f| f.group == "米滕等角共轭点" && f.value.contains("等角"))); + let x58 = fs.iter().find(|f| f.group == "斯皮克等角共轭点" && f.label == "X_{58}").expect("X58"); + let sp = fs.iter().find(|f| f.group == "斯皮克中心" && f.label == "Sp").expect("Sp"); + assert_ne!(x58.value, sp.value); + assert!(fs.iter().any(|f| f.group == "斯皮克等角共轭点" && f.value.contains("等角"))); + let x84 = fs.iter().find(|f| f.group == "己基透视中心" && f.label == "X_{84}").expect("X84"); + let be = fs.iter().find(|f| f.group == "贝万点" && f.label == "Be").expect("Be"); + assert_ne!(x84.value, be.value); + assert!(fs.iter().any(|f| f.group == "己基透视中心" && f.value.contains("等角"))); + assert_ne!(x57.value, x58.value); + assert_ne!(x58.value, x84.value); + + // Equilateral: all collapse to G. + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + for (grp, lab) in [ + ("米滕等角共轭点", "X_{57}"), + ("斯皮克等角共轭点", "X_{58}"), + ("己基透视中心", "X_{84}"), + ] { + let p = fs2.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("missing {lab}")); + assert_eq!(p.value, g.value, "{lab} should = G"); + } + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff 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100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -2767,6 +2767,156 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(12): harmonic conjugate of Feuerbach X(11) w.r.t. I,N (etc.); bary a(1+cos(B−C)). + // X(59): isogonal of Feuerbach X(11); bary a/(1−cos(B−C)); skip isosceles (den=0). + // X(60): isogonal of X(12); bary a/(1+cos(B−C)). + { + let c_bc = (g[1] - g[2]).cos(); + let c_ca = (g[2] - g[0]).cos(); + let c_ab = (g[0] - g[1]).cos(); + // X(12) + { + let wa = a * (1.0 + c_bc); + let wb = b * (1.0 + c_ca); + let wc = c * (1.0 + c_ab); + let den = wa + wb + wc; + if den > 1e-12 { + let x12 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "费尔巴哈调和共轭点", + "X_{12}", + pt(x12[0], x12[1]), + None, + "X(12) = \\bigl(a(1+\\cos(B-C)):\\cdots\\bigr)", + "X(12):费尔巴哈点的调和共轭(九点圆与旁切圆切点三角形透视中心)", + ).with(Shape::Point { + x: x12[0], + y: x12[1], + label: "X12".into(), + })); + } + } + // X(60) = isogonal of X(12) + { + let da = 1.0 + c_bc; + let db = 1.0 + c_ca; + let dc = 1.0 + c_ab; + if da > 1e-12 && db > 1e-12 && dc > 1e-12 { + let wa = a / da; + let wb = b / db; + let wc = c / dc; + let den = wa + wb + wc; + if den > 1e-12 { + let x60 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "X12等角共轭点", + "X_{60}", + pt(x60[0], x60[1]), + None, + "X(60) = \\bigl(a/(1+\\cos(B-C)):\\cdots\\bigr)", + "X(60):X(12) 的等角共轭", + ).with(Shape::Point { + x: x60[0], + y: x60[1], + label: "X60".into(), + })); + out.push(fact( + "X12等角共轭点", + "X_{60} \\leftrightarrow X_{12}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(12)", + "X(60) 与 X(12) 互为等角共轭", + )); + } + } + } + // X(59) = isogonal of Feuerbach Fe X(11) + { + let da = 1.0 - c_bc; + let db = 1.0 - c_ca; + let dc = 1.0 - c_ab; + if da > 1e-12 && db > 1e-12 && dc > 1e-12 { + let wa = a / da; + let wb = b / db; + let wc = c / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x59 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "费尔巴哈等角共轭点", + "X_{59}", + pt(x59[0], x59[1]), + None, + "X(59) = \\bigl(a/(1-\\cos(B-C)):\\cdots\\bigr)", + "X(59):费尔巴哈点的等角共轭", + ).with(Shape::Point { + x: x59[0], + y: x59[1], + label: "X59".into(), + })); + // Cross-check vs isogonal of geometric Fe when available. + let n9 = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; + let r9 = rr / 2.0; + let den_f = r9 - r; + let ni_len = dist2(n9, inc); + if den_f.abs() > 1e-9 && ni_len > 1e-9 { + let fe = [ + (r9 * inc[0] - r * n9[0]) / den_f, + (r9 * inc[1] - r * n9[1]) / den_f, + ]; + if (dist2(n9, fe) - r9).abs() < 1e-4 * (1.0 + r9) + && (dist2(inc, fe) - r).abs() < 1e-4 * (1.0 + r) + { + let area2 = |p: [f64; 2], q: [f64; 2], r: [f64; 2]| { + (q[0] - p[0]) * (r[1] - p[1]) - (q[1] - p[1]) * (r[0] - p[0]) + }; + let aa = area2(fe, pb, pc); + let bb = area2(pa, fe, pc); + let cc_ = area2(pa, pb, fe); + let ssum = aa + bb + cc_; + if ssum.abs() > 1e-12 + && aa.abs() > 1e-14 + && bb.abs() > 1e-14 + && cc_.abs() > 1e-14 + { + let wa = (a * a) / aa; + let wb = (b * b) / bb; + let wc = (c * c) / cc_; + let den2 = wa + wb + wc; + if den2.abs() > 1e-12 { + let iso = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den2, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den2, + ]; + if dist2(iso, x59) < 1e-4 * (1.0 + dist2(circ, orth)) { + out.push(fact( + "费尔巴哈等角共轭点", + "X_{59} \\leftrightarrow Fe", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(11)", + "X(59) 与费尔巴哈点 X(11) 互为等角共轭", + )); + } + } + } + } + } + } + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -6027,6 +6177,46 @@ mod tests { } } + #[test] + fn x12_x59_x60_feuerbach_isogonals() { + // Scalene 6-7-8: X12, X59, X60 distinct; isogonal notes; Fe present. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x12 = fs.iter().find(|f| f.group == "费尔巴哈调和共轭点" && f.label == "X_{12}").expect("X12"); + let x59 = fs.iter().find(|f| f.group == "费尔巴哈等角共轭点" && f.label == "X_{59}").expect("X59"); + let x60 = fs.iter().find(|f| f.group == "X12等角共轭点" && f.label == "X_{60}").expect("X60"); + let fe = fs.iter().find(|f| f.group == "费尔巴哈点" && f.label == "Fe").expect("Fe"); + assert_ne!(x12.value, x59.value); + assert_ne!(x12.value, x60.value); + assert_ne!(x59.value, x60.value); + assert_ne!(x59.value, fe.value); + assert!(fs.iter().any(|f| f.group == "费尔巴哈等角共轭点" && f.value.contains("等角"))); + assert!(fs.iter().any(|f| f.group == "X12等角共轭点" && f.value.contains("等角"))); + + // Isosceles non-eq 5-5-6: X59 skipped (B=C); X12 & X60 present. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().any(|f| f.group == "费尔巴哈调和共轭点" && f.label == "X_{12}")); + assert!(fs2.iter().any(|f| f.group == "X12等角共轭点" && f.label == "X_{60}")); + assert!(fs2.iter().all(|f| f.group != "费尔巴哈等角共轭点"), "X59 skip isosceles"); + + // Equilateral: X12=X60=G; X59 skipped. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + let x12e = fs3.iter().find(|f| f.group == "费尔巴哈调和共轭点" && f.label == "X_{12}").unwrap(); + let x60e = fs3.iter().find(|f| f.group == "X12等角共轭点" && f.label == "X_{60}").unwrap(); + assert_eq!(x12e.value, g.value); + assert_eq!(x60e.value, g.value); + assert!(fs3.iter().all(|f| f.group != "费尔巴哈等角共轭点"), "X59 skip equilateral"); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index eecfe6f5b8c19aaff0d02a65431b8dc4acb4fb73..4e28388cba2609d69eff68e72560bc2342aa2a22 100644 GIT binary patch delta 46224 zcmb?^3tSde(>UksKFb{*6c9ylc?3lf?{~bdisrq{w~JP4X%|dOE4wOaps1+eq6Y;P z5Q`EOg<2|7R5C0yEGjZoG)gQoR8%a=|IFFlhljHF`@Y}r|NeS8J9B2{%$YMY=eGN} zWmA{^Z+FQ*Z*faY{lv*V)=7y=Ex2rHrd~O5K?%+~w~Io%Si1b4g6l5s63yAT$$Jqk z+NeJ7y@i%+RA)c-s=C5Dkmg@eKd=V+S8Y7%qIhJKJYi zs5d(n(cGkh{Gg|SE=lds>GzTGNzkH)+*Y=tHE7IeBHLt3IIX6#m(qxp-9a5X3UR(R zAPT1*<2{{#*ds>CTn~Cg6fBn)inMYq=+Iu3!q(CHwd%H!uc{th9&n9cXV_dF^Y=WjUbWGxfb)BPr? zZvET9|5vnmNFFAS%^d5*|5r0I+xD=!z5ik|S@j+;(&ynJLcSzheYLq z)tmu+p#GZyo#5}y0gwAk9wHPWm7QA6o6$*i^XjR-Kk#QVxgcxMNg_>_`(@c?sxJe74dSSh9n1N_|fW^G`z$2yX58MQhXs?Ri-kn0*IkGHw z&$i8lM!RL(9?#6QJ)zdz?;Acx?vpJ)j@r!C6?tM84B;G<^f>A;SJ&Z*f{rt8i!Srz z5$HAZ)u4yByUsV%nFsziwZLa)0%)8C}%nv*(d!b$^gQri)%`!^>86@ElJV;}FGH zojIpR;6p~Eo{CEhc!~V5y;+EbIrFKzNf04FT;TIWEfr?Tv(%>fU9l{%J^7_bQ&(}N zycfJiGghhV7JToYw+fW%*IKDMq{3Xgfi|rwkQb&4t%iihV1du#MIvpAH{=DV2VZ)e zCMST*1T}r>1MM;sK<+0_tpztE*agR}QssqD6nMXKTcG8))fF#wRr|d02#rU9zUruD zL2Ahx5BR6X|5Lk4lVpQX8-KLm^s-fiJXY{ftQR3qsQ2yoKMeJ*xMyA3bd@`go&Q4Q z;OR#iMrK;$oI}Q{A!~fwKamaYAYUgw&SZJP*OQQ5X=;2NjiyQ4$riQsl}UpX2*ecUeFEC@jGy@}v< za!&)Rc38K8%;HXebKNikkNwsUmS=&Z8hNx~q&#t#ExHAoveIP~mj-Lt1c z9A(+&$aAtG2lH0Op@&E79uBp(EL$`-xl=u`rGu9(nx`*|66Y2p&sK#E>&a};;SCXl zj8lC!275XZj8lhgTtddFiyOMDHR0X`bsL9~faoDY3585;TC#>)61aD=G2UoK=Y8fm#!!pZ_UaEQ%RrC0o8Cj|HLau{#&H7aDO*RWi&SU#|FiTh zyoXcN%+y6Nc;1_XphJoqDS@@XsA~3>A05mQ5IJ_nA0d}P;oA~7$9Qj0cD8PcIp7;}!8iQEr(!d+b(_pV z2bsIe_P9J1o0+XUh>lhJrlq((ZcLh9eA4vU`g8!~OT$1$dtiQOZw?q}y!V`4;0m4O z+0bn3_U7pA&2HV^9KAgqtA=iCY0s0lC#0u9r#GkXhQCo6@gB3~d*ujdg3JCqqeJKa zO*dS&Zy=8Y`xLcy`=jpTvUTTxX!+kbN8%1+_zIrg=|MU_Do>Li&CZs)%iS|~*+OAP zxff=(Y`L4<4PZ0=I)=a)hU#MoBQRBWxM+-vP(3cj6;x$DMSPwZf*IW+cQtG}R=qd- zLDE&t&5nn^k-HMw@reU612zVkVVA8d^nL7BKFio}Ah8*U^sZ=Fpo-Sp!e$`Sb*yU1 z*$AG8zH>3>NitrYuzQC8c!*4h6`0~CfZ!;Y=|FH-wP1JecF;x+wZjfC%IZE+<%VfeVC0!Ftf9*6azU@&vVEPrJ!cd||N5HrAd)GP7-6 zp*b65D{Q(Yxj;oIsAEG8P-cQ7hYd7~;;!2VdIX&f&6az?dI^*QQiu=4_C#!N1FI(I zZGYYi4?{CHXy4v0BBIa?W_yUhE7XJYVeLI-8;If z`TI8+rcTc9Pacl~H=CXrVgm!;Cr^i^)z+~-KS!?E$`%jj(rxmzEL+#VA%Q8&7Wy~j zbbZ99aaRJVq0lerE;!x}zlaICLxFl-b@j%gLruWU5Q@&*RaXzN6VxXUCb&*8)+*6F zx|D+PohP*D1q&@1lyX2kB6k9X)I9}Z{xD~ag;44WQHV-FOo9^QaY9u`YOW7t$}=!* z#-cuslMOg+7symyvY>Kmw%kKsEf0ewr$G;zI!-@8ADsm)jfLrlFPHqhY@UIDm*lSMC{$Yx!~VI84Q`D#IsOfRAhGN3kz; 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43415c304ae5549884e403d41e5e451ffa1f1323 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 16:08:03 +0800 Subject: [PATCH 029/123] =?UTF-8?q?feat:=20Grinberg=20X37,=20isogonal=20X8?= =?UTF-8?q?1,=20I=E2=80=93K=20crosspoint=20X42?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- crates/mathcore/src/geometry.rs | 164 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 627631 -> 630051 bytes 2 files changed, 164 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index f1b74c6..5888f06 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -2917,6 +2917,130 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // Grinberg X(37): crosspoint of I and G; bary a(b+c). Complement of Moses X(75). + // X(81): isogonal of Grinberg; bary a/(b+c). + // X(42): crosspoint of I and K (Lemoine); bary a²(b+c). + { + let wa = a * (b + c); + let wb = b * (c + a); + let wc = c * (a + b); + let den = wa + wb + wc; + if den > 1e-12 { + let gr = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "格林伯格点", + "Gr", + pt(gr[0], gr[1]), + None, + "Gr = \\frac{a(b+c)A+b(c+a)B+c(a+b)C}{\\sum}", + "格林伯格点 X(37):内心与重心的截线交点(摩西点的补点)", + ).with(Shape::Point { + x: gr[0], + y: gr[1], + label: "Gr 格林伯格".into(), + })); + // Complement of Moses: Mo = bc:ca:ab → complement has bary a(b+c) = Gr. + let mwa = b * c; + let mwb = c * a; + let mwc = a * b; + let mden = mwa + mwb + mwc; + if mden > 1e-12 { + let mo = [ + (mwa * pa[0] + mwb * pb[0] + mwc * pc[0]) / mden, + (mwa * pa[1] + mwb * pb[1] + mwc * pc[1]) / mden, + ]; + // Complement map: P ↦ 3G − 2P? Kimberling complement of P with bary x:y:z + // is (y+z):(z+x):(x+y). For Mo=bc:ca:ab, complement = (ca+ab):(ab+bc):(bc+ca) + // = a(b+c):b(c+a):c(a+b) = Gr. Verify Cartesian: midpoint? Actually + // complement C(P) satisfies G divides P C(P) with PG:G C(P) = 2:1 toward C(P)? + // Standard: complement of P is the point Q such that G = (2P+Q)/3? No — + // In ETC, complement of P is anticomplement of P mapped... + // Vectorially often Q = 3G − 2P? Let's check: if Q = 3G-2P then G = (2P+Q)/3 means G divides PQ with PG:GQ = 1:2? + // Actually Kimberling: the complement of P is the image under the homothety h(G,−1/2). + // So Q − G = (−1/2)(P − G) ⇒ Q = G − (1/2)(P−G) = (3G − P)/2? + // Homothety h(G,k): Q = G + k(P−G). + // Complement = h(G, −1/2): Q = G − (1/2)(P−G) = (3/2)G − (1/2)P = (3G−P)/2. + // Anticomplement = h(G, −2): Q = 3G − 2P. + // ETC: X(37) = complement of X(75). So Gr = (3G − Mo)/2. + let q = [ + (3.0 * centroid[0] - mo[0]) / 2.0, + (3.0 * centroid[1] - mo[1]) / 2.0, + ]; + if dist2(q, gr) < 1e-5 * (1.0 + dist2(gr, centroid)) { + out.push(fact( + "格林伯格点", + "Gr = \\text{complement}(Mo)", + "\\checkmark".into(), + None, + "Gr = \\tfrac{3G - Mo}{2}", + "格林伯格点是摩西点关于重心的补点(位似比 −1/2)", + )); + } + } + } + // X(81) isogonal of Grinberg + { + let wa = a / (b + c); + let wb = b / (c + a); + let wc = c / (a + b); + let den = wa + wb + wc; + if den > 1e-12 { + let x81 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "格林伯格等角共轭点", + "X_{81}", + pt(x81[0], x81[1]), + None, + "X(81) = \\bigl(a/(b+c):\\cdots\\bigr)", + "X(81):格林伯格点的等角共轭", + ).with(Shape::Point { + x: x81[0], + y: x81[1], + label: "X81".into(), + })); + out.push(fact( + "格林伯格等角共轭点", + "X_{81} \\leftrightarrow Gr", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(37)", + "X(81) 与格林伯格点 X(37) 互为等角共轭", + )); + } + } + // X(42) crosspoint of I and K + { + let wa = a * a * (b + c); + let wb = b * b * (c + a); + let wc = c * c * (a + b); + let den = wa + wb + wc; + if den > 1e-12 { + let x42 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "内心勒莫恩截点", + "X_{42}", + pt(x42[0], x42[1]), + None, + "X(42) = \\bigl(a^2(b+c):\\cdots\\bigr)", + "X(42):内心与勒莫恩点的截线交点", + ).with(Shape::Point { + x: x42[0], + y: x42[1], + label: "X42".into(), + })); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -6217,6 +6341,46 @@ mod tests { assert!(fs3.iter().all(|f| f.group != "费尔巴哈等角共轭点"), "X59 skip equilateral"); } + #[test] + fn grinberg_x42_x81() { + // Scalene 6-7-8: Gr, X81, X42 distinct; complement & isogonal notes. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let gr = fs.iter().find(|f| f.group == "格林伯格点" && f.label == "Gr").expect("Gr"); + let mo = fs.iter().find(|f| f.group == "摩西点" && f.label == "Mo").expect("Mo"); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let i = fs.iter().find(|f| f.group == "特殊点" && f.label == "I").expect("I"); + assert_ne!(gr.value, mo.value); + assert_ne!(gr.value, g.value); + assert_ne!(gr.value, i.value); + assert!(fs.iter().any(|f| f.group == "格林伯格点" && f.label.contains("complement"))); + let x81 = fs.iter().find(|f| f.group == "格林伯格等角共轭点" && f.label == "X_{81}").expect("X81"); + assert_ne!(x81.value, gr.value); + assert!(fs.iter().any(|f| f.group == "格林伯格等角共轭点" && f.value.contains("等角"))); + let x42 = fs.iter().find(|f| f.group == "内心勒莫恩截点" && f.label == "X_{42}").expect("X42"); + let kpt = fs.iter().find(|f| f.group == "勒莫恩点" && f.label == "K").expect("K"); + assert_ne!(x42.value, kpt.value); + assert_ne!(x42.value, gr.value); + assert_ne!(x42.value, x81.value); + + // Equilateral: all = G. + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g2 = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + for (grp, lab) in [ + ("格林伯格点", "Gr"), + ("格林伯格等角共轭点", "X_{81}"), + ("内心勒莫恩截点", "X_{42}"), + ] { + let p = fs2.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("{lab}")); + assert_eq!(p.value, g2.value, "{lab}"); + } + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 4e28388cba2609d69eff68e72560bc2342aa2a22..9901daa5d06d2994f42bcfca7e563abaf39d9ffd 100644 GIT binary patch delta 44772 zcmb@v3w%x25-^^%_CDw2og?xfA$ATTL_F*L+z7W6rTVzldiJTbrK(R&Xb>ck*pZcR zaPmNC5KY=0npTjuX@!QSni8ZM1VNBiO7P9BeO^)be&7B7{G_v*P1Mks&~};O){gu-S6@9XNm=XjCap|Smb}|q zS?RNwR;MV_r+uI-G4`e9x0Joc;DE-IgD$dJ#|J6b!v|0gqe);2Dene=KqWtJL9fd{s2M1(7LKvrRt(<+)Piea5sjTx~ zLkm(+m@+ZoTUxUgWhq?(_tJXparm9qif^m_DDsI`!2vM}=oi^sze28nGW<@MqPAK{ zixnlWtv`zqNC3-oBRb{9)+cFcl5%4xC>eB-(7Gh0Z=2aPJ6YM#CYa_WD}`;stpv(n zZ3<~=a(-Uh*MKfr32Jv|Savcr=_$38jNpqxI%fotOp-2~R#C}YPFV|;T|gf?9C3ao zAPT3RW4v5|*mI6tycU#+Q1brr%}5la%$tK2SWvo^i`gvU*(^ z{zafrkaSQv@MWj`+_1eKv@wx0#Pr(j9=8UlO!AI32bGB*w58Q+l;?U+FqDHwjHRM- ztoJy@{W0Hs_s7n=)8Yi++D5AqpowF&EO|9>0&fp{HL!)3^2zj<_L_j&(sL8!ZbK$-8;O7VHan{}bYT^aQ8WSYH_(+*$U zRw@4YnSg?o|5T*GMv_QlSLK&4UO~w8{O6)iyOA0BeOD%vfC-rHz7nf6$DLF)+7W(OqF_NN>LyU1Wn5_&CD>(l4fN}gEfIurEXZ;gV!qM z3BAZnMMzA5zsZRocL(CB8K!B{G^8IYnKDf9e*`U?q3D{CE=A3b^3p?O$GFdtrYeKi zEFe>r-D~EMX-ZI1J2EYQU=ksK+RR3_L`%VvsbFbT7PoX7w{)tLrKq4yF^8qolmm*N z@<;MwP;2JeGLV;?K3sWIG5Gv{mzT^<9IseX;z3^II>~^t&}mO@@(-UX^+dOT=S&XI zNmH>4qR?X|o5zyZC4r#aDdUy5QX|RC{Eex0d#7pk&eZIk1syUBWk*ay*)uhxXQAJR zWtn7Y8p@ujb*~LOP3e=iyv4KuLLRtSk_QMm=xT4}#=oMJ7U`3^LrpD(nut-YB1cWR z8+vJ&#rU`0G;@GZjp+8x(X-HN0pMX&Y*vRAl{9kXiQXR=C+LnyK74F7!a)j$D$?<_~!($_vclA@;xc&ST@J_LgMcQq9H}eWqq=5vYx||Mv(?*kp~E{JERE zVMya3bgqhN;45*x$DRq@bWJ

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z8YWv%MZ9#H&)lT=VKRY#ZE(ym`DZiv7pet&vVTE`FdA!-II>V5Gh8O6u0c8P2&0fV zSIh@N4spe-=hc{BfOgQh7S}xLYknzTKU{7O^(e*h2ogTRq9S*+JmfGJnAB^G9N{@) zy8U+}e^|y#*b$Rn8zZloJ3?srSUe*k-#->TL4IMZ?3=hF#O+^-iXa<`r1)O}eZ_o? z;CYAMq(|jI)?bIbMAgqlovz;$4(iN%rq0c6Tma@JP}zGL{HVsf)g@`nTO|C64Jr&n zflm_%2U`u6FB>OQLsPs>-Tu$Wc@B6?6|cuN3o71V<9CBhF_UHAR3*11SZ>*MqCwv5 zR6X~QXF&0THr^D}r)`rFd)}s0iyXg*Y}q>*=m5&&(-Bju{4OkOdOP@fqz3Ke+4wYg zgyzRZ@DM-Kwsf@HqdC>4BQlV;$gp^D1~z~2vJ5N<&BCZMLq6;LuQ0dah2FbiG(J#)M$ax$*fjrs!`x9|~czN?FGTGr7<#Jo`j9n@Y z!lPU?K1)srJ&N*Sv~{|Sq=Q+qo!P}r7qaA#lqGJr{|PG}Gsj0co%sn#aTaz#o@~X- zgG_U?Wm42_*x}=TQ;*yK9376FJJk+vp|a&b--BRYPlqCBzn(zO8|qx-FvW5`bMQVx z$-RSeejaIu9P?-7xhXeCCVA?>9l*R;a2VHl%D3gn??XMu?r{4*#Tkx5cKp~Kv~D_P zqkZf0Bgo^;aVZp9hUs`Fg$9?&6B<)y8Js%S(z@N-A2} Date: Sun, 1 Nov 2026 16:09:11 +0800 Subject: [PATCH 030/123] feat: intouch orthocenter X65, 3rd Brocard X76, X86 conjugates --- crates/mathcore/src/geometry.rs | 184 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 630051 -> 633682 bytes 2 files changed, 184 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 5888f06..a967ea4 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -3041,6 +3041,148 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(65): orthocenter of the intouch triangle; isogonal of Schiffler X(21). + // Bary a(b+c)/(b+c−a). Also perspector of ABC and the extangents triangle. + { + let sa = b + c - a; + let sb = c + a - b; + let sc = a + b - c; + if sa > 1e-12 && sb > 1e-12 && sc > 1e-12 { + let wa = a * (b + c) / sa; + let wb = b * (c + a) / sb; + let wc = c * (a + b) / sc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x65 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "接触垂心", + "X_{65}", + pt(x65[0], x65[1]), + None, + "X(65) = \\bigl(a(b+c)/(b+c-a):\\cdots\\bigr)", + "X(65):接触三角形的垂心(席弗勒点的等角共轭)", + ).with(Shape::Point { + x: x65[0], + y: x65[1], + label: "X65 接触垂心".into(), + })); + // Geometric: orthocenter of intouch feet X_a,X_b,X_c. + let s_a = p - a; + let s_b = p - b; + let s_c = p - c; + if s_a > 1e-12 && s_b > 1e-12 && s_c > 1e-12 { + let xa = section_point(pb, pc, s_b, s_c); + let xb = section_point(pc, pa, s_c, s_a); + let xc = section_point(pa, pb, s_a, s_b); + if let Some((o_in, _)) = circum2(xa, xb, xc) { + let h_in = [ + xa[0] + xb[0] + xc[0] - 2.0 * o_in[0], + xa[1] + xb[1] + xc[1] - 2.0 * o_in[1], + ]; + if dist2(h_in, x65) < 1e-4 * (1.0 + dist2(circ, orth)) { + out.push(fact( + "接触垂心", + "H(X_a X_b X_c) = X_{65}", + "\\checkmark".into(), + None, + "H_{\\text{intouch}} = X(65)", + "接触三角形的垂心与 X(65) 重合", + )); + } + } + } + out.push(fact( + "接触垂心", + "X_{65} \\leftrightarrow Sc", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(21)", + "X(65) 与席弗勒点 X(21) 互为等角共轭", + )); + } + } + } + + // X(76): 3rd Brocard point; bary 1/a²; isotomic conjugate of Lemoine K = X(6). + { + let wa = 1.0 / (a * a); + let wb = 1.0 / (b * b); + let wc = 1.0 / (c * c); + let den = wa + wb + wc; + if den > 1e-12 { + let x76 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "第三布罗卡点", + "X_{76}", + pt(x76[0], x76[1]), + None, + "X(76) = \\bigl(1/a^2:1/b^2:1/c^2\\bigr)", + "第三布罗卡点 X(76):勒莫恩点的等截共轭", + ).with(Shape::Point { + x: x76[0], + y: x76[1], + label: "X76 布罗卡".into(), + })); + out.push(fact( + "第三布罗卡点", + "X_{76} \\leftrightarrow K", + "\\text{等截共轭}".into(), + None, + "\\text{isotomic of }X(6)", + "X(76) 与勒莫恩点 X(6) 互为等截共轭", + )); + } + } + + // X(86): cevapoint of I and G; isogonal of X(42); isotomic of Spieker. + // Bary 1/(b+c). + { + let wa = 1.0 / (b + c); + let wb = 1.0 / (c + a); + let wc = 1.0 / (a + b); + let den = wa + wb + wc; + if den > 1e-12 { + let x86 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "内心重心截点", + "X_{86}", + pt(x86[0], x86[1]), + None, + "X(86) = \\bigl(1/(b+c):\\cdots\\bigr)", + "X(86):内心与重心的截点(X(42) 的等角共轭;斯皮克的等截共轭)", + ).with(Shape::Point { + x: x86[0], + y: x86[1], + label: "X86".into(), + })); + out.push(fact( + "内心重心截点", + "X_{86} \\leftrightarrow X_{42}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(42)", + "X(86) 与 X(42) 互为等角共轭", + )); + out.push(fact( + "内心重心截点", + "X_{86} \\leftrightarrow Sp", + "\\text{等截共轭}".into(), + None, + "\\text{isotomic of }X(10)", + "X(86) 与斯皮克中心 X(10) 互为等截共轭", + )); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -6381,6 +6523,48 @@ mod tests { } } + #[test] + fn x65_intouch_orthocenter_x76_x86() { + // Scalene 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x65 = fs.iter().find(|f| f.group == "接触垂心" && f.label == "X_{65}").expect("X65"); + assert!(fs.iter().any(|f| f.group == "接触垂心" && f.label.contains("H(X_a"))); + assert!(fs.iter().any(|f| f.group == "接触垂心" && f.value.contains("等角"))); + let sc = fs.iter().find(|f| f.group == "席弗勒点" && f.label == "Sc").expect("Sc"); + assert_ne!(x65.value, sc.value); + let x76 = fs.iter().find(|f| f.group == "第三布罗卡点" && f.label == "X_{76}").expect("X76"); + let kpt = fs.iter().find(|f| f.group == "勒莫恩点" && f.label == "K").expect("K"); + assert_ne!(x76.value, kpt.value); + assert!(fs.iter().any(|f| f.group == "第三布罗卡点" && f.value.contains("等截"))); + let x86 = fs.iter().find(|f| f.group == "内心重心截点" && f.label == "X_{86}").expect("X86"); + let x42 = fs.iter().find(|f| f.group == "内心勒莫恩截点" && f.label == "X_{42}").expect("X42"); + let sp = fs.iter().find(|f| f.group == "斯皮克中心" && f.label == "Sp").expect("Sp"); + assert_ne!(x86.value, x42.value); + assert_ne!(x86.value, sp.value); + assert!(fs.iter().any(|f| f.group == "内心重心截点" && f.label.contains("42") && f.value.contains("等角"))); + assert!(fs.iter().any(|f| f.group == "内心重心截点" && f.label.contains("Sp") && f.value.contains("等截"))); + assert_ne!(x65.value, x76.value); + assert_ne!(x76.value, x86.value); + + // Equilateral: all = G. + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + for (grp, lab) in [ + ("接触垂心", "X_{65}"), + ("第三布罗卡点", "X_{76}"), + ("内心重心截点", "X_{86}"), + ] { + let p = fs2.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("{lab}")); + assert_eq!(p.value, g.value, "{lab}"); + } + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 9901daa5d06d2994f42bcfca7e563abaf39d9ffd..4a09b5f0ed3b40e024981ed5c401af68ef61ba93 100644 GIT binary patch delta 43995 zcmb@v34BdQ`#64Q&bjwy&qWr5xCtRa>|$TWQd_BN-)`Ef?oEqob)%Ia2!hKA69hLA z1i>ZYL>mO5Q7O@;8U(3Eg$AKPO7MH0v)tUMzVGMz|NP%2bDn3OZDyW%X689_u65tG z{OMFn#|5KDddgvgXN-Z_QZla?Yp7XHZ93b$bAM)qTYVGFPG0IekrpINGd^o1&GY?+ z79~sLUjIs(VTq!7_oY3Spn!_xg9hen*-WfPMxtn(2b2nfpJe;UC{;Z4lLG5y(VAqb 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158 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 633682 -> 636214 bytes 2 files changed, 158 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index a967ea4..9f4872d 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -3183,6 +3183,118 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(31) 2nd power point: bary a³; isogonal conjugate of Moses X(75). + // X(32) 3rd power point: bary a⁴; isogonal conjugate of 3rd Brocard X(76). + { + let wa = a * a * a; + let wb = b * b * b; + let wc = c * c * c; + let den = wa + wb + wc; + if den > 1e-12 { + let x31 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "第二幂点", + "X_{31}", + pt(x31[0], x31[1]), + None, + "X(31) = (a^3:b^3:c^3)", + "第二幂点 X(31):摩西点的等角共轭", + ).with(Shape::Point { + x: x31[0], + y: x31[1], + label: "X31 幂点".into(), + })); + out.push(fact( + "第二幂点", + "X_{31} \\leftrightarrow Mo", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(75)", + "X(31) 与摩西点 X(75) 互为等角共轭", + )); + } + let wa = a * a * a * a; + let wb = b * b * b * b; + let wc = c * c * c * c; + let den = wa + wb + wc; + if den > 1e-12 { + let x32 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "第三幂点", + "X_{32}", + pt(x32[0], x32[1]), + None, + "X(32) = (a^4:b^4:c^4)", + "第三幂点 X(32):第三布罗卡点的等角共轭", + ).with(Shape::Point { + x: x32[0], + y: x32[1], + label: "X32 幂点".into(), + })); + out.push(fact( + "第三幂点", + "X_{32} \\leftrightarrow X_{76}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(76)", + "X(32) 与第三布罗卡点 X(76) 互为等角共轭", + )); + } + } + + // X(69): bary cot A = b²+c²−a²; isotomic of H; isogonal of X(25). + // Right △: the right-angle component vanishes (point on opposite side) — still emit. + { + let wa = b * b + c * c - a * a; + let wb = c * c + a * a - b * b; + let wc = a * a + b * b - c * c; + let den = wa + wb + wc; + // den = a²+b²+c² > 0 always for a non-degen △ + if den.abs() > 1e-12 { + let x69 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "余切点", + "X_{69}", + pt(x69[0], x69[1]), + None, + "X(69) = (\\cot A:\\cot B:\\cot C) = (b^2+c^2-a^2:\\cdots)", + "X(69):垂心的等截共轭(亦为 X(25) 的等角共轭)", + ).with(Shape::Point { + x: x69[0], + y: x69[1], + label: "X69".into(), + })); + out.push(fact( + "余切点", + "X_{69} \\leftrightarrow H", + "\\text{等截共轭}".into(), + None, + "\\text{isotomic of }X(4)", + "X(69) 与垂心互为等截共轭", + )); + // Cross-check isotomic of H: H bary (tan A or cos? H has bary tan A? + // Actually H bary = tan A : tan B : tan C = 1/cot = a²/(b²+c²-a²)? + // Standard H bary = tan A : … = a²/(b²+c²−a²) wait no: + // H trilinear = sec A? Standard: H bary = tan A : tan B : tan C, or + // (bc[b²+c²−a²])? Actually common: H = (a²(b²+c²−a²))? No — + // Orthocenter barycentrics: tan A : tan B : tan C, equivalently + // a²(b²+c²−a²) is wrong. Simple: tan A = sin/cos, and cos A = (b²+c²−a²)/(2bc), + // so tan A ∝ sin A / (b²+c²−a²) ∝ a / (b²+c²−a²). + // Bary of H = a² / (b²+c²−a²)? Trilinear sec A, bary a sec A = a/cos A ∝ a²/(b²+c²−a²). + // Isotomic of H: if H has bary x:y:z = a²/(b²+c²−a²) : …, then isotomic 1/x ∝ (b²+c²−a²)/a², + // times a² gives (b²+c²−a²) — matches X(69). Good — note only. + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -6565,6 +6677,52 @@ mod tests { } } + #[test] + fn power_points_x31_x32_and_x69() { + // Scalene 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x31 = fs.iter().find(|f| f.group == "第二幂点" && f.label == "X_{31}").expect("X31"); + let mo = fs.iter().find(|f| f.group == "摩西点" && f.label == "Mo").expect("Mo"); + assert_ne!(x31.value, mo.value); + assert!(fs.iter().any(|f| f.group == "第二幂点" && f.value.contains("等角"))); + let x32 = fs.iter().find(|f| f.group == "第三幂点" && f.label == "X_{32}").expect("X32"); + let x76 = fs.iter().find(|f| f.group == "第三布罗卡点" && f.label == "X_{76}").expect("X76"); + assert_ne!(x32.value, x76.value); + assert_ne!(x31.value, x32.value); + assert!(fs.iter().any(|f| f.group == "第三幂点" && f.value.contains("等角"))); + let x69 = fs.iter().find(|f| f.group == "余切点" && f.label == "X_{69}").expect("X69"); + let h = fs.iter().find(|f| f.group == "特殊点" && f.label == "H").expect("H"); + assert_ne!(x69.value, h.value); + assert!(fs.iter().any(|f| f.group == "余切点" && f.value.contains("等截"))); + + // Right 3-4-5: X69 still (on hypotenuse side of right vertex); powers fine. + let k2 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().any(|f| f.group == "第二幂点" && f.label == "X_{31}")); + assert!(fs2.iter().any(|f| f.group == "第三幂点" && f.label == "X_{32}")); + assert!(fs2.iter().any(|f| f.group == "余切点" && f.label == "X_{69}")); + + // Equilateral: all = G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + for (grp, lab) in [ + ("第二幂点", "X_{31}"), + ("第三幂点", "X_{32}"), + ("余切点", "X_{69}"), + ] { + let p = fs3.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("{lab}")); + assert_eq!(p.value, g.value, "{lab}"); + } + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 4a09b5f0ed3b40e024981ed5c401af68ef61ba93..16f985e8a2907d42fd4077fc2b0b3c4934552050 100644 GIT binary patch delta 43536 zcmb@v34Bdg*EoFlK6l8RD8CZ$QS z?=_Q_de5UNY0~7EKaygtkwQZ3ap{n?c|dO3aRc+VW)jiFNF%D@o-n- zCj~airG;ry$-MSCx0^6RQ&K^qU(RUXPYBIRmA>(ttcdIA-#nlq_21$Y@@CSdNq%d+ ziHEe-e-*7sMQPGg0bfwN9fe690uRzG^%3++{{%j%$Q<3Yc|g7$WJWYLvDTT?j}LSu 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DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 16:11:21 +0800 Subject: [PATCH 032/123] feat: circum-inverse X36 of I, power-Ceva X41, double-angle X48 --- crates/mathcore/src/geometry.rs | 167 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 636214 -> 638548 bytes 2 files changed, 167 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 9f4872d..65ebdaa 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -3295,6 +3295,139 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(36): inverse of the incenter in the circumcircle; skip when I=O (equilateral). + // Geometric: X36 = O + R²(I−O)/|OI|². Barycentrics sin A − sin 2A (ETC). + { + let oi2 = { + let dx = inc[0] - circ[0]; + let dy = inc[1] - circ[1]; + dx * dx + dy * dy + }; + if oi2 > 1e-12 { + let scale = (rr * rr) / oi2; + let x36 = [ + circ[0] + scale * (inc[0] - circ[0]), + circ[1] + scale * (inc[1] - circ[1]), + ]; + // Cross-check ETC bary sin A − sin 2A + let wa = g[0].sin() - (2.0 * g[0]).sin(); + let wb = g[1].sin() - (2.0 * g[1]).sin(); + let wc = g[2].sin() - (2.0 * g[2]).sin(); + let den = wa + wb + wc; + let x36u = if den.abs() > 1e-12 { + let xb = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if dist2(xb, x36) < 1e-4 * (1.0 + rr) { + xb + } else { + x36 + } + } else { + x36 + }; + out.push(fact( + "反演内心", + "X_{36}", + pt(x36u[0], x36u[1]), + None, + "X(36) = O + R^2(I-O)/|OI|^2", + "X(36):内心关于外接圆的反演点", + ).with(Shape::Point { + x: x36u[0], + y: x36u[1], + label: "X36 反演I".into(), + })); + // |O X36| · |OI| = R² + let d_ox = dist2(circ, x36u); + let d_oi = oi2.sqrt(); + if d_oi > 1e-12 { + let prod = d_ox * d_oi; + if (prod - rr * rr).abs() < 1e-4 * (1.0 + rr * rr) { + out.push(fact( + "反演内心", + "|OX_{36}|\\cdot|OI|", + nice(rr * rr), + Some(rr * rr), + "|OX_{36}|\\cdot|OI| = R^2", + "反演定义:乘积等于外接圆半径平方", + )); + } + } + // Collinear O, I, X36 + let cross = (inc[0] - circ[0]) * (x36u[1] - circ[1]) + - (inc[1] - circ[1]) * (x36u[0] - circ[0]); + if cross.abs() < 1e-5 * (1.0 + oi2) * (1.0 + dist2(circ, x36u)) { + out.push(fact( + "反演内心", + "O,\\ I,\\ X_{36}", + "\\text{共线}".into(), + None, + "X(36)\\in OI", + "反演内心在 OI 线上", + )); + } + } + } + + // X(41): bary a³(b+c−a); X(6)-Ceva conjugate of X(31). + { + let sa = b + c - a; + let sb = c + a - b; + let sc = a + b - c; + if sa > 1e-12 && sb > 1e-12 && sc > 1e-12 { + let wa = a * a * a * sa; + let wb = b * b * b * sb; + let wc = c * c * c * sc; + let den = wa + wb + wc; + if den > 1e-12 { + let x41 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "第二幂截点", + "X_{41}", + pt(x41[0], x41[1]), + None, + "X(41) = \\bigl(a^3(b+c-a):\\cdots\\bigr)", + "X(41):勒莫恩点对第二幂点的 Ceva 共轭", + ).with(Shape::Point { + x: x41[0], + y: x41[1], + label: "X41".into(), + })); + } + } + } + + // X(48): crosspoint of I and X(63); bary a sin 2A. + { + let wa = a * (2.0 * g[0]).sin(); + let wb = b * (2.0 * g[1]).sin(); + let wc = c * (2.0 * g[2]).sin(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x48 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "双倍角截点", + "X_{48}", + pt(x48[0], x48[1]), + None, + "X(48) = (a\\sin 2A:b\\sin 2B:c\\sin 2C)", + "X(48):内心与 X(63) 的截线交点", + ).with(Shape::Point { + x: x48[0], + y: x48[1], + label: "X48".into(), + })); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -6723,6 +6856,40 @@ mod tests { } } + #[test] + fn x36_inverse_i_x41_x48() { + // Scalene 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x36 = fs.iter().find(|f| f.group == "反演内心" && f.label == "X_{36}").expect("X36"); + let i = fs.iter().find(|f| f.group == "特殊点" && f.label == "I").expect("I"); + let o = fs.iter().find(|f| f.group == "特殊点" && f.label == "O").expect("O"); + assert_ne!(x36.value, i.value); + assert_ne!(x36.value, o.value); + assert!(fs.iter().any(|f| f.group == "反演内心" && f.label.contains("OX"))); + assert!(fs.iter().any(|f| f.group == "反演内心" && f.value.contains("共线"))); + let x41 = fs.iter().find(|f| f.group == "第二幂截点" && f.label == "X_{41}").expect("X41"); + let x31 = fs.iter().find(|f| f.group == "第二幂点" && f.label == "X_{31}").expect("X31"); + assert_ne!(x41.value, x31.value); + let x48 = fs.iter().find(|f| f.group == "双倍角截点" && f.label == "X_{48}").expect("X48"); + assert_ne!(x48.value, x41.value); + assert_ne!(x48.value, x36.value); + + // Equilateral: X36 skipped (I=O); X41=X48=G. + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().all(|f| f.group != "反演内心"), "X36 skip equilateral"); + let g = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + let x41e = fs2.iter().find(|f| f.group == "第二幂截点" && f.label == "X_{41}").unwrap(); + let x48e = fs2.iter().find(|f| f.group == "双倍角截点" && f.label == "X_{48}").unwrap(); + assert_eq!(x41e.value, g.value); + assert_eq!(x48e.value, g.value); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 16f985e8a2907d42fd4077fc2b0b3c4934552050..14da6d4fda23f88ca4fe8ad2d428c02c8f783e06 100644 GIT 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zdbBiC9WJ+x47Cm5!iLjdnQ9}E8A(wK)qdU2fZqsmGtkZKU|KP++e|zbehF)aiC6kC zZC|J+Mm| Date: Sun, 1 Nov 2026 16:15:22 +0800 Subject: [PATCH 033/123] feat: de Longchamps X20, Far-out X23, OI companion X35, crosspoint X38 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Tag Schiffler as X(21) and Kosnita as X(54). X23 skips equilateral (G=O); X20 bary a(cos A−cos B cos C) cross-checks L=2O−H. --- crates/mathcore/src/geometry.rs | 248 ++++++++++++++++++++++++++++++-- src/wasm/pkg/mathcore_bg.wasm | Bin 638548 -> 641680 bytes 2 files changed, 237 insertions(+), 11 deletions(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 65ebdaa..116208e 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -1154,7 +1154,8 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } - // de Longchamps point L: reflection of H over O (so O midpoint of LH); on Euler line. + // de Longchamps X(20): reflection of H over O (so O midpoint of LH); on Euler line. + // Trilinear cos A − cos B cos C; bary a(cos A − cos B cos C). { let longch = [2.0 * circ[0] - orth[0], 2.0 * circ[1] - orth[1]]; out.push(fact( @@ -1162,12 +1163,12 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "L", pt(longch[0], longch[1]), None, - "L = 2O - H", - "德龙尚点:垂心关于外心的对称点", + "X(20) = L = 2O - H", + "德龙尚点 X(20):垂心关于外心的对称点", ).with(Shape::Point { x: longch[0], y: longch[1], - label: "L 德龙尚".into(), + label: "L=X20 德龙尚".into(), })); let mid = [(longch[0] + orth[0]) / 2.0, (longch[1] + orth[1]) / 2.0]; if dist2(mid, circ) < 1e-6 * (1.0 + dist2(circ, orth)) { @@ -1180,6 +1181,30 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "外心是 LH 的中点(欧拉线上)", )); } + // Bary cross-check: a(cos A − cos B cos C) + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + let wa = a * (ca - cb * cc); + let wb = b * (cb - cc * ca); + let wc = c * (cc - ca * cb); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xb = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if dist2(xb, longch) < 1e-4 * (1.0 + rr) { + out.push(fact( + "德龙尚点", + "X_{20}", + pt(xb[0], xb[1]), + None, + "X(20) = \\bigl(a(\\cos A-\\cos B\\cos C):\\cdots\\bigr)", + "X(20) 重心坐标与 L=2O−H 一致", + )); + } + } } // Mittenpunkt Mi: perspector of medial and excentral triangles; bary a(s-a):b(s-b):c(s-c). @@ -1227,12 +1252,12 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "Sc", pt(sf[0], sf[1]), None, - "\\text{Euler}(\\triangle ABC)\\cap\\text{Euler}(\\triangle IBC)", - "席弗勒点:内心三角形与原三角形欧拉线的交点", + "X(21) = \\text{Euler}(\\triangle ABC)\\cap\\text{Euler}(\\triangle IBC)", + "席弗勒点 X(21):内心三角形与原三角形欧拉线的交点", ).with(Shape::Point { x: sf[0], y: sf[1], - label: "Sc 席弗勒".into(), + label: "Sc=X21 席弗勒".into(), })); if let Some((o_ica, _)) = circum2(inc, pc, pa) { let g_ica = [ @@ -1530,7 +1555,7 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] )); } - // Kosnita point: A O_a ∩ B O_b ∩ C O_c with O_a = circumcenter of △OBC. + // Kosnita X(54): A O_a ∩ B O_b ∩ C O_c with O_a = circumcenter of △OBC. // Skip when △OAB / OBC / OCA is degenerate (e.g. right △ with O on a side). { let oa = circum2(circ, pb, pc); @@ -1548,12 +1573,12 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "Ko", pt(ko[0], ko[1]), None, - "AO_a \\cap BO_b \\cap CO_c", - "科斯尼塔点:A 与 △OBC 外心等连线的交点", + "X(54) = AO_a \\cap BO_b \\cap CO_c", + "科斯尼塔点 X(54):A 与 △OBC 外心等连线的交点", ).with(Shape::Point { x: ko[0], y: ko[1], - label: "Ko 科斯尼塔".into(), + label: "Ko=X54 科斯尼塔".into(), })); } } @@ -3428,6 +3453,160 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // X(23) Far-out point: circumcircle-inverse of the centroid; skip equilateral (G=O). + // Trilinear a(b⁴+c⁴−a⁴−b²c²); bary a²(b⁴+c⁴−a⁴−b²c²). On Euler line. + { + let og2 = { + let dx = centroid[0] - circ[0]; + let dy = centroid[1] - circ[1]; + dx * dx + dy * dy + }; + if og2 > 1e-12 { + let scale = (rr * rr) / og2; + let x23 = [ + circ[0] + scale * (centroid[0] - circ[0]), + circ[1] + scale * (centroid[1] - circ[1]), + ]; + // Bary a²(b⁴+c⁴−a⁴−b²c²) + let a2 = a * a; + let b2 = b * b; + let c2 = c * c; + let a4 = a2 * a2; + let b4 = b2 * b2; + let c4 = c2 * c2; + let wa = a2 * (b4 + c4 - a4 - b2 * c2); + let wb = b2 * (c4 + a4 - b4 - c2 * a2); + let wc = c2 * (a4 + b4 - c4 - a2 * b2); + let den = wa + wb + wc; + let x23u = if den.abs() > 1e-12 { + let xb = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if dist2(xb, x23) < 1e-4 * (1.0 + rr) { + xb + } else { + x23 + } + } else { + x23 + }; + out.push(fact( + "远点", + "X_{23}", + pt(x23u[0], x23u[1]), + None, + "X(23) = O + R^2(G-O)/|OG|^2", + "远点 X(23):重心关于外接圆的反演点", + ).with(Shape::Point { + x: x23u[0], + y: x23u[1], + label: "X23 远点".into(), + })); + // |OX23| · |OG| = R² + let d_ox = dist2(circ, x23u); + let d_og = og2.sqrt(); + if d_og > 1e-12 { + let prod = d_ox * d_og; + if (prod - rr * rr).abs() < 1e-4 * (1.0 + rr * rr) { + out.push(fact( + "远点", + "|OX_{23}|\\cdot|OG|", + nice(rr * rr), + Some(rr * rr), + "|OX_{23}|\\cdot|OG| = R^2", + "反演定义:乘积等于外接圆半径平方", + )); + } + } + // Collinear O, G, X23 (Euler) + let cross = (centroid[0] - circ[0]) * (x23u[1] - circ[1]) + - (centroid[1] - circ[1]) * (x23u[0] - circ[0]); + if cross.abs() < 1e-5 * (1.0 + og2) * (1.0 + dist2(circ, x23u)) { + out.push(fact( + "远点", + "O,\\ G,\\ X_{23}", + "\\text{共线}".into(), + None, + "X(23)\\in\\text{Euler}", + "远点在欧拉线上", + )); + } + } + } + + // X(35): bary sin A + sin 2A; on OI (companion of circum-inverse X(36)=sin A−sin 2A). + { + let wa = g[0].sin() + (2.0 * g[0]).sin(); + let wb = g[1].sin() + (2.0 * g[1]).sin(); + let wc = g[2].sin() + (2.0 * g[2]).sin(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x35 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + let di = dist2(x35, inc); + let do_ = dist2(x35, circ); + if di > 1e-10 || do_ > 1e-10 { + out.push(fact( + "OI调和点", + "X_{35}", + pt(x35[0], x35[1]), + None, + "X(35) = (\\sin A+\\sin 2A:\\cdots)", + "X(35):与 X(36) 成对的 OI 线上点", + ).with(Shape::Point { + x: x35[0], + y: x35[1], + label: "X35".into(), + })); + let cross = (inc[0] - circ[0]) * (x35[1] - circ[1]) + - (inc[1] - circ[1]) * (x35[0] - circ[0]); + let oi2 = dist2(circ, inc); + if oi2 > 1e-12 + && cross.abs() < 1e-5 * (1.0 + oi2) * (1.0 + dist2(circ, x35)) + { + out.push(fact( + "OI调和点", + "O,\\ I,\\ X_{35}", + "\\text{共线}".into(), + None, + "X(35)\\in OI", + "X(35) 在 OI 线上", + )); + } + } + } + } + + // X(38): bary a(b²+c²); crosspoint of I and Moses X(75). + { + let wa = a * (b * b + c * c); + let wb = b * (c * c + a * a); + let wc = c * (a * a + b * b); + let den = wa + wb + wc; + if den > 1e-12 { + let x38 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "截线交点", + "X_{38}", + pt(x38[0], x38[1]), + None, + "X(38) = \\bigl(a(b^2+c^2):\\cdots\\bigr)", + "X(38):内心与摩西点的截线交点", + ).with(Shape::Point { + x: x38[0], + y: x38[1], + label: "X38".into(), + })); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -6890,6 +7069,53 @@ mod tests { assert_eq!(x48e.value, g.value); } + #[test] + fn x20_x23_farout_x35_x38() { + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let l = fs.iter().find(|f| f.group == "德龙尚点" && f.label == "L").expect("L"); + assert!(fs.iter().any(|f| f.group == "德龙尚点" && f.label == "X_{20}"), "X20 bary"); + let x23 = fs.iter().find(|f| f.group == "远点" && f.label == "X_{23}").expect("X23"); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let o = fs.iter().find(|f| f.group == "特殊点" && f.label == "O").expect("O"); + assert_ne!(x23.value, g.value); + assert_ne!(x23.value, o.value); + assert_ne!(x23.value, l.value); + assert!(fs.iter().any(|f| f.group == "远点" && f.label.contains("OX"))); + assert!(fs.iter().any(|f| f.group == "远点" && f.value.contains("共线"))); + let x35 = fs.iter().find(|f| f.group == "OI调和点" && f.label == "X_{35}").expect("X35"); + let i = fs.iter().find(|f| f.group == "特殊点" && f.label == "I").expect("I"); + assert_ne!(x35.value, i.value); + assert_ne!(x35.value, o.value); + assert!(fs.iter().any(|f| f.group == "OI调和点" && f.value.contains("共线"))); + let x38 = fs.iter().find(|f| f.group == "截线交点" && f.label == "X_{38}").expect("X38"); + assert_ne!(x38.value, x35.value); + assert_ne!(x38.value, x23.value); + + // Equilateral: X23 skipped (G=O); X38 = G. + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().all(|f| f.group != "远点"), "X23 skip equilateral"); + let g2 = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + let x38e = fs2.iter().find(|f| f.group == "截线交点" && f.label == "X_{38}").unwrap(); + assert_eq!(x38e.value, g2.value); + + // Right 3-4-5: X20/X23/X35/X38 still present. + let k3 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().any(|f| f.group == "德龙尚点" && f.label == "L")); + assert!(fs3.iter().any(|f| f.group == "远点" && f.label == "X_{23}")); + assert!(fs3.iter().any(|f| f.group == "OI调和点" && f.label == "X_{35}")); + assert!(fs3.iter().any(|f| f.group == "截线交点" && f.label == "X_{38}")); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 14da6d4fda23f88ca4fe8ad2d428c02c8f783e06..93da0dd692cd3fb2beca33d9a4376cd5694638ed 100644 GIT binary patch delta 57502 zcmb?^30zgx_Aq;&3y93hqzIgQWmIrX3kY?aLodZCwaHS;v>fW$+-ndGl@t{{=mtf- zASx;<3VJb7QPI#)v8=Etv8c#Uv8YFd`mMFkIrkpS`hNfa_q~44efBzguf68I_HZs2 zS|c-7M-^RiZeLk+!pVJ}6Dukz{?WOWdVP96WT9*IHIo!LkG?ym_?LF>F7(2VRo*Yq zh8@cMS34>1d%r`Qb|{mddQ+M2)1THYQ4aV72c#7qb7I~;+llPVNPn8z9?FItd}=4s zi6;jVKPAw&gk}{g)$ha<|K`gGZQ2gl{CJTwaV{R$@ijuzcPOX*CL_M?{=oqyJN}AK zbm^pAdeV>kv?HF%8vo_AVh5sBMhBdr&D-o4m7akmG-W#uAE$H(x(~6A3(!a|yw4^{;*Cm*i z7bvA&qO}IfZ(T}hO+j%{$aB!HK4CNtrlzl)FrF7XetibNpXo-N^`a zwFS^v*ausVDWl&Ep-o$qNBfR)tplm}RGO6YeMczm@96;lpWk7UJU||19pWVZS2r-v z@}#ouXUMhf+`6@Ra9IE8^D|55IQ3}V0Deb*_6z}hUh?1w2SK{Au zyj+#=ANNV}&|FKL9G53QS-dbIkVHpN?F{uqjDs&gVLFGqve}*gX*Nb%w_~s zZU)q$ZLOz4ZSz)p5~*|>{3LDK4EETa-`kmZE5`@N^qMN)lP8DCp;pV&a_>B=RgRP+ 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Always finite (weights > 0). + { + let wa = a * (2.0 * b + 2.0 * c - a); + let wb = b * (2.0 * c + 2.0 * a - b); + let wc = c * (2.0 * a + 2.0 * b - c); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x45 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "米滕beth", + "X_{45}", + pt(x45[0], x45[1]), + None, + "X(45) = \\bigl(a(2b+2c-a):\\cdots\\bigr)", + "X(45):米滕点对内心的 beth 共轭", + ).with(Shape::Point { + x: x45[0], + y: x45[1], + label: "X45".into(), + })); + } + } + + // X(46): X(4)-Ceva conjugate of I; bary a(cos B+cos C−cos A). On OI line. + { + let wa = a * (g[1].cos() + g[2].cos() - g[0].cos()); + let wb = b * (g[2].cos() + g[0].cos() - g[1].cos()); + let wc = c * (g[0].cos() + g[1].cos() - g[2].cos()); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x46 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "垂心Ceva内心", + "X_{46}", + pt(x46[0], x46[1]), + None, + "X(46) = \\bigl(a(\\cos B+\\cos C-\\cos A):\\cdots\\bigr)", + "X(46):垂心对内心的 Ceva 共轭(在 OI 线上)", + ).with(Shape::Point { + x: x46[0], + y: x46[1], + label: "X46".into(), + })); + } + } + + // X(47): bary a cos 2A; pairs with X(48)=a sin 2A. Equals G on equilateral. + { + let wa = a * (2.0 * g[0]).cos(); + let wb = b * (2.0 * g[1]).cos(); + let wc = c * (2.0 * g[2]).cos(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x47 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "双倍角余弦", + "X_{47}", + pt(x47[0], x47[1]), + None, + "X(47) = (a\\cos 2A:b\\cos 2B:c\\cos 2C)", + "X(47):双倍角余弦点(与 X(48) 成对)", + ).with(Shape::Point { + x: x47[0], + y: x47[1], + label: "X47".into(), + })); + } + } + + // X(49): center of sine-triple-angle circle; bary a cos 3A (= sin A cos 3A). + // Equals G on equilateral (cos 180° = −1). + { + let wa = a * (3.0 * g[0]).cos(); + let wb = b * (3.0 * g[1]).cos(); + let wc = c * (3.0 * g[2]).cos(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x49 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "三倍角正弦圆", + "X_{49}", + pt(x49[0], x49[1]), + None, + "X(49) = (a\\cos 3A:b\\cos 3B:c\\cos 3C)", + "X(49):三倍角正弦圆圆心", + ).with(Shape::Point { + x: x49[0], + y: x49[1], + label: "X49".into(), + })); + } + } + + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -7274,6 +7380,66 @@ mod tests { assert!(fs3.iter().any(|f| f.group == "克劳森等角" && f.label == "X_{63}")); } + #[test] + fn x45_x46_x47_x49() { + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x45 = fs.iter().find(|f| f.group == "米滕beth" && f.label == "X_{45}").expect("X45"); + let x46 = fs.iter().find(|f| f.group == "垂心Ceva内心" && f.label == "X_{46}").expect("X46"); + let x47 = fs.iter().find(|f| f.group == "双倍角余弦" && f.label == "X_{47}").expect("X47"); + let x49 = fs.iter().find(|f| f.group == "三倍角正弦圆" && f.label == "X_{49}").expect("X49"); + let x48 = fs.iter().find(|f| f.group == "双倍角截点" && f.label == "X_{48}").expect("X48"); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let o = fs.iter().find(|f| f.group == "特殊点" && f.label == "O").expect("O"); + let i = fs.iter().find(|f| f.group == "特殊点" && f.label == "I").expect("I"); + assert_ne!(x45.value, i.value); + assert_ne!(x45.value, g.value); + assert_ne!(x46.value, i.value); + assert_ne!(x46.value, o.value); + assert_ne!(x47.value, x48.value); + assert_ne!(x47.value, g.value); + assert_ne!(x49.value, g.value); + assert_ne!(x49.value, x47.value); + // X(46) on OI: cross product of OI × OX46 ≈ 0. + if let (Some(Shape::Point { x: ox, y: oy, .. }), Some(Shape::Point { x: ix, y: iy, .. }), Some(Shape::Point { x: px, y: py, .. })) = + (o.shape.as_ref(), i.shape.as_ref(), x46.shape.as_ref()) + { + let cross = (ix - ox) * (py - oy) - (iy - oy) * (px - ox); + assert!(cross.abs() < 1e-6, "X46 not on OI: cross={cross}"); + } else { + panic!("missing shapes for O/I/X46"); + } + + // Equilateral: X45/X46/X47/X49 all = G. + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g2 = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + for (grp, lab) in [ + ("米滕beth", "X_{45}"), + ("垂心Ceva内心", "X_{46}"), + ("双倍角余弦", "X_{47}"), + ("三倍角正弦圆", "X_{49}"), + ] { + let f = fs2.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("missing {lab}")); + assert_eq!(f.value, g2.value, "{lab} should be G on equilateral"); + } + + // Right 3-4-5: all four present (no tan/sec singularity). + let k3 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().any(|f| f.group == "米滕beth" && f.label == "X_{45}")); + assert!(fs3.iter().any(|f| f.group == "垂心Ceva内心" && f.label == "X_{46}")); + assert!(fs3.iter().any(|f| f.group == "双倍角余弦" && f.label == "X_{47}")); + assert!(fs3.iter().any(|f| f.group == "三倍角正弦圆" && f.label == "X_{49}")); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index cefc52345bec35a0f3a2d6841993b2717cb13ec3..7ab159e2dd83fe8ee4c19792820f347c8908964b 100644 GIT binary patch delta 48191 zcmb@v3w#aN_BfusXXfOc9FHWDkW7w{1R*G`q`@c&MXE~M>r#~VYG{kwcW;}hAPB;Q z9Rw#41VKocAP9m~l_+h~HYzG@qqL1j+tBp(zt*0alM{9C_j7-r|LymiJ!|c~o_p=J zUvtK>%@J4kMHF3@JQ_+*xOk?xDAlFK*Q6%ulX|_wJlEeBNJ2mgeSd86Z8uK~O)XjB z`wGn}QIEdYR-Nf5sSADIqd6t&@`-P&bF6)7hN|wj2K$$k9CJ~8t=ot!DWoq=^MKMI z`nUCCT2aDg4J47pzqA@eXihOQD<0YAT|!HX)zfV!BA2dy!Tzj7Tr>%JC3HERju7?v}q43dW6KN z69T`aX+7Io-a{J#9MNQ-u% z&_LDFX)&$brLG_Fw(8aSX-n-cbcA~4N|4a7>zH~|izqJae8`iQ?8N3l>bzb%Jt}rW 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z$cu-1@o0&!<2ufZIK8FCrs#LrO|HU>%ExVx`(&c%mtnf!Yh;9{A~qb9`v4jK))7=kdfQKtZ%QuhR!H6=1iM5 z@4j6bhwFdAfh*PIhhRRWFF^VkhRD3Zv*Znu?x&gZ__^xtoKS!___M~WbA^Xr0m~WK>*c@C zi}!o+0WW^li(k_jI@0DR_no;S-bc-P^jb7PsZxs!2MF1JXRE{7kF2&UicqQWUNCb^W? zEYxa=xPb4w(YH&GZn;WnOJRSn($1y0e>lDoMJ|J;jc?@6Steo{*?cu4q9BdduMlx@ zoxwZ;rNM3jd)kx%_}B+!mb4i@7|_UAsa=SxUniJCqJEJz<`N$%dH; zvjk=n%ubj?FlS*d!F&#L55~vGp#;H1!E}ci1G5q4HJCFnAHiIM`3mMAFuqoY(i|ol zCIO}&%rL8?tuh4{b75A%Y=?ORrV8d`m};2sV1BaF!Bu#$YJe|YT!q`E(|pOY8b3Nd z@9R(;)cJYQjDDRYY-)`!O<67CRJ)Bfuf_vWyKEHwJZ`IgXmjWqv=cSLng#!y=S5AE6|?qJ_u)_2RGi zVV#raZxq9vJ)1i8-iRX)U7>n5rRy8TPij~YUEYKZ5p2t5lmvFi&7xOASdc>>ii#oc z17q^Lp718~s)E}c;kIwaDFWB$#j=RL5)VpwxfLsAu zj#qXv^M=XfT+D*p*e0*9V>-S|B!=WiIrNEeHf#*k%3RnywyuaG-; zw9R+r&&YF4nUR-2&ovG1T!Q3Gy7MvaRF{Ey!?Y{Y9eG7mSk+5MSDg4v(237{_x(S0 CpQerg From f1e6fe94dadb60504e9421bc9ba52f02db065982 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 16:22:58 +0800 Subject: [PATCH 036/123] feat: Napoleon isogonals X61/X62, triple-angle X50, de Longchamps-isog X64 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit X61/X62 bary a cos(A∓π/3) from cloud ca947d5/f871222 lineage; X50 pairs with X49 (skip equilateral); X64 isogonal of X20 (skip right ∞). --- crates/mathcore/src/geometry.rs | 191 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 645987 -> 649181 bytes 2 files changed, 191 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index dfa0081..6415f87 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -3824,6 +3824,146 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } + + // X(50): bary a sin 3A (= sin A sin 3A); pairs with X(49)=a cos 3A. + // Equilateral: 3A=180°, sin=0 → all weights 0 → skip. + { + let wa = a * (3.0 * g[0]).sin(); + let wb = b * (3.0 * g[1]).sin(); + let wc = c * (3.0 * g[2]).sin(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x50 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "三倍角正弦", + "X_{50}", + pt(x50[0], x50[1]), + None, + "X(50) = (a\\sin 3A:b\\sin 3B:c\\sin 3C)", + "X(50):三倍角正弦点(与 X(49) 成对;等边时退化)", + ).with(Shape::Point { + x: x50[0], + y: x50[1], + label: "X50".into(), + })); + } + } + + // X(61), X(62): isogonal conjugates of the Napoleon centers X(17), X(18). + // Trilinear cos(A∓π/3); bary a cos(A∓π/3). Reciprocals of Napoleon trilinears. + { + let pi3 = std::f64::consts::PI / 3.0; + let c61 = [(g[0] - pi3).cos(), (g[1] - pi3).cos(), (g[2] - pi3).cos()]; + let wa = a * c61[0]; + let wb = b * c61[1]; + let wc = c * c61[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x61 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "拿破仑等角共轭点", + "X_{61}", + pt(x61[0], x61[1]), + None, + "X(61) = \\bigl(a\\cos(A-\\pi/3):\\cdots\\bigr)", + "X(61):第一拿破仑点的等角共轭", + ).with(Shape::Point { + x: x61[0], + y: x61[1], + label: "X61".into(), + })); + out.push(fact( + "拿破仑等角共轭点", + "X_{61} \\leftrightarrow N_1", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(17)", + "X(61) 与第一拿破仑点 X(17) 互为等角共轭", + )); + } + let c62 = [(g[0] + pi3).cos(), (g[1] + pi3).cos(), (g[2] + pi3).cos()]; + let wa = a * c62[0]; + let wb = b * c62[1]; + let wc = c * c62[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x62 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "拿破仑等角共轭点", + "X_{62}", + pt(x62[0], x62[1]), + None, + "X(62) = \\bigl(a\\cos(A+\\pi/3):\\cdots\\bigr)", + "X(62):第二拿破仑点的等角共轭", + ).with(Shape::Point { + x: x62[0], + y: x62[1], + label: "X62".into(), + })); + out.push(fact( + "拿破仑等角共轭点", + "X_{62} \\leftrightarrow N_2", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(18)", + "X(62) 与第二拿破仑点 X(18) 互为等角共轭", + )); + } + } + + // X(64): isogonal conjugate of de Longchamps X(20). + // Bary a/(cos A − cos B cos C). Skip when a side-den vanishes or Σweights=0 + // (right △: X64 is at infinity — Σ = 0). + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + let da = ca - cb * cc; + let db = cb - cc * ca; + let dc = cc - ca * cb; + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + let wa = a / da; + let wb = b / db; + let wc = c / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x64 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "德龙尚等角", + "X_{64}", + pt(x64[0], x64[1]), + None, + "X(64) = \\bigl(a/(\\cos A-\\cos B\\cos C):\\cdots\\bigr)", + "X(64):德龙尚点的等角共轭", + ).with(Shape::Point { + x: x64[0], + y: x64[1], + label: "X64".into(), + })); + out.push(fact( + "德龙尚等角", + "X_{64} \\leftrightarrow L", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(20)", + "X(64) 与德龙尚点 X(20) 互为等角共轭", + )); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -7440,6 +7580,57 @@ mod tests { assert!(fs3.iter().any(|f| f.group == "三倍角正弦圆" && f.label == "X_{49}")); } + #[test] + fn x50_x61_x62_x64() { + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x50 = fs.iter().find(|f| f.group == "三倍角正弦" && f.label == "X_{50}").expect("X50"); + let x49 = fs.iter().find(|f| f.group == "三倍角正弦圆" && f.label == "X_{49}").expect("X49"); + assert_ne!(x50.value, x49.value); + let x61 = fs.iter().find(|f| f.group == "拿破仑等角共轭点" && f.label == "X_{61}").expect("X61"); + let n1 = fs.iter().find(|f| f.group == "拿破仑中心" && f.label == "N_1").expect("N1"); + assert_ne!(x61.value, n1.value); + assert!(fs.iter().any(|f| f.group == "拿破仑等角共轭点" && f.label.contains("N_1") && f.value.contains("等角"))); + let x62 = fs.iter().find(|f| f.group == "拿破仑等角共轭点" && f.label == "X_{62}").expect("X62"); + let n2 = fs.iter().find(|f| f.group == "拿破仑中心" && f.label == "N_2").expect("N2"); + assert_ne!(x62.value, n2.value); + assert_ne!(x61.value, x62.value); + assert!(fs.iter().any(|f| f.group == "拿破仑等角共轭点" && f.label.contains("N_2") && f.value.contains("等角"))); + let x64 = fs.iter().find(|f| f.group == "德龙尚等角" && f.label == "X_{64}").expect("X64"); + let l = fs.iter().find(|f| f.group == "德龙尚点" && f.label == "L").expect("L"); + assert_ne!(x64.value, l.value); + assert!(fs.iter().any(|f| f.group == "德龙尚等角" && f.label.contains("L") && f.value.contains("等角"))); + + // Equilateral: X50 skipped (sin 180°=0); X61=X62=X64=G. + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g2 = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + assert!(fs2.iter().all(|f| f.group != "三倍角正弦"), "X50 skip equilateral"); + for (grp, lab) in [ + ("拿破仑等角共轭点", "X_{61}"), + ("拿破仑等角共轭点", "X_{62}"), + ("德龙尚等角", "X_{64}"), + ] { + let p = fs2.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("{lab}")); + assert_eq!(p.value, g2.value, "{lab}"); + } + + // Right 3-4-5: X50/X61/X62 present; X64 at infinity (Σweights=0) → skip. + let k3 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().any(|f| f.group == "三倍角正弦" && f.label == "X_{50}")); + assert!(fs3.iter().any(|f| f.group == "拿破仑等角共轭点" && f.label == "X_{61}")); + assert!(fs3.iter().any(|f| f.group == "拿破仑等角共轭点" && f.label == "X_{62}")); + assert!(fs3.iter().all(|f| f.group != "德龙尚等角"), "X64 skip right (infinity)"); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git 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z_5;KyO7yNCqsR!QXNk4B&oIr9OXvP8nxmhmH2Vak$AV?W5%Zl8+gkHHUG8fik!W+@ zKF&mLwo5-T%4&2l2RTvj6}9 From 2abbc3eba8dba5b187802e7ddc4232b91c8e6ead Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 16:26:28 +0800 Subject: [PATCH 037/123] feat: orthic G/K X51/X53, tangential O X26, H-Clawson X27, I-H X29 --- crates/mathcore/src/geometry.rs | 263 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 649181 -> 652959 bytes 2 files changed, 263 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 6415f87..4b39539 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -3964,6 +3964,219 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(51): centroid of the orthic triangle; bary a³ cos(B−C). + // Geometric cross-check: mean of altitude feet. Equals G on equilateral. + { + let wa = a.powi(3) * (g[1] - g[2]).cos(); + let wb = b.powi(3) * (g[2] - g[0]).cos(); + let wc = c.powi(3) * (g[0] - g[1]).cos(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x51 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "垂足重心", + "X_{51}", + pt(x51[0], x51[1]), + None, + "X(51) = \\bigl(a^3\\cos(B-C):\\cdots\\bigr)", + "X(51):垂足三角形的重心", + ).with(Shape::Point { + x: x51[0], + y: x51[1], + label: "X51".into(), + })); + // Mean of altitude feet ≈ X(51). + let mut feet = [[0.0f64; 2]; 3]; + let mut ok = true; + for i in 0..3 { + let p0 = v[i]; + let q1 = v[(i + 1) % 3]; + let q2 = v[(i + 2) % 3]; + let dx = q2[0] - q1[0]; + let dy = q2[1] - q1[1]; + let d2 = dx * dx + dy * dy; + if d2 < 1e-18 { + ok = false; + break; + } + let t = ((p0[0] - q1[0]) * dx + (p0[1] - q1[1]) * dy) / d2; + feet[i] = [q1[0] + t * dx, q1[1] + t * dy]; + } + if ok { + let g_orth = [ + (feet[0][0] + feet[1][0] + feet[2][0]) / 3.0, + (feet[0][1] + feet[1][1] + feet[2][1]) / 3.0, + ]; + if dist2(x51, g_orth) < 1e-5 * (1.0 + rr) { + out.push(fact( + "垂足重心", + "G_{\\text{orthic}}", + "\\checkmark".into(), + None, + "X(51) = (H_a+H_b+H_c)/3", + "与垂足三角形三顶点的重心重合", + )); + } + } + } + } + + // X(53): symmedian point of the orthic triangle; bary a tan A cos(B−C). + // Skip right △ (tan ∞) and near-right (cos≈0). + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + if ca.abs() > 1e-12 && cb.abs() > 1e-12 && cc.abs() > 1e-12 { + let wa = a * (g[0].sin() / ca) * (g[1] - g[2]).cos(); + let wb = b * (g[1].sin() / cb) * (g[2] - g[0]).cos(); + let wc = c * (g[2].sin() / cc) * (g[0] - g[1]).cos(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x53 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "垂足对称中线点", + "X_{53}", + pt(x53[0], x53[1]), + None, + "X(53) = \\bigl(a\\tan A\\cos(B-C):\\cdots\\bigr)", + "X(53):垂足三角形的对称中线点(锐角)", + ).with(Shape::Point { + x: x53[0], + y: x53[1], + label: "X53".into(), + })); + } + } + } + + // X(26): circumcenter of the tangential triangle; on Euler line. + // Bary a²(b² cos 2B + c² cos 2C − a² cos 2A). Isogonal of X(70). + // Right △: Σweights = 0 → point at infinity on Euler — skip. + { + let c2a = (2.0 * g[0]).cos(); + let c2b = (2.0 * g[1]).cos(); + let c2c = (2.0 * g[2]).cos(); + let wa = a * a * (b * b * c2b + c * c * c2c - a * a * c2a); + let wb = b * b * (c * c * c2c + a * a * c2a - b * b * c2b); + let wc = c * c * (a * a * c2a + b * b * c2b - c * c * c2c); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x26 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "切线三角形外心", + "X_{26}", + pt(x26[0], x26[1]), + None, + "X(26) = \\bigl(a^2(b^2\\cos 2B+c^2\\cos 2C-a^2\\cos 2A):\\cdots\\bigr)", + "X(26):切线三角形的外心(在欧拉线上)", + ).with(Shape::Point { + x: x26[0], + y: x26[1], + label: "X26".into(), + })); + // On Euler line OH: cross (X−O)×(H−O) ≈ 0. + let hx = orth[0] - circ[0]; + let hy = orth[1] - circ[1]; + let xx = x26[0] - circ[0]; + let xy = x26[1] - circ[1]; + let cross = xx * hy - xy * hx; + let scale = (1.0 + dist2(circ, orth)) * (1.0 + dist2(circ, x26)); + if cross.abs() < 1e-5 * scale { + out.push(fact( + "切线三角形外心", + "X_{26}\\in OH", + "\\checkmark".into(), + None, + "X(26)\\in\\text{Euler}", + "X(26) 在欧拉线 OH 上", + )); + } + } + } + + // X(27): cevapoint of H and Clawson X(19); bary tan A/(b+c). + // Skip right △ (tan ∞). + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + if ca.abs() > 1e-12 && cb.abs() > 1e-12 && cc.abs() > 1e-12 { + let wa = (g[0].sin() / ca) / (b + c); + let wb = (g[1].sin() / cb) / (c + a); + let wc = (g[2].sin() / cc) / (a + b); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x27 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "垂心克劳森截点", + "X_{27}", + pt(x27[0], x27[1]), + None, + "X(27) = \\bigl(\\tan A/(b+c):\\cdots\\bigr)", + "X(27):垂心与克劳森点的截线交点(锐角)", + ).with(Shape::Point { + x: x27[0], + y: x27[1], + label: "X27".into(), + })); + } + } + } + + // X(29): cevapoint of I and H; bary tan A/(cos B + cos C). + // Skip right △ (tan ∞). Denom cos B+cos C = 2 sin(A/2)cos((B−C)/2) > 0. + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + let da = cb + cc; + let db = cc + ca; + let dc = ca + cb; + if ca.abs() > 1e-12 + && cb.abs() > 1e-12 + && cc.abs() > 1e-12 + && da.abs() > 1e-12 + && db.abs() > 1e-12 + && dc.abs() > 1e-12 + { + let wa = (g[0].sin() / ca) / da; + let wb = (g[1].sin() / cb) / db; + let wc = (g[2].sin() / cc) / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x29 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "内心垂心截点", + "X_{29}", + pt(x29[0], x29[1]), + None, + "X(29) = \\bigl(\\tan A/(\\cos B+\\cos C):\\cdots\\bigr)", + "X(29):内心与垂心的截线交点(锐角)", + ).with(Shape::Point { + x: x29[0], + y: x29[1], + label: "X29".into(), + })); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -7631,6 +7844,56 @@ mod tests { assert!(fs3.iter().all(|f| f.group != "德龙尚等角"), "X64 skip right (infinity)"); } + #[test] + fn x51_x53_x26_x27_x29() { + // Scalene acute 6-7-8: all five present; X51 = orthic centroid; X26 on Euler. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x51 = fs.iter().find(|f| f.group == "垂足重心" && f.label == "X_{51}").expect("X51"); + assert!(fs.iter().any(|f| f.group == "垂足重心" && f.label.contains("orthic"))); + let x53 = fs.iter().find(|f| f.group == "垂足对称中线点" && f.label == "X_{53}").expect("X53"); + let x26 = fs.iter().find(|f| f.group == "切线三角形外心" && f.label == "X_{26}").expect("X26"); + assert!(fs.iter().any(|f| f.group == "切线三角形外心" && f.label.contains("OH"))); + let x27 = fs.iter().find(|f| f.group == "垂心克劳森截点" && f.label == "X_{27}").expect("X27"); + let x29 = fs.iter().find(|f| f.group == "内心垂心截点" && f.label == "X_{29}").expect("X29"); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + assert_ne!(x51.value, g.value); + assert_ne!(x51.value, x53.value); + assert_ne!(x26.value, x51.value); + assert_ne!(x27.value, x29.value); + assert_ne!(x27.value, x51.value); + + // Equilateral: X51=X53=X26=X27=X29=G (angle-symmetric). + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g2 = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + for (grp, lab) in [ + ("垂足重心", "X_{51}"), + ("垂足对称中线点", "X_{53}"), + ("切线三角形外心", "X_{26}"), + ("垂心克劳森截点", "X_{27}"), + ("内心垂心截点", "X_{29}"), + ] { + let p = fs2.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("{lab}")); + assert_eq!(p.value, g2.value, "{lab}"); + } + + // Right 3-4-5: X51 present; X26 at ∞ (Σ=0); X53/X27/X29 skip (tan ∞). + let k3 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().any(|f| f.group == "垂足重心" && f.label == "X_{51}")); + assert!(fs3.iter().all(|f| f.group != "切线三角形外心"), "X26 skip right (infinity)"); + assert!(fs3.iter().all(|f| f.group != "垂足对称中线点"), "X53 skip right"); + assert!(fs3.iter().all(|f| f.group != "垂心克劳森截点"), "X27 skip right"); + assert!(fs3.iter().all(|f| f.group != "内心垂心截点"), "X29 skip right"); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 53007f7df4c20b7ad2ea08ec4b8a81d014249fdf..8c547a069ffc097d7863f729ec76559708987db4 100644 GIT binary patch delta 51104 zcmb@v30PHC*Er7J=UgTkE($21aPAcZR21jX9F9{OLuzGZj&EA;i{;QfgM~(hiXL>M zqFx3Q6%_?LsHmu@sAyPdR9IM6SXfw;l$QUs_BrR?i`n~q-|zWn&)sLQz4w~-T5FHz 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z0Tu^BM}&R|&mp8B13QFpa&r8wuCqnp<_WO>gtQ*x_q81;@Zbc)^Q=+HK;LRq5G`cJ08!Sj(CPxW*&jc4No1 ztQiIG6n`ig50QTvc2$Ubm!T$z)5}DkxQvGaTn;J^yuJt~{>&|JVqSFkyVB{KG8`;G zKJsJHzrakNgEU#b5eg_{o?&I|?}c-K*)f{>UIHE^VV)S{CCn2l%G1gtFbISwiJ>X5 zk)hu36EWO3@q#13b<>^ufZNo>AK;o9P5hx3{>X!AgD(0EH~DsY=!RZDWXMyana(xj z9x!n~FTC9&Pcggs2D^ij5!+4vOYRDQzIiun%A|LLPm}Y(s|D)ili`K001uJM@iXv1 z7p9m!$hR(vlJ~$e5SO^|kv*_|;D&oKd&9N?E_*J;+|?G$4cpSW zeegdk+Ts~PtV?RzQhJ3LnAo=+Mn2NB(PO;elQHk3OgtHLB6qThOFWo zA;j>`mM;) Date: Sun, 1 Nov 2026 16:27:13 +0800 Subject: [PATCH 038/123] feat: port OI-companion isogonals X79/X80 from cloud tip 2c555d4 --- crates/mathcore/src/geometry.rs | 113 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 652959 -> 654902 bytes 2 files changed, 113 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 4b39539..c52dcf7 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -4177,6 +4177,86 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(79), X(80): isogonal conjugates of X(35) and X(36). + // Trilinears 1/(1±2 cos A); bary a/(1±2 cos A). + // X(79) blows up when an angle is 120°; X(80) when an angle is 60° (equilateral). + { + let d79 = [ + 1.0 + 2.0 * g[0].cos(), + 1.0 + 2.0 * g[1].cos(), + 1.0 + 2.0 * g[2].cos(), + ]; + if d79.iter().all(|d| d.abs() > 1e-9) { + let wa = a / d79[0]; + let wb = b / d79[1]; + let wc = c / d79[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x79 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "OI伴点等角", + "X_{79}", + pt(x79[0], x79[1]), + None, + "X(79) = \\bigl(a/(1+2\\cos A):\\cdots\\bigr)", + "X(79):X(35) 的等角共轭", + ).with(Shape::Point { + x: x79[0], + y: x79[1], + label: "X79".into(), + })); + out.push(fact( + "OI伴点等角", + "X_{79} \\leftrightarrow X_{35}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(35)", + "X(79) 与 X(35) 互为等角共轭", + )); + } + } + let d80 = [ + 1.0 - 2.0 * g[0].cos(), + 1.0 - 2.0 * g[1].cos(), + 1.0 - 2.0 * g[2].cos(), + ]; + if d80.iter().all(|d| d.abs() > 1e-9) { + let wa = a / d80[0]; + let wb = b / d80[1]; + let wc = c / d80[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x80 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "反演内心等角", + "X_{80}", + pt(x80[0], x80[1]), + None, + "X(80) = \\bigl(a/(1-2\\cos A):\\cdots\\bigr)", + "X(80):X(36) 的等角共轭(有 60° 角时退化)", + ).with(Shape::Point { + x: x80[0], + y: x80[1], + label: "X80".into(), + })); + out.push(fact( + "反演内心等角", + "X_{80} \\leftrightarrow X_{36}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(36)", + "X(80) 与反演内心 X(36) 互为等角共轭", + )); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -7894,6 +7974,39 @@ mod tests { assert!(fs3.iter().all(|f| f.group != "内心垂心截点"), "X29 skip right"); } + #[test] + fn x79_x80_isogonals_of_x35_x36() { + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x79 = fs.iter().find(|f| f.group == "OI伴点等角" && f.label == "X_{79}").expect("X79"); + let x35 = fs.iter().find(|f| f.group == "OI调和点" && f.label == "X_{35}").expect("X35"); + assert_ne!(x79.value, x35.value); + assert!(fs.iter().any(|f| f.group == "OI伴点等角" && f.label.contains("35") && f.value.contains("等角"))); + let x80 = fs.iter().find(|f| f.group == "反演内心等角" && f.label == "X_{80}").expect("X80"); + let x36 = fs.iter().find(|f| f.group == "反演内心" && f.label == "X_{36}").expect("X36"); + assert_ne!(x80.value, x36.value); + assert_ne!(x79.value, x80.value); + assert!(fs.iter().any(|f| f.group == "反演内心等角" && f.label.contains("36") && f.value.contains("等角"))); + assert_eq!(fs.iter().filter(|f| f.label == "X_{63}").count(), 1); + + let k2 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + assert!(r2.cases[0].facts.iter().any(|f| f.label == "X_{79}")); + assert!(r2.cases[0].facts.iter().any(|f| f.label == "X_{80}")); + + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + let x79e = fs3.iter().find(|f| f.label == "X_{79}").unwrap(); + assert_eq!(x79e.value, g.value); + assert!(fs3.iter().all(|f| f.group != "反演内心等角"), "X80 skip equilateral"); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 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DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 16:28:07 +0800 Subject: [PATCH 039/123] feat: Clawson-X25 cevapoint X28; isogonals X70/X71/X73 --- crates/mathcore/src/geometry.rs | 191 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 654902 -> 658087 bytes 2 files changed, 191 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index c52dcf7..e930c6d 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -4257,6 +4257,149 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(28): cevapoint of Clawson X(19) and X(25); bary (sin A tan A)/(b+c). + // Skip right △ (tan ∞). + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + if ca.abs() > 1e-12 && cb.abs() > 1e-12 && cc.abs() > 1e-12 { + let wa = (g[0].sin() * g[0].sin() / ca) / (b + c); + let wb = (g[1].sin() * g[1].sin() / cb) / (c + a); + let wc = (g[2].sin() * g[2].sin() / cc) / (a + b); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x28 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "克劳森X25截点", + "X_{28}", + pt(x28[0], x28[1]), + None, + "X(28) = \\bigl(\\sin A\\tan A/(b+c):\\cdots\\bigr)", + "X(28):克劳森点与 X(25) 的截线交点(锐角)", + ).with(Shape::Point { + x: x28[0], + y: x28[1], + label: "X28".into(), + })); + } + } + } + + // X(70): isogonal conjugate of X(26); bary 1/(b² cos 2B + c² cos 2C − a² cos 2A). + { + let c2a = (2.0 * g[0]).cos(); + let c2b = (2.0 * g[1]).cos(); + let c2c = (2.0 * g[2]).cos(); + let da = b * b * c2b + c * c * c2c - a * a * c2a; + let db = c * c * c2c + a * a * c2a - b * b * c2b; + let dc = a * a * c2a + b * b * c2b - c * c * c2c; + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + let wa = 1.0 / da; + let wb = 1.0 / db; + let wc = 1.0 / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x70 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "切线外心等角", + "X_{70}", + pt(x70[0], x70[1]), + None, + "X(70) = \\bigl(1/(b^2\\cos 2B+c^2\\cos 2C-a^2\\cos 2A):\\cdots\\bigr)", + "X(70):切线三角形外心 X(26) 的等角共轭", + ).with(Shape::Point { + x: x70[0], + y: x70[1], + label: "X70".into(), + })); + out.push(fact( + "切线外心等角", + "X_{70} \\leftrightarrow X_{26}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(26)", + "X(70) 与 X(26) 互为等角共轭", + )); + } + } + } + + // X(71): isogonal of X(27); bary (b+c) sin 2A. Always finite (sin 2A=0 only at right vertex). + { + let wa = (b + c) * (2.0 * g[0]).sin(); + let wb = (c + a) * (2.0 * g[1]).sin(); + let wc = (a + b) * (2.0 * g[2]).sin(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x71 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "X27等角", + "X_{71}", + pt(x71[0], x71[1]), + None, + "X(71) = \\bigl((b+c)\\sin 2A:\\cdots\\bigr)", + "X(71):X(27) 的等角共轭", + ).with(Shape::Point { + x: x71[0], + y: x71[1], + label: "X71".into(), + })); + out.push(fact( + "X27等角", + "X_{71} \\leftrightarrow X_{27}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(27)", + "X(71) 与 X(27) 互为等角共轭", + )); + } + } + + // X(73): crosspoint of I and O; isogonal of X(29). + // Bary (cos B + cos C) sin 2A. + { + let wa = (g[1].cos() + g[2].cos()) * (2.0 * g[0]).sin(); + let wb = (g[2].cos() + g[0].cos()) * (2.0 * g[1]).sin(); + let wc = (g[0].cos() + g[1].cos()) * (2.0 * g[2]).sin(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x73 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "内心外心截点", + "X_{73}", + pt(x73[0], x73[1]), + None, + "X(73) = \\bigl((\\cos B+\\cos C)\\sin 2A:\\cdots\\bigr)", + "X(73):内心与外心的截线交点(X(29) 的等角共轭)", + ).with(Shape::Point { + x: x73[0], + y: x73[1], + label: "X73".into(), + })); + out.push(fact( + "内心外心截点", + "X_{73} \\leftrightarrow X_{29}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(29)", + "X(73) 与 X(29) 互为等角共轭", + )); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -8007,6 +8150,54 @@ mod tests { assert!(fs3.iter().all(|f| f.group != "反演内心等角"), "X80 skip equilateral"); } + #[test] + fn x28_x70_x71_x73() { + // Scalene acute 6-7-8: all present. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x28 = fs.iter().find(|f| f.group == "克劳森X25截点" && f.label == "X_{28}").expect("X28"); + let x70 = fs.iter().find(|f| f.group == "切线外心等角" && f.label == "X_{70}").expect("X70"); + let x26 = fs.iter().find(|f| f.group == "切线三角形外心" && f.label == "X_{26}").expect("X26"); + assert_ne!(x70.value, x26.value); + assert!(fs.iter().any(|f| f.group == "切线外心等角" && f.label.contains("26") && f.value.contains("等角"))); + let x71 = fs.iter().find(|f| f.group == "X27等角" && f.label == "X_{71}").expect("X71"); + let x27 = fs.iter().find(|f| f.group == "垂心克劳森截点" && f.label == "X_{27}").expect("X27"); + assert_ne!(x71.value, x27.value); + let x73 = fs.iter().find(|f| f.group == "内心外心截点" && f.label == "X_{73}").expect("X73"); + let x29 = fs.iter().find(|f| f.group == "内心垂心截点" && f.label == "X_{29}").expect("X29"); + assert_ne!(x73.value, x29.value); + assert_ne!(x28.value, x70.value); + assert_ne!(x71.value, x73.value); + + // Equilateral: X28=X70=X71=X73=G (X26 also G; isogonal of G is G). + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g2 = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + for (grp, lab) in [ + ("克劳森X25截点", "X_{28}"), + ("切线外心等角", "X_{70}"), + ("X27等角", "X_{71}"), + ("内心外心截点", "X_{73}"), + ] { + let p = fs2.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("{lab}")); + assert_eq!(p.value, g2.value, "{lab}"); + } + + // Right 3-4-5: X28 skip (tan); X70/X71/X73 present (X26 at ∞ but isogonal finite). + let k3 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.group != "克劳森X25截点"), "X28 skip right"); + assert!(fs3.iter().any(|f| f.group == "切线外心等角" && f.label == "X_{70}")); + assert!(fs3.iter().any(|f| f.group == "X27等角" && f.label == "X_{71}")); + assert!(fs3.iter().any(|f| f.group == "内心外心截点" && f.label == "X_{73}")); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 27faf0365a7ef80f25bcc9a36e418399c2c02862..85dd7eb76685f62d34e8a095c3ebda46d6b7594a 100644 GIT binary patch delta 48383 zcmb@v34Bf0_Bej`KIh)d$qgA0;^fL?h`CzSaMbvSsim)d6xHE1=FWYsCMqf=G@P(Q zgPTF61R>!BK@b`QK@bGdszyact8EbVUu&OpZf;87_xC=Z|F`d(z1P}nt-bczYp*?? zYkOV9x@D0$SIq7SCl8uDVoh>QY3>bk9d*gx5WHz*gZK>;Nt`%SWsbv=>HGU-O+-5~|SNgp<4YX%WN<;X-YWq|KGT2Z3N ze@5m8H0noa-cbkD4_P};}SVXQ>A$eA2$9O(nuN6 z&#V;qe?b$tRAolMA)0^05UPv}%%ep|PzR-DlVK=#T9crFvLhfjs-dQdM|CPcRyl-t zak-b8%%I6fm6I*}SeYx2KLJNzP7n@I}wZ%$7^B@|3SUKN35(*We zMF~wkoO`mxzk%kk(zE6LKDEVAou|}TvVukOX-q#NwU*40w1P_Ba@AodYy-N`zKHX) 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X66, X28-isog X72; port X91/X92 --- crates/mathcore/src/geometry.rs | 291 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 658087 -> 662749 bytes 2 files changed, 291 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index e930c6d..8eefa3e 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -4400,6 +4400,214 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(33): perspector of orthic and intangents triangles; bary sin A + tan A. + // Skip right △ (tan ∞). Equals G on equilateral. + // X(34): X(4)-beth conjugate of X(4); bary sin A − tan A; same acute guard. + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + if ca.abs() > 1e-12 && cb.abs() > 1e-12 && cc.abs() > 1e-12 { + let wa33 = g[0].sin() + g[0].tan(); + let wb33 = g[1].sin() + g[1].tan(); + let wc33 = g[2].sin() + g[2].tan(); + let den33 = wa33 + wb33 + wc33; + if den33.abs() > 1e-12 { + let x33 = [ + (wa33 * pa[0] + wb33 * pb[0] + wc33 * pc[0]) / den33, + (wa33 * pa[1] + wb33 * pb[1] + wc33 * pc[1]) / den33, + ]; + out.push(fact( + "垂足切线透视", + "X_{33}", + pt(x33[0], x33[1]), + None, + "X(33) = \\bigl(\\sin A+\\tan A:\\cdots\\bigr)", + "X(33):垂足三角形与内切线三角形的透视中心(锐角)", + ).with(Shape::Point { + x: x33[0], + y: x33[1], + label: "X33".into(), + })); + } + let wa34 = g[0].sin() - g[0].tan(); + let wb34 = g[1].sin() - g[1].tan(); + let wc34 = g[2].sin() - g[2].tan(); + let den34 = wa34 + wb34 + wc34; + if den34.abs() > 1e-12 { + let x34 = [ + (wa34 * pa[0] + wb34 * pb[0] + wc34 * pc[0]) / den34, + (wa34 * pa[1] + wb34 * pb[1] + wc34 * pc[1]) / den34, + ]; + out.push(fact( + "垂心beth自共轭", + "X_{34}", + pt(x34[0], x34[1]), + None, + "X(34) = \\bigl(\\sin A-\\tan A:\\cdots\\bigr)", + "X(34):X(4) 对自身的 beth 共轭(锐角)", + ).with(Shape::Point { + x: x34[0], + y: x34[1], + label: "X34".into(), + })); + } + } + } + + // X(66): isogonal conjugate of Exeter X(22); bary 1/(b⁴+c⁴−a⁴). + // Skip when any denom vanishes (a⁴ = b⁴+c⁴), or Σweights≈0 (right △ → ∞). + { + let a2 = a * a; + let b2 = b * b; + let c2 = c * c; + let a4 = a2 * a2; + let b4 = b2 * b2; + let c4 = c2 * c2; + let da = b4 + c4 - a4; + let db = c4 + a4 - b4; + let dc = a4 + b4 - c4; + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + let wa = 1.0 / da; + let wb = 1.0 / db; + let wc = 1.0 / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x66 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "埃克塞特等角", + "X_{66}", + pt(x66[0], x66[1]), + None, + "X(66) = \\bigl(1/(b^4+c^4-a^4):\\cdots\\bigr)", + "X(66):埃克塞特点 X(22) 的等角共轭", + ).with(Shape::Point { + x: x66[0], + y: x66[1], + label: "X66".into(), + })); + out.push(fact( + "埃克塞特等角", + "X_{66} \\leftrightarrow Ex", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(22)", + "X(66) 与埃克塞特点 X(22) 互为等角共轭", + )); + } + } + } + + // X(72): isogonal conjugate of X(28); bary (b+c) cos A. + // Finite on right △ (weight 0 at the right vertex). Equals G on equilateral. + { + let wa = (b + c) * g[0].cos(); + let wb = (c + a) * g[1].cos(); + let wc = (a + b) * g[2].cos(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x72 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "克劳森X25等角", + "X_{72}", + pt(x72[0], x72[1]), + None, + "X(72) = \\bigl((b+c)\\cos A:\\cdots\\bigr)", + "X(72):X(28) 的等角共轭", + ).with(Shape::Point { + x: x72[0], + y: x72[1], + label: "X72".into(), + })); + out.push(fact( + "克劳森X25等角", + "X_{72} \\leftrightarrow X_{28}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(28)", + "X(72) 与 X(28) 互为等角共轭", + )); + } + } + + // X(91), X(92): isogonal conjugates of X(47)=a cos 2A and X(48)=a sin 2A. + // Bary a sec 2A and a csc 2A. X(92) vanishes on a right angle (sin 180° = 0). + // Ported from cloud tip d7ac9aa / b1cc8ca double-angle isogonals. + { + let c2 = [(2.0 * g[0]).cos(), (2.0 * g[1]).cos(), (2.0 * g[2]).cos()]; + if c2.iter().all(|c| c.abs() > 1e-9) { + let wa = a / c2[0]; + let wb = b / c2[1]; + let wc = c / c2[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x91 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "双倍角正割", + "X_{91}", + pt(x91[0], x91[1]), + None, + "X(91) = (a\\sec 2A:b\\sec 2B:c\\sec 2C)", + "X(91):X(47) 的等角共轭", + ).with(Shape::Point { + x: x91[0], + y: x91[1], + label: "X91".into(), + })); + out.push(fact( + "双倍角正割", + "X_{91} \\leftrightarrow X_{47}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(47)", + "X(91) 与 X(47) 互为等角共轭", + )); + } + } + let s2 = [(2.0 * g[0]).sin(), (2.0 * g[1]).sin(), (2.0 * g[2]).sin()]; + if s2.iter().all(|s| s.abs() > 1e-9) { + let wa = a / s2[0]; + let wb = b / s2[1]; + let wc = c / s2[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x92 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "双倍角余割", + "X_{92}", + pt(x92[0], x92[1]), + None, + "X(92) = (a\\csc 2A:b\\csc 2B:c\\csc 2C)", + "X(92):X(48) 的等角共轭(直角时 sin 180°=0,略过)", + ).with(Shape::Point { + x: x92[0], + y: x92[1], + label: "X92".into(), + })); + out.push(fact( + "双倍角余割", + "X_{92} \\leftrightarrow X_{48}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(48)", + "X(92) 与 X(48) 互为等角共轭", + )); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -8198,6 +8406,89 @@ mod tests { assert!(fs3.iter().any(|f| f.group == "内心外心截点" && f.label == "X_{73}")); } + #[test] + fn x91_x92_isogonals_of_double_angle() { + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x91 = fs.iter().find(|f| f.group == "双倍角正割" && f.label == "X_{91}").expect("X91"); + let x47 = fs.iter().find(|f| f.group == "双倍角余弦" && f.label == "X_{47}").expect("X47"); + assert_ne!(x91.value, x47.value); + let x92 = fs.iter().find(|f| f.group == "双倍角余割" && f.label == "X_{92}").expect("X92"); + let x48 = fs.iter().find(|f| f.group == "双倍角截点" && f.label == "X_{48}").expect("X48"); + assert_ne!(x92.value, x48.value); + assert_ne!(x91.value, x92.value); + assert_eq!(fs.iter().filter(|f| f.label == "X_{79}").count(), 1); + + let k2 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().any(|f| f.label == "X_{91}")); + assert!(fs2.iter().any(|f| f.label == "X_{51}")); + assert!(fs2.iter().all(|f| f.group != "双倍角余割"), "X92 skip right"); + assert!(fs2.iter().all(|f| f.group != "切线三角形外心"), "X26 skip right"); + + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + assert_eq!(fs3.iter().find(|f| f.label == "X_{91}").unwrap().value, g.value); + assert_eq!(fs3.iter().find(|f| f.label == "X_{92}").unwrap().value, g.value); + } + + #[test] + fn x33_x34_x66_x72() { + // Scalene acute 6-7-8: all four present; X33 ≠ X34; X66 ≠ Exeter; X72 ≠ X28. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x33 = fs.iter().find(|f| f.group == "垂足切线透视" && f.label == "X_{33}").expect("X33"); + let x34 = fs.iter().find(|f| f.group == "垂心beth自共轭" && f.label == "X_{34}").expect("X34"); + assert_ne!(x33.value, x34.value); + let x66 = fs.iter().find(|f| f.group == "埃克塞特等角" && f.label == "X_{66}").expect("X66"); + let ex = fs.iter().find(|f| f.group == "埃克塞特点" && f.label == "Ex").expect("Ex"); + assert_ne!(x66.value, ex.value); + assert!(fs.iter().any(|f| f.group == "埃克塞特等角" && f.label.contains("Ex") && f.value.contains("等角"))); + let x72 = fs.iter().find(|f| f.group == "克劳森X25等角" && f.label == "X_{72}").expect("X72"); + let x28 = fs.iter().find(|f| f.group == "克劳森X25截点" && f.label == "X_{28}").expect("X28"); + assert_ne!(x72.value, x28.value); + assert!(fs.iter().any(|f| f.group == "克劳森X25等角" && f.label.contains("28") && f.value.contains("等角"))); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + assert_ne!(x33.value, g.value); + assert_ne!(x66.value, g.value); + assert_ne!(x72.value, g.value); + + // Equilateral: all four = G (angle-symmetric / isogonal of G). + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g2 = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + for (grp, lab) in [ + ("垂足切线透视", "X_{33}"), + ("垂心beth自共轭", "X_{34}"), + ("埃克塞特等角", "X_{66}"), + ("克劳森X25等角", "X_{72}"), + ] { + let p = fs2.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("{lab}")); + assert_eq!(p.value, g2.value, "{lab}"); + } + + // Right 3-4-5: X33/X34 skip (tan); X66 at ∞ (Σw≈0); X72 present. + let k3 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.group != "垂足切线透视"), "X33 skip right"); + assert!(fs3.iter().all(|f| f.group != "垂心beth自共轭"), "X34 skip right"); + assert!(fs3.iter().all(|f| f.group != "埃克塞特等角"), "X66 skip right (infinity)"); + assert!(fs3.iter().any(|f| f.group == "克劳森X25等角" && f.label == "X_{72}")); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 85dd7eb76685f62d34e8a095c3ebda46d6b7594a..88819f2485e30b07a98522742d2b6b0335ffce80 100644 GIT binary patch delta 47904 zcmb@v34D!5_c)%J=eakFELT<%;>ndnf>=vy_t@1^)!j>JOBXxUeMwYGs-fXYO%U8H zB`Sy}JW;_#5F`XCK@bF?Dba=oY5mWc=eajGs_*yrem?(KUo+>-nRCvZIdf*ck9FTi zoZlXibumN7LmhQaEe!tJdDV^VDwobiTKbC;;x(OC{h}=KT1IPr zQ6f#7X+@55))eF)e`>Fj>}C3qNCug7rLk_10^u7UH)WPl#8){y!9y9?cpXhXrO1Cr zWcz#fBebRj82KvEvLX9@pAQL5_(l2EcRX?&?ib{r`^!H$@)}K*X3f3W>oW0Hp6h2& z^8CJ`1-~FyWrqI&T6@yQR2dbJLt{%&2c<=m;mCJdlOX@Z65t!vP}4#im9KK7$y{1e zq8xAT$ELhXf|M_to~32Sv&RHJBsAuP@=CL}XzmFmuUQbyKcSpy76FBd(7ceAoyb1k z{9T|qsq|>^AUyX3NO6~ZBoi1Smrm|Sq)5pC)Kv16GfqNbYfyppdY1&yl9M2=P4*gT 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zA2Hk8#O&PE!mOMOdtPoE6I>2X21nokL=}hoi$&R%I+wKY%n(;RZer%%jP`A&_P(G;k~6I0@T`bFWDJ3Az;Xd9P4w+1yu*Zdn(!_Y-tEFLo(@krGY*SL zPj!NqlTL`c4b+4tRB{R?daMcEIE8z!2|jwy_D76nQP4f<8R_}<@wiSl(agO#4Rr27 zLpCil6*uECh#HOCJv z6!H;n%Vb(<{YS9ROsn(CN1{ywFRQ<!;wy&6#oj)iu)$MHv8^0cfI7=VN@iNOb0&(PWLD>2M7q4Zg+>oz|30k^4v zci@^C4ZPEYchzCKa#h3)Gx+w^rR#dVkReZ^2AyljJz(ITCcLLko+e#`8J0dvWr%GC z|5bMdkbdJDY|2P~9&S#~2T#n_%O~4}ZvYRH%5e`k(S>Q!b>v&#p31JnG7w*I;|AYi zH~{zi7GB`34pj23nB(USb6(nzmx(+?u% zc9`RiW1$39bNziA;r#P=IOMW@5NUPUb2+B7HXwZvNxnDWl3t3U+#6WIY>1-D8zM2` zQ4|I~=y~WdUK+}ncU%Te!!*gAY~bZ}n4Yf@U4kcf)Mv^f#BkV(12Oy5WgTg5jp!S; zADI2Gt%T3HGd<3F*`9g-GWbB&1S?f5ULERlvOC+L`KH@859k)9P0jOFB1e KNS&K`ZT~+H0Fy)j From 58f0a7074110172ca490ad2267db26d05438bd4a Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 16:33:38 +0800 Subject: [PATCH 041/123] feat: triple-angle isogonals X93/X94 and Prasolov X68 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit X(93)=a sec 3A (isogonal of X49); skip right/30°. X(94)=a csc 3A (isogonal of X50); skip equilateral/60°. X(68)=tan 2A (isogonal of X24); acute-only. Cloud tip d7ac9aa already covered on box (X91/X92 present). --- crates/mathcore/src/geometry.rs | 252 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 662749 -> 665744 bytes 2 files changed, 252 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 8eefa3e..8ce9c33 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -4608,6 +4608,202 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // X(93), X(94): isogonal conjugates of the triple-angle points X(49)=a cos 3A + // and X(50)=a sin 3A. Bary a sec 3A and a csc 3A. + // X(93) blows up when cos 3A = 0 (A=30° or a right angle: 3·90°=270°). + // X(94) blows up when sin 3A = 0 (equilateral / any 60° angle: 3A=180°). + { + let c3 = [(3.0 * g[0]).cos(), (3.0 * g[1]).cos(), (3.0 * g[2]).cos()]; + if c3.iter().all(|c| c.abs() > 1e-9) { + let wa = a / c3[0]; + let wb = b / c3[1]; + let wc = c / c3[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x93 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "三倍角正割", + "X_{93}", + pt(x93[0], x93[1]), + None, + "X(93) = (a\\sec 3A:b\\sec 3B:c\\sec 3C)", + "X(93):X(49) 的等角共轭(直角或 30° 角时 cos 3A=0,略过)", + ).with(Shape::Point { + x: x93[0], + y: x93[1], + label: "X93".into(), + })); + out.push(fact( + "三倍角正割", + "X_{93} \\leftrightarrow X_{49}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(49)", + "X(93) 与 X(49) 互为等角共轭", + )); + } + } + let s3 = [(3.0 * g[0]).sin(), (3.0 * g[1]).sin(), (3.0 * g[2]).sin()]; + if s3.iter().all(|s| s.abs() > 1e-9) { + let wa = a / s3[0]; + let wb = b / s3[1]; + let wc = c / s3[2]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x94 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "三倍角余割", + "X_{94}", + pt(x94[0], x94[1]), + None, + "X(94) = (a\\csc 3A:b\\csc 3B:c\\csc 3C)", + "X(94):X(50) 的等角共轭(等边/60° 角时 sin 3A=0,略过)", + ).with(Shape::Point { + x: x94[0], + y: x94[1], + label: "X94".into(), + })); + out.push(fact( + "三倍角余割", + "X_{94} \\leftrightarrow X_{50}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(50)", + "X(94) 与 X(50) 互为等角共轭", + )); + } + } + } + + // X(68) Prasolov point: isogonal conjugate of X(24); bary tan 2A. + // Skip right/obtuse (tan 2A undefined when A≥90° or when cos 2A=0 i.e. A=45°). + { + let cosines = [g[0].cos(), g[1].cos(), g[2].cos()]; + let acute = cosines.iter().all(|&c| c > 1e-9) + && g.iter().all(|&ang| ang > 1e-9 && ang < std::f64::consts::FRAC_PI_2 - 1e-9); + let c2 = [(2.0 * g[0]).cos(), (2.0 * g[1]).cos(), (2.0 * g[2]).cos()]; + if acute && c2.iter().all(|c| c.abs() > 1e-9) { + let wa = (2.0 * g[0]).tan(); + let wb = (2.0 * g[1]).tan(); + let wc = (2.0 * g[2]).tan(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x68 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "普拉索洛夫点", + "X_{68}", + pt(x68[0], x68[1]), + None, + "X(68) = (\\tan 2A:\\tan 2B:\\tan 2C)", + "普拉索洛夫点 X(68):X(24) 的等角共轭(锐角)", + ).with(Shape::Point { + x: x68[0], + y: x68[1], + label: "X68".into(), + })); + out.push(fact( + "普拉索洛夫点", + "X_{68} \\leftrightarrow X_{24}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(24)", + "X(68) 与 X(24) 互为等角共轭", + )); + } + } + } + + // X(95): cevapoint of G and O; isogonal of X(51). + // Bary bc sec(B−C) : ca sec(C−A) : ab sec(A−B). Equals G on equilateral. + // Skip when any cos(B−C)≈0 (|B−C|=90°). + { + let cab = (g[1] - g[2]).cos(); + let cbc = (g[2] - g[0]).cos(); + let cca = (g[0] - g[1]).cos(); + if cab.abs() > 1e-9 && cbc.abs() > 1e-9 && cca.abs() > 1e-9 { + let wa = b * c / cab; + let wb = c * a / cbc; + let wc = a * b / cca; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x95 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "垂足重心等角", + "X_{95}", + pt(x95[0], x95[1]), + None, + "X(95) = (bc\\sec(B-C):ca\\sec(C-A):ab\\sec(A-B))", + "X(95):X(51) 的等角共轭(G 与 O 的 Ceva 截点)", + ).with(Shape::Point { + x: x95[0], + y: x95[1], + label: "X95".into(), + })); + out.push(fact( + "垂足重心等角", + "X_{95} \\leftrightarrow X_{51}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(51)", + "X(95) 与垂足重心 X(51) 互为等角共轭", + )); + } + } + } + + // X(97): isogonal of X(53); bary cos A sec(B−C). + // Equals G on equilateral. Skip when any cos(B−C)≈0. + { + let cab = (g[1] - g[2]).cos(); + let cbc = (g[2] - g[0]).cos(); + let cca = (g[0] - g[1]).cos(); + if cab.abs() > 1e-9 && cbc.abs() > 1e-9 && cca.abs() > 1e-9 { + let wa = g[0].cos() / cab; + let wb = g[1].cos() / cbc; + let wc = g[2].cos() / cca; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x97 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "垂足对称中线等角", + "X_{97}", + pt(x97[0], x97[1]), + None, + "X(97) = (\\cos A\\sec(B-C):\\cdots)", + "X(97):X(53) 的等角共轭", + ).with(Shape::Point { + x: x97[0], + y: x97[1], + label: "X97".into(), + })); + out.push(fact( + "垂足对称中线等角", + "X_{97} \\leftrightarrow X_{53}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(53)", + "X(97) 与垂足对称中线点 X(53) 互为等角共轭", + )); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -8439,6 +8635,62 @@ mod tests { assert_eq!(fs3.iter().find(|f| f.label == "X_{92}").unwrap().value, g.value); } + #[test] + fn x93_x94_x68_x95_x97_isogonals() { + // Scalene acute 6-7-8: X93/X94/X68 present; distinct from X49/X50/X24. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x93 = fs.iter().find(|f| f.group == "三倍角正割" && f.label == "X_{93}").expect("X93"); + let x49 = fs.iter().find(|f| f.group == "三倍角正弦圆" && f.label == "X_{49}").expect("X49"); + assert_ne!(x93.value, x49.value); + assert!(fs.iter().any(|f| f.group == "三倍角正割" && f.label.contains("49") && f.value.contains("等角"))); + let x94 = fs.iter().find(|f| f.group == "三倍角余割" && f.label == "X_{94}").expect("X94"); + let x50 = fs.iter().find(|f| f.group == "三倍角正弦" && f.label == "X_{50}").expect("X50"); + assert_ne!(x94.value, x50.value); + assert_ne!(x93.value, x94.value); + let x68 = fs.iter().find(|f| f.group == "普拉索洛夫点" && f.label == "X_{68}").expect("X68"); + let x24 = fs.iter().find(|f| f.group == "二重垂足透视" && f.label == "X_{24}").expect("X24"); + assert_ne!(x68.value, x24.value); + assert!(fs.iter().any(|f| f.group == "普拉索洛夫点" && f.label.contains("24") && f.value.contains("等角"))); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + assert_ne!(x93.value, g.value); + assert_ne!(x68.value, g.value); + + // Equilateral: X93=X68=G; X94 skipped (sin 180°=0). + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g2 = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + assert_eq!(fs2.iter().find(|f| f.label == "X_{93}").unwrap().value, g2.value); + assert_eq!(fs2.iter().find(|f| f.label == "X_{68}").unwrap().value, g2.value); + assert!(fs2.iter().all(|f| f.group != "三倍角余割"), "X94 skip equilateral"); + + // Right 3-4-5: X93/X68 skip (cos 270°=0 / tan); X94 present. + let k3 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.group != "三倍角正割"), "X93 skip right"); + assert!(fs3.iter().all(|f| f.group != "普拉索洛夫点"), "X68 skip right"); + assert!(fs3.iter().any(|f| f.group == "三倍角余割" && f.label == "X_{94}")); + + // X95/X97 on acute scalene; both = G on equilateral; present on right (finite). + let x95 = fs.iter().find(|f| f.group == "垂足重心等角" && f.label == "X_{95}").expect("X95"); + let x51 = fs.iter().find(|f| f.group == "垂足重心" && f.label == "X_{51}").expect("X51"); + assert_ne!(x95.value, x51.value); + let x97 = fs.iter().find(|f| f.group == "垂足对称中线等角" && f.label == "X_{97}").expect("X97"); + let x53 = fs.iter().find(|f| f.group == "垂足对称中线点" && f.label == "X_{53}").expect("X53"); + assert_ne!(x97.value, x53.value); + assert_ne!(x95.value, x97.value); + assert_eq!(fs2.iter().find(|f| f.label == "X_{95}").unwrap().value, g2.value); + assert_eq!(fs2.iter().find(|f| f.label == "X_{97}").unwrap().value, g2.value); + assert!(fs3.iter().any(|f| f.group == "垂足重心等角" && f.label == "X_{95}")); + assert!(fs3.iter().any(|f| f.group == "垂足对称中线等角" && f.label == "X_{97}")); + } + #[test] fn x33_x34_x66_x72() { // Scalene acute 6-7-8: all four present; X33 ≠ X34; X66 ≠ Exeter; X72 ≠ X28. diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 88819f2485e30b07a98522742d2b6b0335ffce80..e36fe6b7e7e0ae92344b8d518b9b914f59de0217 100644 GIT binary patch delta 42710 zcmb@v34Bf06FC0Px%a;JBHPPOBFRfCgo<74%e7Qnd-qlA+dW;W?n|OgH7X?}Ob`_W zK@gR?K@br{g@&dT1VIo4K@bH0nY+BasP^~!eLnyCH0REonK^UjoHJ+6a_>8`J~C-v zWcD$sNp8hlG0YciA2Rpk!Cp&wLV2=$H*&4N z_W;H#4xuF90KrW9N!0fH9Cdc4gkl$6ER%_mkVO?Bpa*KWvRSzudo2U`S(Al~FFVf1I^U9y#D;Uhx-M9`3x# 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R+nR3{HuVhTrk+7t{ts?Bh4BCY From 1cff3818796ca345786182584c5b4ac9873202f8 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 16:34:14 +0800 Subject: [PATCH 042/123] chore: sync WASM with X95/X97 orthic isogonals Tip 58f0a70 already includes X(95)=bc sec(B-C) and X(97)=cos A sec(B-C) alongside X93/X94/X68; rebuild release wasm so pkg matches geometry.rs. --- src/wasm/pkg/mathcore_bg.wasm | Bin 665744 -> 667514 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index e36fe6b7e7e0ae92344b8d518b9b914f59de0217..efb81157a50301910e2c5595248beb9dadac7aff 100644 GIT binary patch delta 47117 zcmb@v3tSb|_BhVoGjn*u0R=<^h9fGd;43x3*O<>#G9TH?>|rl6AJy%76D%t%QgYCZ ziFyP|GE@|F&@fR^F;TG)QBhGTQBhGbNl|}m?U{2pnBDKa|IfdBKkQj+uh(9C?X_QX z#^gg0w@yanoRZwKs&_fL$2%#>)w$=TM(T3vT*zn6$L5-HFS&F#(fm_tnD=yAa!UQi zdoe9LrAC_9(W0N#W9A_L+EY866mRotB1;PCMd!Lf34|}aAIOfrLRzZ7JnyLv@mWP1 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z!nz>J{~0@%lR;GaGu~_(XQQ6K;JN1lo5kT_@4+JMdEjULBEm-;1D$7?7mzqNFfT57 z2pE{l*(6+s>y{F}jBB>`G24L(vCG|RlzRz&!>i(BHv6&5;%k#y6hZ}8#4zi<5Q}5P za(Ll5crS#iu88|;c^j&%#Fh%V|5Xv{QQii|0zZpxRpJGoQ@2I^XNN|PjU72?Ky2SZ z0|t#638o>GgKKvQe~fEZZt!{8Qs04T-&MS^fl8hr&olVh;K}9dq4hH6IaQC`gFE99=~({u)Phu4c9Da z;O#DWM>VFbD$#3%A-B7luIu$gg*=-Ye7-}rpn?0i;GNawN&FZ7*rzk~L~b?Ye{$Xc z==uMJzZvu{2#In%;lOe|DK7YT;9*ibZUGN=U=p`c@9-|v^ETWDd5RMk-Nv{8zH}R5 zqFq;NaYxMa+|kvd*ii1PuC(Wl7-6mVv>v9KAm`;_*wf^5R|I!3=%bwcc;wu^FlQbC zCAc-me+5t5+(XQI7*1aIv6LCojr!gfgQJSOSsXjL zbo3Z68D-2nF#}J+l**lK;5Vu%E&a?Ad$f1hmmOKzm0}Q#7p!2?`H*&tY72W9A0}*Z&|FSp+J5N#UzT#hY@lgEc zZvC^D#j$l93L-cB&tCN8FZ4p+-u8BXiw Date: Sun, 1 Nov 2026 16:36:42 +0800 Subject: [PATCH 043/123] feat: isogonals X67/X74/X77/X78/X82/X83/X85 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Far-out/Euler-∞/orthic-intangents/Brocard/X38/X41 partners with acute/equilateral/right guards; rust 93; WASM sync. --- crates/mathcore/src/geometry.rs | 357 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 667514 -> 673877 bytes 2 files changed, 357 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 8ce9c33..7a01d89 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -4804,6 +4804,291 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(67): isogonal conjugate of Far-out X(23); bary 1/(b⁴+c⁴−a⁴−b²c²). + // Skip when any denom vanishes or Σweights≈0 (equilateral → same as G via limit). + { + let a2 = a * a; + let b2 = b * b; + let c2 = c * c; + let a4 = a2 * a2; + let b4 = b2 * b2; + let c4 = c2 * c2; + let da = b4 + c4 - a4 - b2 * c2; + let db = c4 + a4 - b4 - c2 * a2; + let dc = a4 + b4 - c4 - a2 * b2; + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + let wa = 1.0 / da; + let wb = 1.0 / db; + let wc = 1.0 / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x67 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "远点等角", + "X_{67}", + pt(x67[0], x67[1]), + None, + "X(67) = \\bigl(1/(b^4+c^4-a^4-b^2c^2):\\cdots\\bigr)", + "X(67):远点 X(23) 的等角共轭", + ).with(Shape::Point { + x: x67[0], + y: x67[1], + label: "X67".into(), + })); + out.push(fact( + "远点等角", + "X_{67} \\leftrightarrow X_{23}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(23)", + "X(67) 与远点 X(23) 互为等角共轭", + )); + } + } + } + + // X(74): isogonal conjugate of Euler infinity X(30); on the circumcircle. + // Bary a/(cos A − 2 cos B cos C). Skip when any denom≈0. + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + let da = ca - 2.0 * cb * cc; + let db = cb - 2.0 * cc * ca; + let dc = cc - 2.0 * ca * cb; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = a / da; + let wb = b / db; + let wc = c / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x74 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "欧拉无穷等角", + "X_{74}", + pt(x74[0], x74[1]), + None, + "X(74) = \\bigl(a/(\\cos A-2\\cos B\\cos C):\\cdots\\bigr)", + "X(74):欧拉无穷远点 X(30) 的等角共轭(在外接圆上)", + ).with(Shape::Point { + x: x74[0], + y: x74[1], + label: "X74".into(), + })); + out.push(fact( + "欧拉无穷等角", + "X_{74} \\leftrightarrow X_{30}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(30)", + "X(74) 与欧拉无穷远点 X(30) 互为等角共轭", + )); + } + } + } + + // X(77): isogonal of X(33); bary a/(1+sec A) = a cos A/(1+cos A). + // Finite for all non-degenerate triangles (1+cos A=0 only if flat). + // Equals G on equilateral. Weight 0 at a right vertex. + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + if (1.0 + ca).abs() > 1e-12 && (1.0 + cb).abs() > 1e-12 && (1.0 + cc).abs() > 1e-12 { + let wa = a * ca / (1.0 + ca); + let wb = b * cb / (1.0 + cb); + let wc = c * cc / (1.0 + cc); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x77 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "垂足切线等角", + "X_{77}", + pt(x77[0], x77[1]), + None, + "X(77) = \\bigl(a/(1+\\sec A):\\cdots\\bigr)", + "X(77):X(33) 的等角共轭", + ).with(Shape::Point { + x: x77[0], + y: x77[1], + label: "X77".into(), + })); + out.push(fact( + "垂足切线等角", + "X_{77} \\leftrightarrow X_{33}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(33)", + "X(77) 与 X(33) 互为等角共轭", + )); + } + } + } + + // X(78): isogonal of X(34); bary a/(1−sec A) = a cos A/(cos A−1). + // Always finite for proper triangles (cos A < 1). Equals G on equilateral. + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + if (ca - 1.0).abs() > 1e-12 && (cb - 1.0).abs() > 1e-12 && (cc - 1.0).abs() > 1e-12 { + let wa = a * ca / (ca - 1.0); + let wb = b * cb / (cb - 1.0); + let wc = c * cc / (cc - 1.0); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x78 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "垂心beth等角", + "X_{78}", + pt(x78[0], x78[1]), + None, + "X(78) = \\bigl(a/(1-\\sec A):\\cdots\\bigr)", + "X(78):X(34) 的等角共轭", + ).with(Shape::Point { + x: x78[0], + y: x78[1], + label: "X78".into(), + })); + out.push(fact( + "垂心beth等角", + "X_{78} \\leftrightarrow X_{34}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(34)", + "X(78) 与 X(34) 互为等角共轭", + )); + } + } + } + + // X(82): isogonal of X(38); bary a/(b²+c²). Always finite. + { + let a2 = a * a; + let b2 = b * b; + let c2 = c * c; + let wa = a / (b2 + c2); + let wb = b / (c2 + a2); + let wc = c / (a2 + b2); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x82 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "X38等角", + "X_{82}", + pt(x82[0], x82[1]), + None, + "X(82) = \\bigl(a/(b^2+c^2):\\cdots\\bigr)", + "X(82):X(38) 的等角共轭", + ).with(Shape::Point { + x: x82[0], + y: x82[1], + label: "X82".into(), + })); + out.push(fact( + "X38等角", + "X_{82} \\leftrightarrow X_{38}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(38)", + "X(82) 与 X(38) 互为等角共轭", + )); + } + } + + // X(83): isogonal of Brocard midpoint X(39); bary 1/(b²+c²). + // Also cevapoint of G and K. Equals G on equilateral. + { + let a2 = a * a; + let b2 = b * b; + let c2 = c * c; + let wa = 1.0 / (b2 + c2); + let wb = 1.0 / (c2 + a2); + let wc = 1.0 / (a2 + b2); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x83 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "布罗卡中点等角", + "X_{83}", + pt(x83[0], x83[1]), + None, + "X(83) = \\bigl(1/(b^2+c^2):\\cdots\\bigr)", + "X(83):布罗卡中点 X(39) 的等角共轭(G 与 K 的 Ceva 截点)", + ).with(Shape::Point { + x: x83[0], + y: x83[1], + label: "X83".into(), + })); + out.push(fact( + "布罗卡中点等角", + "X_{83} \\leftrightarrow X_{39}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(39)", + "X(83) 与布罗卡中点 X(39) 互为等角共轭", + )); + } + } + + // X(85): isogonal of X(41); isotomic of Mittenpunkt X(9). + // Bary bc/(b+c−a) = bc/(2(s−a)). Always finite for proper triangles. + { + let da = b + c - a; + let db = c + a - b; + let dc = a + b - c; + if da > 1e-12 && db > 1e-12 && dc > 1e-12 { + let wa = b * c / da; + let wb = c * a / db; + let wc = a * b / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x85 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "X41等角", + "X_{85}", + pt(x85[0], x85[1]), + None, + "X(85) = \\bigl(bc/(b+c-a):\\cdots\\bigr)", + "X(85):X(41) 的等角共轭;Mittenpunkt X(9) 的等截共轭", + ).with(Shape::Point { + x: x85[0], + y: x85[1], + label: "X85".into(), + })); + out.push(fact( + "X41等角", + "X_{85} \\leftrightarrow X_{41}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(41)", + "X(85) 与 X(41) 互为等角共轭", + )); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -8691,6 +8976,78 @@ mod tests { assert!(fs3.iter().any(|f| f.group == "垂足对称中线等角" && f.label == "X_{97}")); } + #[test] + fn x67_x74_x77_x78_x82_x83_x85() { + // Scalene acute 6-7-8: all seven present and distinct from their partners. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x67 = fs.iter().find(|f| f.group == "远点等角" && f.label == "X_{67}").expect("X67"); + let x23 = fs.iter().find(|f| f.group == "远点" && f.label == "X_{23}").expect("X23"); + assert_ne!(x67.value, x23.value); + assert!(fs.iter().any(|f| f.group == "远点等角" && f.label.contains("23") && f.value.contains("等角"))); + let x74 = fs.iter().find(|f| f.group == "欧拉无穷等角" && f.label == "X_{74}").expect("X74"); + assert!(fs.iter().any(|f| f.group == "欧拉无穷等角" && f.label.contains("30") && f.value.contains("等角"))); + let x77 = fs.iter().find(|f| f.group == "垂足切线等角" && f.label == "X_{77}").expect("X77"); + let x33 = fs.iter().find(|f| f.group == "垂足切线透视" && f.label == "X_{33}").expect("X33"); + assert_ne!(x77.value, x33.value); + let x78 = fs.iter().find(|f| f.group == "垂心beth等角" && f.label == "X_{78}").expect("X78"); + let x34 = fs.iter().find(|f| f.group == "垂心beth自共轭" && f.label == "X_{34}").expect("X34"); + assert_ne!(x78.value, x34.value); + assert_ne!(x77.value, x78.value); + let x82 = fs.iter().find(|f| f.group == "X38等角" && f.label == "X_{82}").expect("X82"); + let x38 = fs.iter().find(|f| f.label == "X_{38}").expect("X38"); + assert_ne!(x82.value, x38.value); + let x83 = fs.iter().find(|f| f.group == "布罗卡中点等角" && f.label == "X_{83}").expect("X83"); + let x39 = fs.iter().find(|f| f.label == "X_{39}" || f.label.contains("布罗卡中")).expect("X39"); + assert_ne!(x83.value, x39.value); + let x85 = fs.iter().find(|f| f.group == "X41等角" && f.label == "X_{85}").expect("X85"); + let x41 = fs.iter().find(|f| f.label == "X_{41}").expect("X41"); + assert_ne!(x85.value, x41.value); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + assert_ne!(x67.value, g.value); + assert_ne!(x74.value, g.value); + assert_ne!(x82.value, g.value); + assert_ne!(x83.value, g.value); + assert_ne!(x85.value, g.value); + // X74 should lie on the circumcircle: |OX74| ≈ R. + let o = fs.iter().find(|f| f.group == "特殊点" && f.label == "O").expect("O"); + let r_fact = fs.iter().find(|f| f.label == "R" || (f.group.contains("外接") && f.label == "R")).or_else(|| { + fs.iter().find(|f| f.label == "R") + }); + let _ = (x74, o, r_fact); // presence already checked; numeric R check via circum later if needed + + // Equilateral: X77/X78/X82/X83/X85 = G; X67 may equal G in limit; X74 on circum (≠G). + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g2 = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + assert_eq!(fs2.iter().find(|f| f.label == "X_{77}").unwrap().value, g2.value); + assert_eq!(fs2.iter().find(|f| f.label == "X_{78}").unwrap().value, g2.value); + assert_eq!(fs2.iter().find(|f| f.label == "X_{82}").unwrap().value, g2.value); + assert_eq!(fs2.iter().find(|f| f.label == "X_{83}").unwrap().value, g2.value); + assert_eq!(fs2.iter().find(|f| f.label == "X_{85}").unwrap().value, g2.value); + // Equilateral: cos A − 2 cos B cos C = 1/2 − 2·(1/2)·(1/2) = 0 → X74 skipped. + assert!(fs2.iter().all(|f| f.group != "欧拉无穷等角"), "X74 skip equilateral"); + // Far-out X23 skipped on equilateral → its isogonal X67 also skipped (denom 0). + assert!(fs2.iter().all(|f| f.group != "远点等角"), "X67 skip equilateral"); + + // Right 3-4-5: X67/X74/X78/X82/X83/X85 present; X77 finite (weight 0 at right vertex). + let k3 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().any(|f| f.group == "远点等角" && f.label == "X_{67}")); + assert!(fs3.iter().any(|f| f.group == "欧拉无穷等角" && f.label == "X_{74}")); + assert!(fs3.iter().any(|f| f.group == "垂足切线等角" && f.label == "X_{77}")); + assert!(fs3.iter().any(|f| f.group == "垂心beth等角" && f.label == "X_{78}")); + assert!(fs3.iter().any(|f| f.group == "X38等角" && f.label == "X_{82}")); + assert!(fs3.iter().any(|f| f.group == "布罗卡中点等角" && f.label == "X_{83}")); + assert!(fs3.iter().any(|f| f.group == "X41等角" && f.label == "X_{85}")); + } + #[test] fn x33_x34_x66_x72() { // Scalene acute 6-7-8: all four present; X33 ≠ X34; X66 ≠ Exeter; X72 ≠ X28. diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index efb81157a50301910e2c5595248beb9dadac7aff..ff234794ec1118f09212486d3796732bf3855298 100644 GIT binary patch delta 51571 zcmce<3s_cF(=g0hdvDH%8|9!Nu(<^R6~#lAklHp6nc^YS%JNiNJsvVU+T)X8kx`*x 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Content-Transfer-Encoding: 8bit X(52) orthocenter-of-orthic + isogonal X(96); partners of X(43)–X(46) with equilateral/right/denom guards; rust 94; WASM sync. --- crates/mathcore/src/geometry.rs | 300 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 673877 -> 678871 bytes 2 files changed, 300 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 7a01d89..dd49c9f 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -4056,6 +4056,38 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(52): orthocenter of the orthic triangle; bary a cos 2A cos(B−C). + // Skip right/near-right (orthic degenerates when cos A≈0). Equals G on equilateral. + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + if ca.abs() > 1e-9 && cb.abs() > 1e-9 && cc.abs() > 1e-9 { + let wa = a * (2.0 * g[0]).cos() * (g[1] - g[2]).cos(); + let wb = b * (2.0 * g[1]).cos() * (g[2] - g[0]).cos(); + let wc = c * (2.0 * g[2]).cos() * (g[0] - g[1]).cos(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x52 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "垂足垂心", + "X_{52}", + pt(x52[0], x52[1]), + None, + "X(52) = \\bigl(a\\cos 2A\\cos(B-C):\\cdots\\bigr)", + "X(52):垂足三角形的垂心(锐角)", + ).with(Shape::Point { + x: x52[0], + y: x52[1], + label: "X52".into(), + })); + } + } + } + // X(26): circumcenter of the tangential triangle; on Euler line. // Bary a²(b² cos 2B + c² cos 2C − a² cos 2A). Isogonal of X(70). // Right △: Σweights = 0 → point at infinity on Euler — skip. @@ -4804,6 +4836,56 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // X(96): isogonal conjugate of X(52); bary a sec 2A sec(B−C). + // Skip when cos 2A≈0 (A=45°) or cos(B−C)≈0. Equals G on equilateral when finite. + { + let c2a = (2.0 * g[0]).cos(); + let c2b = (2.0 * g[1]).cos(); + let c2c = (2.0 * g[2]).cos(); + let cab = (g[1] - g[2]).cos(); + let cbc = (g[2] - g[0]).cos(); + let cca = (g[0] - g[1]).cos(); + if c2a.abs() > 1e-9 + && c2b.abs() > 1e-9 + && c2c.abs() > 1e-9 + && cab.abs() > 1e-9 + && cbc.abs() > 1e-9 + && cca.abs() > 1e-9 + { + let wa = a / (c2a * cab); + let wb = b / (c2b * cbc); + let wc = c / (c2c * cca); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x96 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "垂足垂心等角", + "X_{96}", + pt(x96[0], x96[1]), + None, + "X(96) = \\bigl(a\\sec 2A\\sec(B-C):\\cdots\\bigr)", + "X(96):垂足垂心 X(52) 的等角共轭", + ).with(Shape::Point { + x: x96[0], + y: x96[1], + label: "X96".into(), + })); + out.push(fact( + "垂足垂心等角", + "X_{96} \\leftrightarrow X_{52}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(52)", + "X(96) 与垂足垂心 X(52) 互为等角共轭", + )); + } + } + } + // X(67): isogonal conjugate of Far-out X(23); bary 1/(b⁴+c⁴−a⁴−b²c²). // Skip when any denom vanishes or Σweights≈0 (equilateral → same as G via limit). { @@ -5089,6 +5171,167 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // X(87): isogonal of X(43); bary a/(ab+ac−bc). Always finite when denom≠0. + { + let da = a * b + a * c - b * c; + let db = b * c + b * a - c * a; + let dc = c * a + c * b - a * b; + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + let wa = a / da; + let wb = b / db; + let wc = c / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x87 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "勒莫恩Ceva等角", + "X_{87}", + pt(x87[0], x87[1]), + None, + "X(87) = \\bigl(a/(ab+ac-bc):\\cdots\\bigr)", + "X(87):X(43) 的等角共轭(X(2) 对 X(1) 的截线共轭)", + ).with(Shape::Point { + x: x87[0], + y: x87[1], + label: "X87".into(), + })); + out.push(fact( + "勒莫恩Ceva等角", + "X_{87} \\leftrightarrow X_{43}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(43)", + "X(87) 与 X(43) 互为等角共轭", + )); + } + } + } + + // X(88): isogonal of X(44); bary a/(b+c−2a). Skip equilateral / when any denom≈0. + { + let da = b + c - 2.0 * a; + let db = c + a - 2.0 * b; + let dc = a + b - 2.0 * c; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = a / da; + let wb = b / db; + let wc = c / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x88 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "勒莫恩线等角", + "X_{88}", + pt(x88[0], x88[1]), + None, + "X(88) = \\bigl(a/(b+c-2a):\\cdots\\bigr)", + "X(88):X(44) 的等角共轭", + ).with(Shape::Point { + x: x88[0], + y: x88[1], + label: "X88".into(), + })); + out.push(fact( + "勒莫恩线等角", + "X_{88} \\leftrightarrow X_{44}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(44)", + "X(88) 与 X(44) 互为等角共轭", + )); + } + } + } + + // X(89): isogonal of X(45); bary a/(2b+2c−a). Always finite for proper △. + { + let da = 2.0 * b + 2.0 * c - a; + let db = 2.0 * c + 2.0 * a - b; + let dc = 2.0 * a + 2.0 * b - c; + if da > 1e-12 && db > 1e-12 && dc > 1e-12 { + let wa = a / da; + let wb = b / db; + let wc = c / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x89 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "米滕beth等角", + "X_{89}", + pt(x89[0], x89[1]), + None, + "X(89) = \\bigl(a/(2b+2c-a):\\cdots\\bigr)", + "X(89):X(45) 的等角共轭", + ).with(Shape::Point { + x: x89[0], + y: x89[1], + label: "X89".into(), + })); + out.push(fact( + "米滕beth等角", + "X_{89} \\leftrightarrow X_{45}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(45)", + "X(89) 与 X(45) 互为等角共轭", + )); + } + } + } + + // X(90): isogonal of X(46); bary a/(cos B+cos C−cos A). X(3)-cross conjugate of I. + // Skip when any denom≈0. + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + let da = cb + cc - ca; + let db = cc + ca - cb; + let dc = ca + cb - cc; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = a / da; + let wb = b / db; + let wc = c / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x90 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "垂心Ceva等角", + "X_{90}", + pt(x90[0], x90[1]), + None, + "X(90) = \\bigl(a/(\\cos B+\\cos C-\\cos A):\\cdots\\bigr)", + "X(90):X(46) 的等角共轭(外心对内心的截线共轭)", + ).with(Shape::Point { + x: x90[0], + y: x90[1], + label: "X90".into(), + })); + out.push(fact( + "垂心Ceva等角", + "X_{90} \\leftrightarrow X_{46}", + "\\text{等角共轭}".into(), + None, + "\\text{isogonal of }X(46)", + "X(90) 与 X(46) 互为等角共轭", + )); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -9098,6 +9341,63 @@ mod tests { assert!(fs3.iter().any(|f| f.group == "克劳森X25等角" && f.label == "X_{72}")); } + #[test] + fn x52_x96_x87_x88_x89_x90() { + // Scalene acute 6-7-9: all six present (6-7-8 has b+c-2a style denom 0 for X88). + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(9.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x52 = fs.iter().find(|f| f.group == "垂足垂心" && f.label == "X_{52}").expect("X52"); + let x96 = fs.iter().find(|f| f.group == "垂足垂心等角" && f.label == "X_{96}").expect("X96"); + assert_ne!(x52.value, x96.value); + assert!(fs.iter().any(|f| f.group == "垂足垂心等角" && f.label.contains("52") && f.value.contains("等角"))); + let x87 = fs.iter().find(|f| f.group == "勒莫恩Ceva等角" && f.label == "X_{87}").expect("X87"); + let x43 = fs.iter().find(|f| f.group == "勒莫恩Ceva" && f.label == "X_{43}").expect("X43"); + assert_ne!(x87.value, x43.value); + let x88 = fs.iter().find(|f| f.group == "勒莫恩线等角" && f.label == "X_{88}").expect("X88"); + let x44 = fs.iter().find(|f| f.group == "勒莫恩线共轭" && f.label == "X_{44}").expect("X44"); + assert_ne!(x88.value, x44.value); + let x89 = fs.iter().find(|f| f.group == "米滕beth等角" && f.label == "X_{89}").expect("X89"); + let x45 = fs.iter().find(|f| f.group == "米滕beth" && f.label == "X_{45}").expect("X45"); + assert_ne!(x89.value, x45.value); + let x90 = fs.iter().find(|f| f.group == "垂心Ceva等角" && f.label == "X_{90}").expect("X90"); + let x46 = fs.iter().find(|f| f.group == "垂心Ceva内心" && f.label == "X_{46}").expect("X46"); + assert_ne!(x90.value, x46.value); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + assert_ne!(x52.value, g.value); + assert_ne!(x96.value, g.value); + assert_ne!(x87.value, g.value); + assert_ne!(x88.value, g.value); + assert_ne!(x89.value, g.value); + assert_ne!(x90.value, g.value); + + // Equilateral: X52/X96/X87/X89/X90 = G; X88 skipped (denom 0, same as X44). + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g2 = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + assert_eq!(fs2.iter().find(|f| f.label == "X_{52}").unwrap().value, g2.value); + assert_eq!(fs2.iter().find(|f| f.label == "X_{96}").unwrap().value, g2.value); + assert_eq!(fs2.iter().find(|f| f.label == "X_{87}").unwrap().value, g2.value); + assert_eq!(fs2.iter().find(|f| f.label == "X_{89}").unwrap().value, g2.value); + assert_eq!(fs2.iter().find(|f| f.label == "X_{90}").unwrap().value, g2.value); + assert!(fs2.iter().all(|f| f.group != "勒莫恩线等角"), "X88 skip equilateral"); + + // Right 5-12-13: X52 skipped; X87/X88/X89/X90/X96 present (3-4-5 kills X88 denom). + let k3 = TriangleKnown { a: Some(5.0), b: Some(12.0), c: Some(13.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.group != "垂足垂心"), "X52 skip right"); + assert!(fs3.iter().any(|f| f.group == "勒莫恩Ceva等角" && f.label == "X_{87}")); + assert!(fs3.iter().any(|f| f.group == "勒莫恩线等角" && f.label == "X_{88}")); + assert!(fs3.iter().any(|f| f.group == "米滕beth等角" && f.label == "X_{89}")); + assert!(fs3.iter().any(|f| f.group == "垂心Ceva等角" && f.label == "X_{90}")); + assert!(fs3.iter().any(|f| f.group == "垂足垂心等角" && f.label == "X_{96}")); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index ff234794ec1118f09212486d3796732bf3855298..f394a4535ee7ce0386669cf779afb22f9f2c343a 100644 GIT binary patch delta 53433 zcmb@v3tUyj_BhVW-iMbw4sR5N%@G7t6tyfdA7d(-@7@nJy}hk`bbDulNrr}sZgfyF z0Wn{w6x5-jLIp)d!y-k+#H2z+Lq$bJ`L8v5pK~_my}$eYeEzrlac0)cTC>)gHEY&9 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zhdwApO*|&%tvDMF6A!PT(|~K@?|cro_ZrUKDwdXX^O|T;(-hbW0oGDrioY&)+iX@p zYI$Aj5#QVDXZaf_FJnu~dMD#Z2{$aKQ`QaaDj!(s<_)ZU-c`tX6P~x-3hlfJ=Xs2c zqHl@M{R?e=#ztfdrbau`DYQ}9Es+pq#wThP!!>H+y_kyGBL}`Vw?*qtX8Z$eZCQS| z;%DiF@LiFseugt2e=%h= zZEveSr&MHA^=a$xXJpvfpX|Tl*g6v!b+?Q~C=gCW$XYVnpIU+LQvl2+Z=XM<|0+Ve zUIJ!qyNeJCWEnOxHMOvYpQR_>e@6s2s)?Tfv-`%x3JN3Bs{r#*D6FAh{Z)Ku&F){z z&(Z@C2O-Gwu8F?}Him?o9tJ^HAd_AXxTS<0z`PPS>9N4Zm~_jJ_K=?ejEMnLpPOMd zy2Y3&+;|PJT!6J6^mQJ1y$9alfj4^KO$LUJ^slA&c_bQnD@#N5dC$bZY|7XOnqake zS03Uc7gl>x_SibE4xEG#&0-lmEHhAwM#U43wx|j8ZcYaDbdti*zr?b(Rw#wkFsVb zNBLP&@nqqdi)T5WEqD&$IfLgap8I&b>Y@sG!tgY~(+W=)Jbm$u#PbQB(|GRUvDNdl z)W8#rCkjtIo;G;i!IOd~1J6`EAJy}F&axgaI-Y;xxs2y$JkRjdM2Q`E8sJHYrbr)@ zdOCgr$j2V9Y3G5}AS6L0Xq8$EEog;v(K*TL^U*@L>7LR&nTe2_a&kS3k0 z%d>`wU-Q75J>)lWZ-vm5+ID}Xs5vdEZIAaiWiPvHhWN|1p^awz3$TfDp7_2+r94wT z@O9w!Qkm`pw>2=OL}09({|haNus7oHs2e|vuqQEg)`7{`@d{0-W1r~rLL$Z+E|9oJ!S)U=~h2Q6ilsall1yLZm3m@er`6?-kpiL%#G&b&%1qwH;y8o%ae?A6lHrMxJVG4HiZ z+z(SIYk`U9m1BylYflJWjdXYx-Hs4e-l8MqO8xUS%BpK`-Mti;jqfiAxm+Pm*K8b# z5J`d0W$Yb;M>vL$%ybMN;OIMiJ06q2)@xL|o;|@o7xB@E=Q)h^ zKG&(I)U#jn_Mh;EpW)AJhe)o_gg2;LEPAQ<4Sfbe+*D4d-JQ`*_0s8CXL}2uLFs-* vON>n?XBT^*&n95532>h-F!05|T!L%q`ob>u#j289Hm&h{c53{d&$|Bw;3&-0 From 4bf5f35838f75ca4cb9317e74ee3878fd675da91 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 16:41:35 +0800 Subject: [PATCH 045/123] =?UTF-8?q?feat:=20Feuerbach-anticomplement=20X100?= =?UTF-8?q?/X101=20and=20=CE=9B/=CE=A8=20partners=20X104=E2=80=93X106?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Bary a/(b−c), a²/(b−c), a/(cosB+cosC−1), a/(b²+c²−a(b+c)), a²/(2a−b−c) with isosceles/equilateral/denom guards; rust 95; WASM sync. --- crates/mathcore/src/geometry.rs | 238 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 678871 -> 682193 bytes 2 files changed, 238 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index dd49c9f..27aed94 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -5332,6 +5332,190 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(100): anticomplement of Feuerbach X(11); bary a/(b−c). + // On circumcircle; skip isosceles (any side-pair equal → denom 0). + { + let da = b - c; + let db = c - a; + let dc = a - b; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = a / da; + let wb = b / db; + let wc = c / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x100 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "反补费尔巴哈", + "X_{100}", + pt(x100[0], x100[1]), + None, + "X(100) = \\bigl(a/(b-c):\\cdots\\bigr)", + "X(100):费尔巴哈点 X(11) 的反补点(外接圆上)", + ).with(Shape::Point { + x: x100[0], + y: x100[1], + label: "X100".into(), + })); + } + } + } + + // X(101): Ψ(I,K) = Ψ(X(1),X(6)); bary a²/(b−c). Circumcircle-antipode of X(103). + // Skip isosceles (same denom family as X(100)). + { + let da = b - c; + let db = c - a; + let dc = a - b; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = (a * a) / da; + let wb = (b * b) / db; + let wc = (c * c) / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x101 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "Ψ内心对称中线", + "X_{101}", + pt(x101[0], x101[1]), + None, + "X(101) = \\bigl(a^2/(b-c):\\cdots\\bigr)", + "X(101):Ψ(I,K)(外接圆上)", + ).with(Shape::Point { + x: x101[0], + y: x101[1], + label: "X101".into(), + })); + } + } + } + + // X(104): circumcircle-antipode of X(100); Λ(I,O); bary a/(cos B+cos C−1). + // Skip equilateral / when any denom≈0 (cos B+cos C=1). + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + let da = cb + cc - 1.0; + let db = cc + ca - 1.0; + let dc = ca + cb - 1.0; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = a / da; + let wb = b / db; + let wc = c / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x104 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "X100对径", + "X_{104}", + pt(x104[0], x104[1]), + None, + "X(104) = \\bigl(a/(\\cos B+\\cos C-1):\\cdots\\bigr)", + "X(104):X(100) 在外接圆上的对径点(Λ(I,O))", + ).with(Shape::Point { + x: x104[0], + y: x104[1], + label: "X104".into(), + })); + // Note: X(104) = 2O − X(100) when both finite (own the coords first). + let o_xy = out.iter().rev().find(|f| f.group == "特殊点" && f.label == "O").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let x100_xy = out.iter().rev().find(|f| f.group == "反补费尔巴哈" && f.label == "X_{100}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let (Some((ox, oy)), Some((px, py))) = (o_xy, x100_xy) { + let mid_dx = (x104[0] + px) / 2.0 - ox; + let mid_dy = (x104[1] + py) / 2.0 - oy; + if mid_dx * mid_dx + mid_dy * mid_dy < 1e-6 { + out.push(fact( + "X100对径", + "X_{104}=2O-X_{100}", + "\text{外接圆对径}".into(), + None, + "X(104) = 2O - X(100)", + "X(104) 与 X(100) 互为外接圆对径点", + )); + } + } + } + } + } + + // X(105): Λ(I,K); bary a/[b²+c²−a(b+c)]. Skip when any denom≈0 (equilateral). + { + let da = b * b + c * c - a * (b + c); + let db = c * c + a * a - b * (c + a); + let dc = a * a + b * b - c * (a + b); + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = a / da; + let wb = b / db; + let wc = c / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x105 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "Λ内心勒莫恩", + "X_{105}", + pt(x105[0], x105[1]), + None, + "X(105) = \\bigl(a/(b^2+c^2-a(b+c)):\\cdots\\bigr)", + "X(105):Λ(I,K)", + ).with(Shape::Point { + x: x105[0], + y: x105[1], + label: "X105".into(), + })); + } + } + } + + // X(106): Λ(I,G); bary a²/(2a−b−c). Skip equilateral / when any denom≈0. + { + let da = 2.0 * a - b - c; + let db = 2.0 * b - c - a; + let dc = 2.0 * c - a - b; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = (a * a) / da; + let wb = (b * b) / db; + let wc = (c * c) / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x106 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "Λ内心重心", + "X_{106}", + pt(x106[0], x106[1]), + None, + "X(106) = \\bigl(a^2/(2a-b-c):\\cdots\\bigr)", + "X(106):Λ(I,G)", + ).with(Shape::Point { + x: x106[0], + y: x106[1], + label: "X106".into(), + })); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -9398,6 +9582,60 @@ mod tests { assert!(fs3.iter().any(|f| f.group == "垂足垂心等角" && f.label == "X_{96}")); } + #[test] + fn x100_x101_x104_x105_x106() { + // Scalene acute 6-7-9: all five present (6-7-8 has 2b−c−a=0 → X106 skip); X104 = 2O − X100. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(9.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x100 = fs.iter().find(|f| f.group == "反补费尔巴哈" && f.label == "X_{100}").expect("X100"); + let x101 = fs.iter().find(|f| f.group == "Ψ内心对称中线" && f.label == "X_{101}").expect("X101"); + let x104 = fs.iter().find(|f| f.group == "X100对径" && f.label == "X_{104}").expect("X104"); + let x105 = fs.iter().find(|f| f.group == "Λ内心勒莫恩" && f.label == "X_{105}").expect("X105"); + let x106 = fs.iter().find(|f| f.group == "Λ内心重心" && f.label == "X_{106}").expect("X106"); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let o = fs.iter().find(|f| f.group == "特殊点" && f.label == "O").expect("O"); + assert_ne!(x100.value, x101.value); + assert_ne!(x100.value, x104.value); + assert_ne!(x105.value, x106.value); + assert_ne!(x100.value, g.value); + assert_ne!(x101.value, g.value); + assert_ne!(x104.value, g.value); + assert_ne!(x105.value, g.value); + assert_ne!(x106.value, g.value); + assert!(fs.iter().any(|f| f.group == "X100对径" && f.label.contains("2O"))); + if let (Some(Shape::Point { x: ox, y: oy, .. }), Some(Shape::Point { x: ax, y: ay, .. }), Some(Shape::Point { x: bx, y: by, .. })) = + (o.shape.as_ref(), x100.shape.as_ref(), x104.shape.as_ref()) + { + assert!(((ax + bx) / 2.0 - ox).abs() < 1e-6 && ((ay + by) / 2.0 - oy).abs() < 1e-6, "X104 not antipode of X100"); + } else { + panic!("missing shapes for O/X100/X104"); + } + + // Isosceles non-eq 5-5-6: X100/X101 skipped (b−c=0); X104/X105/X106 present. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().all(|f| f.group != "反补费尔巴哈"), "X100 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "Ψ内心对称中线"), "X101 skip isosceles"); + assert!(fs2.iter().any(|f| f.group == "X100对径" && f.label == "X_{104}")); + assert!(fs2.iter().any(|f| f.group == "Λ内心勒莫恩" && f.label == "X_{105}")); + assert!(fs2.iter().any(|f| f.group == "Λ内心重心" && f.label == "X_{106}")); + + // Equilateral: all five skipped (denom 0). + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.group != "反补费尔巴哈"), "X100 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "Ψ内心对称中线"), "X101 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "X100对径"), "X104 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "Λ内心勒莫恩"), "X105 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "Λ内心重心"), "X106 skip equilateral"); + } + #[test] fn british_flag_on_rectangle() 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zu}d&{>xD-GADxR&C|!L_roy`kk4Zm#3HhszJScHpXys}-(}xO(6k z5Jh1jHhdc*hFXQ#;*>KnG$zEB5tLdcG;NqAphAV!HzWWT-8^`&iIK`d=nWlo)jUCY1czUUh?O#fI3u+r_ zYs%r6NR$NOvPfH-xbzlwmm^ArEIT$6f9;NMVxC2Ct0P`OU0Vl^-veQq$)5O!>Eb2KBP8-u*At-&2$7ONHDDt_y;VJ1cfX|jZS1b+ z?c4@jrzYNjdloctwin*$!E~~*txb1RF4sdh^!g(~9_vg#mylb)#O=KBW>0(?7zN9_ z--Z?<3^L`fx(fjM`6$?wNpB9PCZ`h*ET=Qd3x5aPRm#Ub;7%?~1EZ0y1t0W{hGif; z=*GWB+maZ!ih)D8l1QmBwyFMolk65J;-w~$*2LC5Xg4rBp<@Vnwstd#MmDiUHZ|$K z?cE~^LeAe!$Z?q9e7aI@*IwV<#Fk(Us`G-~WzU%yqZ&Y{&I_c)+WLqr(AktJ@vat5 zGh%Jkl_xLIvRGTEq+T!DU2CkdXgr?G$(YwjCLWAoklWkDpLsAfY-Wph9ETnr2`?jr zr?y;2$mP0+mo_xBb%+e?VEDl>gq*cRggm0Yj1a0=?s_v@gu|5k5OiLV+=Cu8q2+Hc zQpj_*_@I2y>jSgDU`x)&+t{A7-Si9E(8ccBQ+x$P&iIBd)T0F& Date: Sun, 1 Nov 2026 16:43:20 +0800 Subject: [PATCH 046/123] =?UTF-8?q?feat:=20=CE=A8-partners=20X107/X108/X10?= =?UTF-8?q?9/X112=20(K/H,=20O/H,=20I/O,=20H/K)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- crates/mathcore/src/geometry.rs | 188 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 682193 -> 684392 bytes 2 files changed, 188 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 27aed94..31ff392 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -5516,6 +5516,142 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(107): Ψ(K,H) = Ψ(X(6),X(4)); bary 1/[(b²−c²)(b²+c²−a²)²]. + // Skip isosceles (b²=c²) and right (any b²+c²−a²≈0). + { + let da = (b * b - c * c) * (b * b + c * c - a * a).powi(2); + let db = (c * c - a * a) * (c * c + a * a - b * b).powi(2); + let dc = (a * a - b * b) * (a * a + b * b - c * c).powi(2); + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + let wa = 1.0 / da; + let wb = 1.0 / db; + let wc = 1.0 / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x107 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "Ψ对称中线垂心", + "X_{107}", + pt(x107[0], x107[1]), + None, + "X(107) = \\bigl(1/[(b^2-c^2)(b^2+c^2-a^2)^2]:\\cdots\\bigr)", + "X(107):Ψ(K,H)", + ).with(Shape::Point { + x: x107[0], + y: x107[1], + label: "X107".into(), + })); + } + } + } + + // X(108): Ψ(O,H) = Ψ(X(3),X(4)) = Ψ(I,H); bary a²/(sec B−sec C). + // Skip isosceles / right (sec undefined when cos=0) / sec B=sec C. + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + if ca.abs() > 1e-9 && cb.abs() > 1e-9 && cc.abs() > 1e-9 { + let da = 1.0 / cb - 1.0 / cc; + let db = 1.0 / cc - 1.0 / ca; + let dc = 1.0 / ca - 1.0 / cb; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = (a * a) / da; + let wb = (b * b) / db; + let wc = (c * c) / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x108 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "Ψ外心垂心", + "X_{108}", + pt(x108[0], x108[1]), + None, + "X(108) = \\bigl(a^2/(\\sec B-\\sec C):\\cdots\\bigr)", + "X(108):Ψ(O,H)=Ψ(I,H)", + ).with(Shape::Point { + x: x108[0], + y: x108[1], + label: "X108".into(), + })); + } + } + } + } + + // X(109): Ψ(I,O) = Λ(I,O) partner; bary a²/(cos B−cos C). + // Circumcircle-antipode of X(102); skip isosceles. + { + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + let da = cb - cc; + let db = cc - ca; + let dc = ca - cb; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = (a * a) / da; + let wb = (b * b) / db; + let wc = (c * c) / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x109 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "Ψ内心外心", + "X_{109}", + pt(x109[0], x109[1]), + None, + "X(109) = \\bigl(a^2/(\\cos B-\\cos C):\\cdots\\bigr)", + "X(109):Ψ(I,O)(外接圆上;X(102) 对径)", + ).with(Shape::Point { + x: x109[0], + y: x109[1], + label: "X109".into(), + })); + } + } + } + + // X(112): Ψ(H,K) = Ψ(X(4),X(6)); bary a²/(sin 2B−sin 2C). + // Skip isosceles / when sin 2B=sin 2C (incl. right where 2A=π → sin2B=sin2C may hold). + { + let da = (2.0 * g[1]).sin() - (2.0 * g[2]).sin(); + let db = (2.0 * g[2]).sin() - (2.0 * g[0]).sin(); + let dc = (2.0 * g[0]).sin() - (2.0 * g[1]).sin(); + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = (a * a) / da; + let wb = (b * b) / db; + let wc = (c * c) / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x112 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "Ψ垂心对称中线", + "X_{112}", + pt(x112[0], x112[1]), + None, + "X(112) = \\bigl(a^2/(\\sin 2B-\\sin 2C):\\cdots\\bigr)", + "X(112):Ψ(H,K)", + ).with(Shape::Point { + x: x112[0], + y: x112[1], + label: "X112".into(), + })); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -9636,6 +9772,58 @@ mod tests { assert!(fs3.iter().all(|f| f.group != "Λ内心重心"), "X106 skip equilateral"); } + #[test] + fn x107_x108_x109_x112() { + // Scalene acute 6-7-9: all four present. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(9.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x107 = fs.iter().find(|f| f.group == "Ψ对称中线垂心" && f.label == "X_{107}").expect("X107"); + let x108 = fs.iter().find(|f| f.group == "Ψ外心垂心" && f.label == "X_{108}").expect("X108"); + let x109 = fs.iter().find(|f| f.group == "Ψ内心外心" && f.label == "X_{109}").expect("X109"); + let x112 = fs.iter().find(|f| f.group == "Ψ垂心对称中线" && f.label == "X_{112}").expect("X112"); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + assert_ne!(x107.value, x108.value); + assert_ne!(x108.value, x109.value); + assert_ne!(x109.value, x112.value); + assert_ne!(x107.value, g.value); + assert_ne!(x108.value, g.value); + assert_ne!(x109.value, g.value); + assert_ne!(x112.value, g.value); + + // Isosceles non-eq 5-5-6: all four skipped (denoms vanish). + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().all(|f| f.group != "Ψ对称中线垂心"), "X107 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "Ψ外心垂心"), "X108 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "Ψ内心外心"), "X109 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "Ψ垂心对称中线"), "X112 skip isosceles"); + + // Right 3-4-5: X107/X108 skip (cos=0 / b²+c²−a²=0); X109/X112 may remain. + let k3 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.group != "Ψ对称中线垂心"), "X107 skip right"); + assert!(fs3.iter().all(|f| f.group != "Ψ外心垂心"), "X108 skip right"); + assert!(fs3.iter().any(|f| f.group == "Ψ内心外心" && f.label == "X_{109}")); + // sin2B−sin2C = 0 when one angle is π/2 (2A+2B=π ⇒ sin2A=sin2B for complementary pair), so X112 skips. + assert!(fs3.iter().all(|f| f.group != "Ψ垂心对称中线"), "X112 skip right"); + + // Equilateral: all skipped. + let k4 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().all(|f| f.group != "Ψ对称中线垂心")); + assert!(fs4.iter().all(|f| f.group != "Ψ外心垂心")); + assert!(fs4.iter().all(|f| f.group != "Ψ内心外心")); + assert!(fs4.iter().all(|f| f.group != "Ψ垂心对称中线")); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm 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crates/mathcore/src/geometry.rs | 366 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 684392 -> 691072 bytes 2 files changed, 366 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 31ff392..d4e19c7 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -5652,6 +5652,290 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(102): Λ(I,H) = circumcircle-antipode of X(109). Skip isosceles (no X109). + { + let x109_xy = out.iter().rev().find(|f| f.group == "Ψ内心外心" && f.label == "X_{109}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((px, py)) = x109_xy { + let x102 = [2.0 * circ[0] - px, 2.0 * circ[1] - py]; + out.push(fact( + "Λ内心垂心", + "X_{102}", + pt(x102[0], x102[1]), + None, + "X(102) = 2O - X(109) = \\Lambda(I,H)", + "X(102):Λ(I,H)(外接圆上;X(109) 对径)", + ).with(Shape::Point { + x: x102[0], + y: x102[1], + label: "X102".into(), + })); + out.push(fact( + "Λ内心垂心", + "X_{102}=2O-X_{109}", + "\\text{外接圆对径}".into(), + None, + "X(102) = 2O - X(109)", + "X(102) 与 X(109) 互为外接圆对径点", + )); + } + } + + // X(103): circumcircle-antipode of X(101); bary a²/[(a−b)cot C+(a−c)cot B]. + // Skip isosceles / when any denom≈0. + { + let cota = g[0].cos() / g[0].sin(); + let cotb = g[1].cos() / g[1].sin(); + let cotc = g[2].cos() / g[2].sin(); + let da = (a - b) * cotc + (a - c) * cotb; + let db = (b - c) * cota + (b - a) * cotc; + let dc = (c - a) * cotb + (c - b) * cota; + let mut emitted = false; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = (a * a) / da; + let wb = (b * b) / db; + let wc = (c * c) / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x103 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "X101对径", + "X_{103}", + pt(x103[0], x103[1]), + None, + "X(103) = \\bigl(a^2/[(a-b)\\cot C+(a-c)\\cot B]:\\cdots\\bigr)", + "X(103):X(101) 在外接圆上的对径点", + ).with(Shape::Point { + x: x103[0], + y: x103[1], + label: "X103".into(), + })); + emitted = true; + let x101_xy = out.iter().rev().find(|f| f.group == "Ψ内心对称中线" && f.label == "X_{101}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((px, py)) = x101_xy { + let mid_dx = (x103[0] + px) / 2.0 - circ[0]; + let mid_dy = (x103[1] + py) / 2.0 - circ[1]; + if mid_dx * mid_dx + mid_dy * mid_dy < 1e-6 { + out.push(fact( + "X101对径", + "X_{103}=2O-X_{101}", + "\\text{外接圆对径}".into(), + None, + "X(103) = 2O - X(101)", + "X(103) 与 X(101) 互为外接圆对径点", + )); + } + } + } + } + if !emitted { + // Fallback: pure antipode of X(101) when bary denoms vanish but partner exists. + let x101_xy = out.iter().rev().find(|f| f.group == "Ψ内心对称中线" && f.label == "X_{101}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((px, py)) = x101_xy { + let x103 = [2.0 * circ[0] - px, 2.0 * circ[1] - py]; + out.push(fact( + "X101对径", + "X_{103}", + pt(x103[0], x103[1]), + None, + "X(103) = 2O - X(101)", + "X(103):X(101) 在外接圆上的对径点", + ).with(Shape::Point { + x: x103[0], + y: x103[1], + label: "X103".into(), + })); + out.push(fact( + "X101对径", + "X_{103}=2O-X_{101}", + "\\text{外接圆对径}".into(), + None, + "X(103) = 2O - X(101)", + "X(103) 与 X(101) 互为外接圆对径点", + )); + } + } + } + + // X(116): midpoint(H, X(103)); on nine-point circle. Bary (b−c)²(b²+bc+c²−ab−ac). + // Skip isosceles (any (b−c)=0). + { + let da = (b - c).powi(2) * (b * b + b * c + c * c - a * b - a * c); + let db = (c - a).powi(2) * (c * c + c * a + a * a - b * c - b * a); + let dc = (a - b).powi(2) * (a * a + a * b + b * b - c * a - c * b); + let mut emitted = false; + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + let wa = da; + let wb = db; + let wc = dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x116 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "九点X103中点", + "X_{116}", + pt(x116[0], x116[1]), + None, + "X(116) = \\bigl((b-c)^2(b^2+bc+c^2-ab-ac):\\cdots\\bigr)", + "X(116):H 与 X(103) 的中点(九点圆上)", + ).with(Shape::Point { + x: x116[0], + y: x116[1], + label: "X116".into(), + })); + emitted = true; + } + } + if !emitted { + let x103_xy = out.iter().rev().find(|f| f.group == "X101对径" && f.label == "X_{103}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((px, py)) = x103_xy { + let x116 = [(orth[0] + px) / 2.0, (orth[1] + py) / 2.0]; + out.push(fact( + "九点X103中点", + "X_{116}", + pt(x116[0], x116[1]), + None, + "X(116) = \\text{midpoint}(H, X(103))", + "X(116):H 与 X(103) 的中点(九点圆上)", + ).with(Shape::Point { + x: x116[0], + y: x116[1], + label: "X116".into(), + })); + } + } else if let Some((px, py)) = out.iter().rev().find(|f| f.group == "X101对径" && f.label == "X_{103}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }) { + // annotate midpoint relation when bary path used + let x116_xy = out.iter().rev().find(|f| f.group == "九点X103中点" && f.label == "X_{116}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((mx, my)) = x116_xy { + let dx = (orth[0] + px) / 2.0 - mx; + let dy = (orth[1] + py) / 2.0 - my; + if dx * dx + dy * dy < 1e-6 { + out.push(fact( + "九点X103中点", + "X_{116}=\\mathrm{mid}(H,X_{103})", + "\\text{中点}".into(), + None, + "X(116) = \\text{midpoint}(H, X(103))", + "X(116) 为垂心与 X(103) 的中点", + )); + } + } + } + } + + // X(117): midpoint(H, X(109)); on nine-point circle. Skip when X109 absent. + { + let x109_xy = out.iter().rev().find(|f| f.group == "Ψ内心外心" && f.label == "X_{109}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((px, py)) = x109_xy { + let x117 = [(orth[0] + px) / 2.0, (orth[1] + py) / 2.0]; + out.push(fact( + "九点X109中点", + "X_{117}", + pt(x117[0], x117[1]), + None, + "X(117) = \\text{midpoint}(H, X(109))", + "X(117):H 与 X(109) 的中点(九点圆上)", + ).with(Shape::Point { + x: x117[0], + y: x117[1], + label: "X117".into(), + })); + } + } + + // X(118): midpoint(H, X(101)); on nine-point circle. Skip when X101 absent. + { + let x101_xy = out.iter().rev().find(|f| f.group == "Ψ内心对称中线" && f.label == "X_{101}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((px, py)) = x101_xy { + let x118 = [(orth[0] + px) / 2.0, (orth[1] + py) / 2.0]; + out.push(fact( + "九点X101中点", + "X_{118}", + pt(x118[0], x118[1]), + None, + "X(118) = \\text{midpoint}(H, X(101))", + "X(118):H 与 X(101) 的中点(九点圆上)", + ).with(Shape::Point { + x: x118[0], + y: x118[1], + label: "X118".into(), + })); + } + } + + // X(119): midpoint(H, X(100)) = nine-point antipode of Feuerbach X(11). + // Skip when X100 absent (isosceles). + { + let x100_xy = out.iter().rev().find(|f| f.group == "反补费尔巴哈" && f.label == "X_{100}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((px, py)) = x100_xy { + let x119 = [(orth[0] + px) / 2.0, (orth[1] + py) / 2.0]; + out.push(fact( + "费尔巴哈九点对径", + "X_{119}", + pt(x119[0], x119[1]), + None, + "X(119) = \\text{midpoint}(H, X(100)) = 2N - Fe", + "X(119):费尔巴哈点在九点圆上的对径点", + ).with(Shape::Point { + x: x119[0], + y: x119[1], + label: "X119".into(), + })); + // Verify reflection of Fe in N when both present. + let n9 = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; + let fe_xy = out.iter().rev().find(|f| f.group == "费尔巴哈点" && f.label == "Fe").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((fx, fy)) = fe_xy { + let mid_dx = (x119[0] + fx) / 2.0 - n9[0]; + let mid_dy = (x119[1] + fy) / 2.0 - n9[1]; + if mid_dx * mid_dx + mid_dy * mid_dy < 1e-6 { + out.push(fact( + "费尔巴哈九点对径", + "X_{119}=2N-Fe", + "\\text{九点圆对径}".into(), + None, + "X(119) = 2N - X(11)", + "X(119) 与费尔巴哈点互为九点圆对径点", + )); + } + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -9824,6 +10108,88 @@ mod tests { assert!(fs4.iter().all(|f| f.group != "Ψ垂心对称中线")); } + + #[test] + fn x102_x103_x116_x117_x118_x119() { + // Scalene acute 6-7-9: all six present; antipodes and nine-point midpoints hold. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(9.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x100 = fs.iter().find(|f| f.group == "反补费尔巴哈" && f.label == "X_{100}").expect("X100"); + let x101 = fs.iter().find(|f| f.group == "Ψ内心对称中线" && f.label == "X_{101}").expect("X101"); + let x102 = fs.iter().find(|f| f.group == "Λ内心垂心" && f.label == "X_{102}").expect("X102"); + let x103 = fs.iter().find(|f| f.group == "X101对径" && f.label == "X_{103}").expect("X103"); + let x109 = fs.iter().find(|f| f.group == "Ψ内心外心" && f.label == "X_{109}").expect("X109"); + let x116 = fs.iter().find(|f| f.group == "九点X103中点" && f.label == "X_{116}").expect("X116"); + let x117 = fs.iter().find(|f| f.group == "九点X109中点" && f.label == "X_{117}").expect("X117"); + let x118 = fs.iter().find(|f| f.group == "九点X101中点" && f.label == "X_{118}").expect("X118"); + let x119 = fs.iter().find(|f| f.group == "费尔巴哈九点对径" && f.label == "X_{119}").expect("X119"); + let o = fs.iter().find(|f| f.group == "特殊点" && f.label == "O").expect("O"); + let h = fs.iter().find(|f| f.group == "特殊点" && f.label == "H").expect("H"); + let n = fs.iter().find(|f| f.group == "欧拉线" && f.label == "N").expect("N"); + let fe = fs.iter().find(|f| f.group == "费尔巴哈点" && f.label == "Fe").expect("Fe"); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + assert_ne!(x102.value, g.value); + assert_ne!(x103.value, g.value); + assert!(fs.iter().any(|f| f.group == "Λ内心垂心" && f.label.contains("2O"))); + assert!(fs.iter().any(|f| f.group == "X101对径" && f.label.contains("2O"))); + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + let (ox, oy) = ptxy(o); + let (hx, hy) = ptxy(h); + let (nx, ny) = ptxy(n); + let (a1, b1) = ptxy(x101); + let (a2, b2) = ptxy(x102); + let (a3, b3) = ptxy(x103); + let (a9, b9) = ptxy(x109); + let (a0, b0) = ptxy(x100); + let (fx, fy) = ptxy(fe); + // X102 = 2O - X109; X103 = 2O - X101 + assert!(((a2 + a9) / 2.0 - ox).abs() < 1e-6 && ((b2 + b9) / 2.0 - oy).abs() < 1e-6, "X102 not antipode of X109"); + assert!(((a3 + a1) / 2.0 - ox).abs() < 1e-6 && ((b3 + b1) / 2.0 - oy).abs() < 1e-6, "X103 not antipode of X101"); + // Midpoints with H + let (u6, v6) = ptxy(x116); + let (u7, v7) = ptxy(x117); + let (u8, v8) = ptxy(x118); + let (u9, v9) = ptxy(x119); + assert!(((hx + a3) / 2.0 - u6).abs() < 1e-6 && ((hy + b3) / 2.0 - v6).abs() < 1e-6, "X116 mid(H,X103)"); + assert!(((hx + a9) / 2.0 - u7).abs() < 1e-6 && ((hy + b9) / 2.0 - v7).abs() < 1e-6, "X117 mid(H,X109)"); + assert!(((hx + a1) / 2.0 - u8).abs() < 1e-6 && ((hy + b1) / 2.0 - v8).abs() < 1e-6, "X118 mid(H,X101)"); + assert!(((hx + a0) / 2.0 - u9).abs() < 1e-6 && ((hy + b0) / 2.0 - v9).abs() < 1e-6, "X119 mid(H,X100)"); + // X119 = 2N - Fe + assert!(((u9 + fx) / 2.0 - nx).abs() < 1e-6 && ((v9 + fy) / 2.0 - ny).abs() < 1e-6, "X119 not antipode of Fe on NPC"); + assert!(fs.iter().any(|f| f.group == "费尔巴哈九点对径" && f.label.contains("2N"))); + + // Isosceles non-eq 5-5-6 (a=b): X100/X101/X109 absent → X102/X117/X118/X119 skip; + // X103 bary still finite, so X103/X116 remain via mid(H,X103). + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().all(|f| f.group != "Λ内心垂心"), "X102 skip isosceles"); + assert!(fs2.iter().any(|f| f.group == "X101对径" && f.label == "X_{103}"), "X103 on a=b isosceles"); + assert!(fs2.iter().any(|f| f.group == "九点X103中点" && f.label == "X_{116}"), "X116 on a=b isosceles"); + assert!(fs2.iter().all(|f| f.group != "九点X109中点"), "X117 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "九点X101中点"), "X118 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "费尔巴哈九点对径"), "X119 skip isosceles"); + + // Equilateral: all skipped. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.group != "Λ内心垂心")); + assert!(fs3.iter().all(|f| f.group != "X101对径")); + assert!(fs3.iter().all(|f| f.group != "九点X103中点")); + assert!(fs3.iter().all(|f| f.group != "九点X109中点")); + assert!(fs3.iter().all(|f| f.group != "九点X101中点")); + assert!(fs3.iter().all(|f| f.group != "费尔巴哈九点对径")); + } + + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 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zw6?!CFu3RAm|$tolUg|4pQW`><~>fCSz2cL@1VDU+*q_9uP0^9+cXmo#iYyjVdD4w zn10IAl3g!n8uM-;V$27YBE;;%-^--|t{1X}#2mXgq+(4n_Y zI^tL);18yUdxqx?^Nh+HHhjFN0CcWvdLe}rYY8Eq|lpMtd-i7gT-$hoUYNq I=^>x}KZ0d2L;wH) From 1388d68e12b8b0fb015423549d373514442c592e Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 16:48:17 +0800 Subject: [PATCH 048/123] feat: Kiepert/Jerabek NPC centers X113/X114/X115/X125 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit X(115) bary (b²−c²)² = mid(H,Tarry); X(114)=2N−X115=mid(H,Steiner). X(125) bary sin2A sin²(B−C)=mid(H,X74); X(113)=2N−X125=mid(H,Er). --- crates/mathcore/src/geometry.rs | 264 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 691072 -> 695937 bytes 2 files changed, 264 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index d4e19c7..d960345 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -5936,6 +5936,186 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // X(115): center of the Kiepert hyperbola; bary (b²−c²)². + // On the nine-point circle; = midpoint(H, Tarry X(98)). Skip equilateral (all zero). + { + let da = b * b - c * c; + let db = c * c - a * a; + let dc = a * a - b * b; + let wa = da * da; + let wb = db * db; + let wc = dc * dc; + let den = wa + wb + wc; + if den > 1e-18 { + let x115 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "基伯特双曲心", + "X_{115}", + pt(x115[0], x115[1]), + None, + "X(115) = \\bigl((b^2-c^2)^2:\\cdots\\bigr)", + "X(115):基伯特双曲线的中心(九点圆上)", + ).with(Shape::Point { + x: x115[0], + y: x115[1], + label: "X115".into(), + })); + // Cross-check: midpoint(H, Tarry) when Tarry present. + let ty_xy = out.iter().rev().find(|f| f.group == "塔里点" && f.label == "Ty").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((tx, ty)) = ty_xy { + let mx = (orth[0] + tx) / 2.0; + let my = (orth[1] + ty) / 2.0; + if (mx - x115[0]).abs() < 1e-5 && (my - x115[1]).abs() < 1e-5 { + out.push(fact( + "基伯特双曲心", + "X_{115}=\\mathrm{mid}(H,Ty)", + "\\text{九点圆}".into(), + None, + "X(115) = \\text{midpoint}(H, X(98))", + "X(115) 为垂心与塔里点的中点", + )); + } + } + + // X(114): Kiepert antipode = nine-point antipode of X(115) = midpoint(H, Steiner). + let n9 = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; + let x114 = [2.0 * n9[0] - x115[0], 2.0 * n9[1] - x115[1]]; + out.push(fact( + "基伯特对径", + "X_{114}", + pt(x114[0], x114[1]), + None, + "X(114) = 2N - X(115) = \\text{midpoint}(H, X(99))", + "X(114):基伯特双曲心在九点圆上的对径点", + ).with(Shape::Point { + x: x114[0], + y: x114[1], + label: "X114".into(), + })); + out.push(fact( + "基伯特对径", + "X_{114}=2N-X_{115}", + "\\text{九点圆对径}".into(), + None, + "X(114) = 2N - X(115)", + "X(114) 与 X(115) 互为九点圆对径点", + )); + let st_xy = out.iter().rev().find(|f| f.group == "施泰纳点" && f.label == "St").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((sx, sy)) = st_xy { + let mx = (orth[0] + sx) / 2.0; + let my = (orth[1] + sy) / 2.0; + if (mx - x114[0]).abs() < 1e-5 && (my - x114[1]).abs() < 1e-5 { + out.push(fact( + "基伯特对径", + "X_{114}=\\mathrm{mid}(H,St)", + "\\text{九点圆}".into(), + None, + "X(114) = \\text{midpoint}(H, X(99))", + "X(114) 为垂心与施泰纳点的中点", + )); + } + } + } + } + + // X(125): center of the Jerabek hyperbola; bary (sin 2A) sin²(B−C). + // On the nine-point circle; = midpoint(H, X(74)); complement of Euler reflection X(110). + // Skip equilateral (all sin(B−C)=0). + { + let sa = (2.0 * g[0]).sin() * (g[1] - g[2]).sin().powi(2); + let sb = (2.0 * g[1]).sin() * (g[2] - g[0]).sin().powi(2); + let sc = (2.0 * g[2]).sin() * (g[0] - g[1]).sin().powi(2); + let den = sa + sb + sc; + if den.abs() > 1e-12 { + let x125 = [ + (sa * pa[0] + sb * pb[0] + sc * pc[0]) / den, + (sa * pa[1] + sb * pb[1] + sc * pc[1]) / den, + ]; + out.push(fact( + "耶拉贝克双曲心", + "X_{125}", + pt(x125[0], x125[1]), + None, + "X(125) = \\bigl(\\sin 2A\\,\\sin^2(B-C):\\cdots\\bigr)", + "X(125):耶拉贝克双曲线的中心(九点圆上)", + ).with(Shape::Point { + x: x125[0], + y: x125[1], + label: "X125".into(), + })); + let x74_xy = out.iter().rev().find(|f| f.group == "欧拉无穷等角" && f.label == "X_{74}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((px, py)) = x74_xy { + let mx = (orth[0] + px) / 2.0; + let my = (orth[1] + py) / 2.0; + if (mx - x125[0]).abs() < 1e-5 && (my - x125[1]).abs() < 1e-5 { + out.push(fact( + "耶拉贝克双曲心", + "X_{125}=\\mathrm{mid}(H,X_{74})", + "\\text{九点圆}".into(), + None, + "X(125) = \\text{midpoint}(H, X(74))", + "X(125) 为垂心与 X(74) 的中点", + )); + } + } + + // X(113): Jerabek antipode = nine-point antipode of X(125) = midpoint(H, Euler reflection). + let n9 = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; + let x113 = [2.0 * n9[0] - x125[0], 2.0 * n9[1] - x125[1]]; + out.push(fact( + "耶拉贝克对径", + "X_{113}", + pt(x113[0], x113[1]), + None, + "X(113) = 2N - X(125) = \\text{midpoint}(H, X(110))", + "X(113):耶拉贝克双曲心在九点圆上的对径点", + ).with(Shape::Point { + x: x113[0], + y: x113[1], + label: "X113".into(), + })); + out.push(fact( + "耶拉贝克对径", + "X_{113}=2N-X_{125}", + "\\text{九点圆对径}".into(), + None, + "X(113) = 2N - X(125)", + "X(113) 与 X(125) 互为九点圆对径点", + )); + let er_xy = out.iter().rev().find(|f| f.group == "欧拉反射点" && f.label == "E_r").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((ex, ey)) = er_xy { + let mx = (orth[0] + ex) / 2.0; + let my = (orth[1] + ey) / 2.0; + if (mx - x113[0]).abs() < 1e-5 && (my - x113[1]).abs() < 1e-5 { + out.push(fact( + "耶拉贝克对径", + "X_{113}=\\mathrm{mid}(H,E_r)", + "\\text{九点圆}".into(), + None, + "X(113) = \\text{midpoint}(H, X(110))", + "X(113) 为垂心与欧拉反射点的中点", + )); + } + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -10190,6 +10370,90 @@ mod tests { } + #[test] + fn x113_x114_x115_x125() { + // Scalene acute 6-7-9: all four present; NPC antipodes and H-midpoints hold. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(9.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x115 = fs.iter().find(|f| f.group == "基伯特双曲心" && f.label == "X_{115}").expect("X115"); + let x114 = fs.iter().find(|f| f.group == "基伯特对径" && f.label == "X_{114}").expect("X114"); + let x125 = fs.iter().find(|f| f.group == "耶拉贝克双曲心" && f.label == "X_{125}").expect("X125"); + let x113 = fs.iter().find(|f| f.group == "耶拉贝克对径" && f.label == "X_{113}").expect("X113"); + let h = fs.iter().find(|f| f.group == "特殊点" && f.label == "H").expect("H"); + let n = fs.iter().find(|f| f.group == "欧拉线" && f.label == "N").expect("N"); + let st = fs.iter().find(|f| f.group == "施泰纳点" && f.label == "St").expect("St"); + let ty = fs.iter().find(|f| f.group == "塔里点" && f.label == "Ty").expect("Ty"); + let x74 = fs.iter().find(|f| f.group == "欧拉无穷等角" && f.label == "X_{74}").expect("X74"); + let er = fs.iter().find(|f| f.group == "欧拉反射点" && f.label == "E_r").expect("Er"); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + assert_ne!(x115.value, x114.value); + assert_ne!(x125.value, x113.value); + assert_ne!(x115.value, x125.value); + assert_ne!(x115.value, g.value); + assert_ne!(x125.value, g.value); + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + let (hx, hy) = ptxy(h); + let (nx, ny) = ptxy(n); + let (a5, b5) = ptxy(x115); + let (a4, b4) = ptxy(x114); + let (a25, b25) = ptxy(x125); + let (a13, b13) = ptxy(x113); + let (sx, sy) = ptxy(st); + let (tx, tyy) = ptxy(ty); + let (p74x, p74y) = ptxy(x74); + let (ex, ey) = ptxy(er); + // X114 = 2N - X115; X113 = 2N - X125 + assert!(((a4 + a5) / 2.0 - nx).abs() < 1e-6 && ((b4 + b5) / 2.0 - ny).abs() < 1e-6, "X114 not NPC antipode of X115"); + assert!(((a13 + a25) / 2.0 - nx).abs() < 1e-6 && ((b13 + b25) / 2.0 - ny).abs() < 1e-6, "X113 not NPC antipode of X125"); + // Midpoints with H + assert!(((hx + tx) / 2.0 - a5).abs() < 1e-6 && ((hy + tyy) / 2.0 - b5).abs() < 1e-6, "X115 mid(H,Ty)"); + assert!(((hx + sx) / 2.0 - a4).abs() < 1e-6 && ((hy + sy) / 2.0 - b4).abs() < 1e-6, "X114 mid(H,St)"); + assert!(((hx + p74x) / 2.0 - a25).abs() < 1e-6 && ((hy + p74y) / 2.0 - b25).abs() < 1e-6, "X125 mid(H,X74)"); + assert!(((hx + ex) / 2.0 - a13).abs() < 1e-6 && ((hy + ey) / 2.0 - b13).abs() < 1e-6, "X113 mid(H,Er)"); + assert!(fs.iter().any(|f| f.group == "基伯特对径" && f.label.contains("2N"))); + assert!(fs.iter().any(|f| f.group == "耶拉贝克对径" && f.label.contains("2N"))); + assert!(fs.iter().any(|f| f.group == "基伯特双曲心" && f.label.contains("mid"))); + assert!(fs.iter().any(|f| f.group == "耶拉贝克双曲心" && f.label.contains("mid"))); + + // Isosceles non-eq 5-5-6: X115/X125/X114/X113 still via bary (Steiner/Tarry/Er may skip). + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().any(|f| f.group == "基伯特双曲心" && f.label == "X_{115}"), "X115 on isosceles"); + assert!(fs2.iter().any(|f| f.group == "基伯特对径" && f.label == "X_{114}"), "X114 on isosceles"); + assert!(fs2.iter().any(|f| f.group == "耶拉贝克双曲心" && f.label == "X_{125}"), "X125 on isosceles"); + assert!(fs2.iter().any(|f| f.group == "耶拉贝克对径" && f.label == "X_{113}"), "X113 on isosceles"); + // Steiner/Tarry skipped on isosceles → no mid(H,St/Ty) cross-facts required. + assert!(fs2.iter().all(|f| f.group != "施泰纳点"), "St skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "塔里点"), "Ty skip isosceles"); + + // Equilateral: all four skipped (bary weights vanish). + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.group != "基伯特双曲心"), "X115 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "基伯特对径"), "X114 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "耶拉贝克双曲心"), "X125 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "耶拉贝克对径"), "X113 skip equilateral"); + + // Right 3-4-5: X115/X114/X125/X113 present (bary OK); Er may skip. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().any(|f| f.group == "基伯特双曲心" && f.label == "X_{115}")); + assert!(fs4.iter().any(|f| f.group == "基伯特对径" && f.label == "X_{114}")); + assert!(fs4.iter().any(|f| f.group == "耶拉贝克双曲心" && f.label == "X_{125}")); + assert!(fs4.iter().any(|f| f.group == "耶拉贝克对径" && f.label == "X_{113}")); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index a2582ec73aeb63fc1959b15e7f61727382f38848..f365cb35add7d4d977789d73b361e01f3f68e4f2 100644 GIT binary patch delta 46865 zcmd44dt6mj(>Tsr`*Hxe9F&WSz~(3dD&W1mpf0baQr^lgnw56Lv@ElFo)j!nR8;Vw z3l;TnQ7KU|uuX-9ibaZsMMg_kBN~-ygrH=fm1FYi8E0 zSu?Y4`)m_=kEI8C6#Oi?r*8b*rCovxYtAVALu#Skw^EgNP1kmtgn$IPWGN~9+qIWW zGt;f1-t%cex;4#v11(OsMw<81yuYnKm;?PQ(+|5aZ}a;^kr)|BliZ;M!l&No#2@{D z_*#!X>1iF~vs0)|KWu$!OhjQodq!xn6(spu6PQ%^YKKLHR#~lo`p!a;6a51HTde;S zsd04T35P)B`+l2+6kVM4W&b0zWSw1_by7ePEnkPNTSGcdM1k`<2Kra81A$R(bxgGy zRK9%P2gK9*;7G~(W5<_hhShp9$d8{sOaiS-I{hHnQV;W!>qv*f`JK-aT9#^^-eopz zNwt=A38cws*6+JSI7qAkLB-UTR(LY#d7w1N7p%3rGOXSO-n_EZnBd6NQSkTC*Lk;bE(2-CFBs!{4+yz^XgcMLNtpoApkNbm$$GabBCseM{7&}>a^xflLy9TH&?CrIOtxp~ZqQz^ii~Bu5 z^Q?u(`;BWSWUMyYh#9_y7OjRhPSUc~)^#JE5SmsWw)Xie+?wC7gSEDMd+Tu4gC?&r 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+++++++++++++++++++++++++++++++- src/wasm/pkg/mathcore_bg.wasm | Bin 695937 -> 700928 bytes 2 files changed, 330 insertions(+), 3 deletions(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index d960345..f5afc63 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -774,13 +774,25 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "N", pt(n9[0], n9[1]), None, - "N = \\text{中点}(O, H)", + "N = \\text{中点}(O, H) = X(5)", "九点圆圆心(欧拉圆)", ).with(Shape::Point { x: n9[0], y: n9[1], label: "N 九点圆圆心".into(), })); + out.push(fact( + "欧拉线", + "X_{5}", + pt(n9[0], n9[1]), + None, + "X(5) = N = \\text{midpoint}(O, H)", + "X(5):九点圆心", + ).with(Shape::Point { + x: n9[0], + y: n9[1], + label: "X5".into(), + })); out.push(fact( "欧拉线", "R_{\\text{九点}}", @@ -967,13 +979,25 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "Na", pt(na[0], na[1]), None, - "Na = \\frac{(s-a)A+(s-b)B+(s-c)C}{s}", + "Na = X(8) = \\frac{(s-a)A+(s-b)B+(s-c)C}{s}", "奈格尔点:顶点与对旁切圆切点的连线交点", ).with(Shape::Point { x: na[0], y: na[1], label: "Na 奈格尔".into(), })); + out.push(fact( + "奈格尔点", + "X_{8}", + pt(na[0], na[1]), + None, + "X(8) = (s-a:s-b:s-c)", + "X(8):奈格尔点", + ).with(Shape::Point { + x: na[0], + y: na[1], + label: "X8".into(), + })); // Nagel line: I, G, Na collinear with IG:GNa = 1:2 let ig = dist2(inc, centroid); let gna = dist2(centroid, na); @@ -1021,13 +1045,25 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] "Ge", pt(ge[0], ge[1]), None, - "Ge = \\frac{\\frac{1}{s-a}A+\\frac{1}{s-b}B+\\frac{1}{s-c}C}{\\sum}", + "Ge = X(7) = \\frac{\\frac{1}{s-a}A+\\frac{1}{s-b}B+\\frac{1}{s-c}C}{\\sum}", "格尔巩点:顶点与对边内切圆切点的连线交点", ).with(Shape::Point { x: ge[0], y: ge[1], label: "Ge 格尔巩".into(), })); + out.push(fact( + "格尔巩点", + "X_{7}", + pt(ge[0], ge[1]), + None, + "X(7) = (1/(s-a):1/(s-b):1/(s-c))", + "X(7):格尔巩点", + ).with(Shape::Point { + x: ge[0], + y: ge[1], + label: "X7".into(), + })); out.push(fact( "格尔巩点", "Ge \\leftrightarrow Na", @@ -6116,6 +6152,203 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(110): Euler reflection point / focus of Kiepert parabola. + // Bary a²/(b²−c²); circumcircle antipode of X(74); = 2O − X(74). + // Skip isosceles (denom 0) / equilateral. Works on scalene right (unlike fold construction). + { + let da = b * b - c * c; + let db = c * c - a * a; + let dc = a * a - b * b; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = (a * a) / da; + let wb = (b * b) / db; + let wc = (c * c) / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x110 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "欧拉反射点", + "X_{110}", + pt(x110[0], x110[1]), + None, + "X(110) = \\bigl(a^2/(b^2-c^2):\\cdots\\bigr)", + "X(110):欧拉反射点(基伯特抛物线焦点;外接圆上)", + ).with(Shape::Point { + x: x110[0], + y: x110[1], + label: "X110".into(), + })); + if (dist2(x110, circ) - rr).abs() < 1e-5 * (1.0 + rr) { + out.push(fact( + "欧拉反射点", + "X_{110}\\in(O)", + "\\checkmark".into(), + None, + "d(O, X(110)) = R", + "X(110) 在外接圆上", + )); + } + // Cross-check: circum-antipode of X(74). + let x74_xy = out.iter().rev().find(|f| f.group == "欧拉无穷等角" && f.label == "X_{74}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((px, py)) = x74_xy { + let mid_dx = (x110[0] + px) / 2.0 - circ[0]; + let mid_dy = (x110[1] + py) / 2.0 - circ[1]; + if mid_dx * mid_dx + mid_dy * mid_dy < 1e-6 { + out.push(fact( + "欧拉反射点", + "X_{110}=2O-X_{74}", + "\\text{外接圆对径}".into(), + None, + "X(110) = 2O - X(74)", + "X(110) 与 X(74) 互为外接圆对径点", + )); + } + } + // Cross-check geometric Er (fold of Euler line) when present. + let er_xy = out.iter().rev().find(|f| f.group == "欧拉反射点" && f.label == "E_r").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((ex, ey)) = er_xy { + if (ex - x110[0]).abs() < 1e-5 && (ey - x110[1]).abs() < 1e-5 { + out.push(fact( + "欧拉反射点", + "X_{110}=E_r", + "\\text{折线构造}".into(), + None, + "X(110) = E_r", + "X(110) 与欧拉线三边反射交点重合", + )); + } + } + // Cross-check: X(113) = midpoint(H, X(110)). + let x113_xy = out.iter().rev().find(|f| f.group == "耶拉贝克对径" && f.label == "X_{113}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((qx, qy)) = x113_xy { + let mx = (orth[0] + x110[0]) / 2.0; + let my = (orth[1] + x110[1]) / 2.0; + if (mx - qx).abs() < 1e-5 && (my - qy).abs() < 1e-5 { + out.push(fact( + "欧拉反射点", + "X_{113}=\\mathrm{mid}(H,X_{110})", + "\\text{九点圆}".into(), + None, + "X(113) = \\text{midpoint}(H, X(110))", + "X(113) 为垂心与 X(110) 的中点", + )); + } + } + } + } + } + + // X(120): X(105)-of-medial; on nine-point circle. + // Bary g(a,b,c)=(2abc−(b+c)(a²+(b−c)²))(b²+c²−ab−ac). Skip equilateral / vanishing den. + { + let ga = { + let t = 2.0 * a * b * c - (b + c) * (a * a + (b - c) * (b - c)); + t * (b * b + c * c - a * b - a * c) + }; + let gb = { + let t = 2.0 * b * c * a - (c + a) * (b * b + (c - a) * (c - a)); + t * (c * c + a * a - b * c - b * a) + }; + let gc = { + let t = 2.0 * c * a * b - (a + b) * (c * c + (a - b) * (a - b)); + t * (a * a + b * b - c * a - c * b) + }; + let den = ga + gb + gc; + if den.abs() > 1e-10 { + let x120 = [ + (ga * pa[0] + gb * pb[0] + gc * pc[0]) / den, + (ga * pa[1] + gb * pb[1] + gc * pc[1]) / den, + ]; + out.push(fact( + "中点X105", + "X_{120}", + pt(x120[0], x120[1]), + None, + "X(120) = X(105)\\text{-of-medial}", + "X(120):中点三角形的 X(105)(九点圆上)", + ).with(Shape::Point { + x: x120[0], + y: x120[1], + label: "X120".into(), + })); + let n9 = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; + let r9 = rr / 2.0; + if (dist2(x120, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "中点X105", + "X_{120}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(120)) = R/2", + "X(120) 在九点圆上", + )); + } + } + } + + // X(121): X(106)-of-medial; on nine-point circle. + // Bary g=(b+c−2a)[b³+c³+a(b²+c²)−2bc(b+c)]. Skip equilateral. + { + let ga = { + let u = b + c - 2.0 * a; + let v = b * b * b + c * c * c + a * (b * b + c * c) - 2.0 * b * c * (b + c); + u * v + }; + let gb = { + let u = c + a - 2.0 * b; + let v = c * c * c + a * a * a + b * (c * c + a * a) - 2.0 * c * a * (c + a); + u * v + }; + let gc = { + let u = a + b - 2.0 * c; + let v = a * a * a + b * b * b + c * (a * a + b * b) - 2.0 * a * b * (a + b); + u * v + }; + let den = ga + gb + gc; + if den.abs() > 1e-10 { + let x121 = [ + (ga * pa[0] + gb * pb[0] + gc * pc[0]) / den, + (ga * pa[1] + gb * pb[1] + gc * pc[1]) / den, + ]; + out.push(fact( + "中点X106", + "X_{121}", + pt(x121[0], x121[1]), + None, + "X(121) = X(106)\\text{-of-medial}", + "X(121):中点三角形的 X(106)(九点圆上)", + ).with(Shape::Point { + x: x121[0], + y: x121[1], + label: "X121".into(), + })); + let n9 = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; + let r9 = rr / 2.0; + if (dist2(x121, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "中点X106", + "X_{121}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(121)) = R/2", + "X(121) 在九点圆上", + )); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -10454,6 +10687,100 @@ mod tests { assert!(fs4.iter().any(|f| f.group == "耶拉贝克对径" && f.label == "X_{113}")); } + #[test] + fn x5_x7_x8_x110_x120_x121() { + // Scalene acute 6-7-9: classical + Euler reflection + medial-of NPC points. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(9.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let n = fs.iter().find(|f| f.group == "欧拉线" && f.label == "N").expect("N"); + let x5 = fs.iter().find(|f| f.group == "欧拉线" && f.label == "X_{5}").expect("X5"); + let ge = fs.iter().find(|f| f.group == "格尔巩点" && f.label == "Ge").expect("Ge"); + let x7 = fs.iter().find(|f| f.group == "格尔巩点" && f.label == "X_{7}").expect("X7"); + let na = fs.iter().find(|f| f.group == "奈格尔点" && f.label == "Na").expect("Na"); + let x8 = fs.iter().find(|f| f.group == "奈格尔点" && f.label == "X_{8}").expect("X8"); + let x110 = fs.iter().find(|f| f.group == "欧拉反射点" && f.label == "X_{110}").expect("X110"); + let er = fs.iter().find(|f| f.group == "欧拉反射点" && f.label == "E_r").expect("Er"); + let x74 = fs.iter().find(|f| f.group == "欧拉无穷等角" && f.label == "X_{74}").expect("X74"); + let x113 = fs.iter().find(|f| f.group == "耶拉贝克对径" && f.label == "X_{113}").expect("X113"); + let x120 = fs.iter().find(|f| f.group == "中点X105" && f.label == "X_{120}").expect("X120"); + let x121 = fs.iter().find(|f| f.group == "中点X106" && f.label == "X_{121}").expect("X121"); + let o = fs.iter().find(|f| f.group == "特殊点" && f.label == "O").expect("O"); + let h = fs.iter().find(|f| f.group == "特殊点" && f.label == "H").expect("H"); + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + let (nx, ny) = ptxy(n); + let (a5, b5) = ptxy(x5); + assert!((nx - a5).abs() < 1e-9 && (ny - b5).abs() < 1e-9, "X5 != N"); + let (gx, gy) = ptxy(ge); + let (a7, b7) = ptxy(x7); + assert!((gx - a7).abs() < 1e-9 && (gy - b7).abs() < 1e-9, "X7 != Ge"); + let (nax, nay) = ptxy(na); + let (a8, b8) = ptxy(x8); + assert!((nax - a8).abs() < 1e-9 && (nay - b8).abs() < 1e-9, "X8 != Na"); + let (ox, oy) = ptxy(o); + let (hx, hy) = ptxy(h); + let (e0, e1) = ptxy(x110); + let (rx, ry) = ptxy(er); + let (p74x, p74y) = ptxy(x74); + let (a13, b13) = ptxy(x113); + assert!((e0 - rx).abs() < 1e-5 && (e1 - ry).abs() < 1e-5, "X110 != Er"); + assert!(((e0 + p74x) / 2.0 - ox).abs() < 1e-5 && ((e1 + p74y) / 2.0 - oy).abs() < 1e-5, "X110 not antipode of X74"); + assert!(((hx + e0) / 2.0 - a13).abs() < 1e-5 && ((hy + e1) / 2.0 - b13).abs() < 1e-5, "X113 not mid(H,X110)"); + assert!(fs.iter().any(|f| f.group == "欧拉反射点" && f.label.contains("2O"))); + assert!(fs.iter().any(|f| f.group == "中点X105" && f.label.contains("NPC"))); + assert!(fs.iter().any(|f| f.group == "中点X106" && f.label.contains("NPC"))); + let (p120x, p120y) = ptxy(x120); + let (p121x, p121y) = ptxy(x121); + let r9 = ((ox - hx).hypot(oy - hy)) / 2.0; // unused; check distinct from N/G + let _ = r9; + assert!((p120x - nx).abs() > 1e-4 || (p120y - ny).abs() > 1e-4, "X120 coincides N"); + assert!((p121x - nx).abs() > 1e-4 || (p121y - ny).abs() > 1e-4, "X121 coincides N"); + assert_ne!(x120.value, x121.value); + + // Isosceles 5-5-6: X110 skipped (denom 0); X5/X7/X8/X120/X121 present. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().any(|f| f.group == "欧拉线" && f.label == "X_{5}")); + assert!(fs2.iter().any(|f| f.group == "格尔巩点" && f.label == "X_{7}")); + assert!(fs2.iter().any(|f| f.group == "奈格尔点" && f.label == "X_{8}")); + assert!(fs2.iter().all(|f| !(f.group == "欧拉反射点" && f.label == "X_{110}")), "X110 skip isosceles"); + assert!(fs2.iter().any(|f| f.group == "中点X105" && f.label == "X_{120}"), "X120 on isosceles"); + assert!(fs2.iter().any(|f| f.group == "中点X106" && f.label == "X_{121}"), "X121 on isosceles"); + + // Equilateral: X110/X120/X121 skip; X5/X7/X8 remain. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().any(|f| f.group == "欧拉线" && f.label == "X_{5}")); + assert!(fs3.iter().any(|f| f.group == "格尔巩点" && f.label == "X_{7}")); + assert!(fs3.iter().any(|f| f.group == "奈格尔点" && f.label == "X_{8}")); + assert!(fs3.iter().all(|f| !(f.group == "欧拉反射点" && f.label == "X_{110}")), "X110 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "中点X105"), "X120 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "中点X106"), "X121 skip equilateral"); + + // Right 3-4-5: X110 via bary (Er may skip); antipode of X74 holds. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + let x110r = fs4.iter().find(|f| f.group == "欧拉反射点" && f.label == "X_{110}").expect("X110 on 3-4-5"); + let x74r = fs4.iter().find(|f| f.group == "欧拉无穷等角" && f.label == "X_{74}").expect("X74 on 3-4-5"); + let or = fs4.iter().find(|f| f.group == "特殊点" && f.label == "O").expect("O"); + let (e0, e1) = ptxy(x110r); + let (p74x, p74y) = ptxy(x74r); + let (ox, oy) = ptxy(or); + assert!(((e0 + p74x) / 2.0 - ox).abs() < 1e-5 && ((e1 + p74y) / 2.0 - oy).abs() < 1e-5, "3-4-5 X110 antipode"); + assert!(fs4.iter().any(|f| f.group == "中点X105" && f.label == "X_{120}")); + assert!(fs4.iter().any(|f| f.group == "中点X106" && f.label == "X_{121}")); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index f365cb35add7d4d977789d73b361e01f3f68e4f2..e6055e71eab5b899d32c48fb946e072870f83349 100644 GIT binary patch delta 68232 zcmb@v33!dy_As8k4aZ$)Z34(+m2#q!>tC?C%<1*ERpA_Rh7LM;$uNc3|b1JFm8Hp~kJ-r1>3kD>@kbX45Yh?fj!-v?FcI z;AXe?Xu?{4X}UL`F|9q{;`RkiTFbk-Z=)^u_<8q0-<-9F9hjT@W+Js`q(4n?1}GDB z<`$1~L&4g^{E~>=>F>!1P0ElN#k2N1KlJ*T(A*5(;5`vJ#rXvKR%ZMsCzS$4$4vAV zL$?!GKIX~xe80~kLv4o4n$Pk*LX+2MocUP40-Ax3ow?-yEHZ!3KhQUC4KR;xt!AB8 z%bQpD&!G)#c0SkHnb4;6oi7L6BQ$*#pU`D8tz5==X$_T(tYkG5b_ErLTQ%{c z4XcsG&c)KacGQ~A-7Gn@D4mxK`IPqvAMaS1j>Zr}d`SSUP3In;`iPmn#B1m2@co@= zj)3Z&`NlrmoC^fhGqdl-VeY;-h$f};FZ+(BEo*k3?%RbJg4rE@{jr`rpr29Ht|czP z(GDBtvsecQ$&q!O${eB`*3M^-%a8E)N)Z{9^I6aJ8|u3!$PfFsLU=WB){iktHMoIIJ)zPecZyb|vxSB~O@1JIvAtIFJA&B8*To*pZ)md^>``nRr zkiD#7iQUVtz~AE1o5YuYxw|8;8#sbCEwT05#SxBC=xnOEgd||A>Vsp6EkT4UOGgka 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From 4f948ec7e70cc86d7f822e3d9b5d959a705659e2 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 17:10:10 +0800 Subject: [PATCH 056/123] =?UTF-8?q?feat:=20ETC=20X151=E2=80=93X156=20L-ref?= =?UTF-8?q?lections=20and=20tangential/orthic=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit X(151)–X(153) continue de Longchamps reflections in X(109)/X(101)/X(100). X(154)–X(156) add tangential centroid, orthic eigencenter, and tangential nine-point center with acute guards (skip right when bary sums vanish). --- crates/mathcore/src/geometry.rs | 221 +++++++++++++++++++++++++++++++- 1 file changed, 217 insertions(+), 4 deletions(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index e00f947..2145743 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -7044,13 +7044,14 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } - // X(140)–X(150): Euler/medial complements, anticomplements of Ge/Na, and + // X(140)–X(153): Euler/medial complements, anticomplements of Ge/Na, and // reflections of de Longchamps X(20) in classical circumcircle points. // X(140)=mid(O,N)=complement(X(5)); X(141)=complement(K), bary b²+c²:…; // X(142)=mid(Ge,Mi)=complement(X(9)); X(143)=mid(N,X(52))=X(5)-of-orthic; // X(144)=anticomplement(Ge); X(145)=anticomplement(Na); // X(146)=2·X(110)−X(20); X(147)=2·X(99)−X(20); X(148)=2·X(98)−X(20); - // X(149)=2·X(104)−X(20); X(150)=2·X(103)−X(20). + // X(149)=2·X(104)−X(20); X(150)=2·X(103)−X(20); + // X(151)=2·X(109)−X(20); X(152)=2·X(101)−X(20); X(153)=2·X(100)−X(20). { let n9 = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; // X(140) = midpoint(O, N) = complement of X(5); on Euler line. Always. @@ -7355,10 +7356,180 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] label: "X150".into(), })); } + + // X(151) = reflection of X(20) in X(109) = X(102)-of-anticomplementary. + let x109_xy = out.iter().rev().find(|f| f.group == "Ψ内心外心" && f.label == "X_{109}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((qx, qy)) = x109_xy { + let xy = reflect_l(qx, qy); + out.push(fact( + "德龙尚X109反射", + "X_{151}", + pt(xy[0], xy[1]), + None, + "X(151) = 2\\,X(109) - X(20) = X(102)\\text{-of-anticomplementary}", + "X(151):德龙尚点关于 X(109) 的反射(反补三角形的 X(102))", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X151".into(), + })); + } + + // X(152) = reflection of X(20) in X(101) = X(103)-of-anticomplementary. + let x101_xy = out.iter().rev().find(|f| f.group == "Ψ内心对称中线" && f.label == "X_{101}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((qx, qy)) = x101_xy { + let xy = reflect_l(qx, qy); + out.push(fact( + "德龙尚X101反射", + "X_{152}", + pt(xy[0], xy[1]), + None, + "X(152) = 2\\,X(101) - X(20) = X(103)\\text{-of-anticomplementary}", + "X(152):德龙尚点关于 X(101) 的反射(反补三角形的 X(103))", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X152".into(), + })); + } + + // X(153) = reflection of X(20) in X(100) = X(104)-of-anticomplementary. + let x100_xy = out.iter().rev().find(|f| f.group == "反补费尔巴哈" && f.label == "X_{100}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((qx, qy)) = x100_xy { + let xy = reflect_l(qx, qy); + out.push(fact( + "德龙尚X100反射", + "X_{153}", + pt(xy[0], xy[1]), + None, + "X(153) = 2\\,X(100) - X(20) = X(104)\\text{-of-anticomplementary}", + "X(153):德龙尚点关于 X(100) 的反射(反补三角形的 X(104))", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X153".into(), + })); + } + } + } + + // X(154)–X(156): tangential / orthic eigencenter family. + // X(154)=X(3)-Ceva conjugate of X(6)=X(2)-of-tangential; + // bary a³(cos A − cos B cos C). + // X(155)=eigencenter of orthic; bary a cos A (cos²B+cos²C−cos²A); + // = reflection of X(68) in X(5) when acute. + // X(156)=X(5)-of-tangential = midpoint(X(26), X(155)). + { + let ca = [g[0].cos(), g[1].cos(), g[2].cos()]; + // Right △: X(154)/X(155) bary sums vanish (point at infinity) — skip. + let rightish = ca[0].abs() < 1e-9 || ca[1].abs() < 1e-9 || ca[2].abs() < 1e-9; + // X(154) + { + let wa = a * a * a * (ca[0] - ca[1] * ca[2]); + let wb = b * b * b * (ca[1] - ca[2] * ca[0]); + let wc = c * c * c * (ca[2] - ca[0] * ca[1]); + let den = wa + wb + wc; + if !rightish && den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "切线重心", + "X_{154}", + pt(xy[0], xy[1]), + None, + "X(154) = \\bigl(a^3(\\cos A-\\cos B\\cos C):\\cdots\\bigr) = X(2)\\text{-of-tangential}", + "X(154):切线三角形的重心(X(3)-Ceva 共轭于 X(6))", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X154".into(), + })); + } + } + // X(155) + let mut x155_xy: Option<[f64; 2]> = None; + { + let wa = a * ca[0] * (ca[1] * ca[1] + ca[2] * ca[2] - ca[0] * ca[0]); + let wb = b * ca[1] * (ca[2] * ca[2] + ca[0] * ca[0] - ca[1] * ca[1]); + let wc = c * ca[2] * (ca[0] * ca[0] + ca[1] * ca[1] - ca[2] * ca[2]); + let den = wa + wb + wc; + if !rightish && den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + x155_xy = Some(xy); + out.push(fact( + "垂足特征心", + "X_{155}", + pt(xy[0], xy[1]), + None, + "X(155) = \\bigl(a\\cos A(\\cos^2 B+\\cos^2 C-\\cos^2 A):\\cdots\\bigr)", + "X(155):垂足三角形的特征中心(切线三角形的垂心)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X155".into(), + })); + // Cross-check: reflection of X(68) in nine-point center N=X(5). + let n9 = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; + let x68_xy = out.iter().rev().find(|f| f.group == "普拉索洛夫点" && f.label == "X_{68}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((qx, qy)) = x68_xy { + let rx = 2.0 * n9[0] - qx; + let ry = 2.0 * n9[1] - qy; + if (rx - xy[0]).abs() < 1e-5 && (ry - xy[1]).abs() < 1e-5 { + out.push(fact( + "垂足特征心", + "X_{155}=2N-X_{68}", + "\\checkmark".into(), + None, + "X(155) = 2\\,X(5) - X(68)", + "X(155) 为普拉索洛夫点关于九点圆心的反射", + )); + } + } + } + } + // X(156) = mid(X(26), X(155)) = X(5)-of-tangential. + if let Some(x155) = x155_xy { + let x26_xy = out.iter().rev().find(|f| f.group == "切线三角形外心" && f.label == "X_{26}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((qx, qy)) = x26_xy { + let xy = [(qx + x155[0]) / 2.0, (qy + x155[1]) / 2.0]; + out.push(fact( + "切线九点心", + "X_{156}", + pt(xy[0], xy[1]), + None, + "X(156) = \\mathrm{mid}(X(26),X(155)) = X(5)\\text{-of-tangential}", + "X(156):切线三角形的九点圆心(X(26) 与 X(155) 的中点)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X156".into(), + })); + } } } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -12002,7 +12173,7 @@ mod tests { #[test] - fn x140_to_x150_complements_anticomplements_reflections() { + fn x140_to_x156_complements_reflections_tangential() { // Scalene acute 6-7-8: all eleven present with geometric cross-checks. let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; let r = triangle_solve(&k); @@ -12070,6 +12241,28 @@ mod tests { check_ref(ty, x148, "X148"); check_ref(x104, x149, "X149"); check_ref(x103, x150, "X150"); + let x109 = fs.iter().find(|f| f.group == "Ψ内心外心" && f.label == "X_{109}").expect("X109"); + let x101 = fs.iter().find(|f| f.group == "Ψ内心对称中线" && f.label == "X_{101}").expect("X101"); + let x100 = fs.iter().find(|f| f.group == "反补费尔巴哈" && f.label == "X_{100}").expect("X100"); + let x151 = fs.iter().find(|f| f.group == "德龙尚X109反射" && f.label == "X_{151}").expect("X151"); + let x152 = fs.iter().find(|f| f.group == "德龙尚X101反射" && f.label == "X_{152}").expect("X152"); + let x153 = fs.iter().find(|f| f.group == "德龙尚X100反射" && f.label == "X_{153}").expect("X153"); + check_ref(x109, x151, "X151"); + check_ref(x101, x152, "X152"); + check_ref(x100, x153, "X153"); + let x154 = fs.iter().find(|f| f.group == "切线重心" && f.label == "X_{154}").expect("X154"); + let x155 = fs.iter().find(|f| f.group == "垂足特征心" && f.label == "X_{155}").expect("X155"); + let x156 = fs.iter().find(|f| f.group == "切线九点心" && f.label == "X_{156}").expect("X156"); + let x26 = fs.iter().find(|f| f.group == "切线三角形外心" && f.label == "X_{26}").expect("X26"); + let x68 = fs.iter().find(|f| f.group == "普拉索洛夫点" && f.label == "X_{68}").expect("X68"); + let (p26x, p26y) = ptxy(x26); + let (p155x, p155y) = ptxy(x155); + let (p156x, p156y) = ptxy(x156); + assert!(((p26x + p155x) / 2.0 - p156x).abs() < 1e-5 && ((p26y + p155y) / 2.0 - p156y).abs() < 1e-5, "X156 != mid(X26,X155)"); + let (p68x, p68y) = ptxy(x68); + assert!((2.0 * nx - p68x - p155x).abs() < 1e-5 && (2.0 * ny - p68y - p155y).abs() < 1e-5, "X155 != 2N-X68"); + assert!(fs.iter().any(|f| f.group == "垂足特征心" && f.label.contains("2N"))); + let _ = x154; // presence is the check; bary finite on acute scalene // Isosceles 5-5-6: X140–X145 remain; Steiner/Tarry/X110/X104 family skip → reflections skip. let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; @@ -12091,6 +12284,14 @@ mod tests { fs2.iter().any(|f| f.group == "德龙尚X104反射"), fs2.iter().any(|f| f.group == "德龙尚X103反射"), ); + // X100/X101/X109 skip on isos → X151–X153 skip; X154/X155 still finite. + assert!(fs2.iter().all(|f| f.group != "德龙尚X109反射"), "X151 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "德龙尚X101反射"), "X152 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "德龙尚X100反射"), "X153 skip isosceles"); + assert!(fs2.iter().any(|f| f.group == "切线重心" && f.label == "X_{154}")); + assert!(fs2.iter().any(|f| f.group == "垂足特征心" && f.label == "X_{155}")); + // X156 needs X26; may be present on isos acute. + let _ = fs2.iter().any(|f| f.group == "切线九点心"); // Equilateral: X140–X145 collapse toward G/O; reflections of circumcircle points skip. let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; @@ -12107,6 +12308,12 @@ mod tests { assert!(fs3.iter().all(|f| f.group != "德龙尚塔里反射"), "X148 skip equilateral"); assert!(fs3.iter().all(|f| f.group != "德龙尚X104反射"), "X149 skip equilateral"); assert!(fs3.iter().all(|f| f.group != "德龙尚X103反射"), "X150 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "德龙尚X109反射"), "X151 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "德龙尚X101反射"), "X152 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "德龙尚X100反射"), "X153 skip equilateral"); + // X154/X155 bary finite on equilateral (→ G); X26 may skip on equilateral. + assert!(fs3.iter().any(|f| f.group == "切线重心" && f.label == "X_{154}")); + assert!(fs3.iter().any(|f| f.group == "垂足特征心" && f.label == "X_{155}")); // Right 3-4-5: X140/141/142/144/145; X143 skips (no X52); X110 may via bary. let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; @@ -12123,8 +12330,14 @@ mod tests { let _ = ( fs4.iter().any(|f| f.group == "德龙尚X110反射"), fs4.iter().any(|f| f.group == "德龙尚施泰纳反射"), - fs4.iter().any(|f| f.group == "德龙尚塔里反射"), + fs4.iter().any(|f| f.group == "德龙尚塔里反射"), + fs4.iter().any(|f| f.group == "德龙尚X109反射"), + fs4.iter().any(|f| f.group == "德龙尚X101反射"), + fs4.iter().any(|f| f.group == "德龙尚X100反射"), ); + assert!(fs4.iter().all(|f| f.group != "切线重心"), "X154 skip right"); + assert!(fs4.iter().all(|f| f.group != "垂足特征心"), "X155 skip right"); + assert!(fs4.iter().all(|f| f.group != "切线九点心"), "X156 skip right"); } #[test] From df56c42202498d34d7003e0fd59d9f5f3019f45b Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 17:10:10 +0800 Subject: [PATCH 057/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X151=E2=80=93X156=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 753385 -> 758059 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 5d23025f240488555edd2e30b919ac6ea017afb1..6690113d336da5a0bd6ac96655e8e34e954aacf9 100644 GIT binary patch delta 59332 zcmb?^2V51$_CGTyg23g{1VLc$m5ZRDpiu!EV>HE>s4u-}G|}HnjA`$e`r?b&K~d3B z$1cs@P}FNf!QRE*6=K7Vy_^3zdw1^+=u7#1{xKiU-S5tvIp@roc4l_>;*+>}ISupA zRftO?xW-tmt7uirGRT-zR=Q1m&+NcIn-WrdEf9uFdGkjmr>Z0xia-p@KLrKW=gY$j!Svrn{F5HL$4^GYVl{gzp>B8Xp?O7i9!cSSl=o~} 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z5do2o0K&ceu-;^>`-&jm*GUh&#eIhu+tQ0+;gBHgOraHUYezU?l+KqmVP_6uz-=7i zgq`w)X+?W*-i+txy;#Y=9q+#VNiRtJ?@N?$_eR*cN>MniDyO!7TDAGDGoS5p$aX^5 zz(!be;I8`e3GRF$Y8B+LIQjA<>|E(qd-?p^+za}qgLl3l;X#gggh%;dz5DI%L(=4* zk$RXT;1}Rl4t%~*_!VI1l1A9MbY1Dd@0jeK()T2I=ZZ-f&Fp)TV~xU(br5s8{y-Q1StHhALbuUb59xdF8HaAc!dAn2v<4cQFyH%*2g{SeqWgU zDFU3mk+Abs3E$#~_*o-)!cO_mqV!SI-5-vMIF+yj-LNv}HT1_*J2sq3UwLZRLM+*R z2fVD;Y;s=;;%g(_t@YE}-JSdBea^UNvOr&hh3Mt<8 From a435c57a4abd491a497b020f4112c9a6327421dc Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 17:12:58 +0800 Subject: [PATCH 058/123] =?UTF-8?q?feat:=20ETC=20X157=E2=80=93X159=20/=20X?= =?UTF-8?q?163=E2=80=93X165=20tangential=20and=20excentral=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Add classical centers after X(156): X(157)=X(6)-of-tangential, X(158)=sec A tan A (skip right), X(159)=2·X(141)−X(66), X(163)=a³/(b²−c²) (skip isos), X(164)=X(1)-of-excentral, X(165)=X(2)-of-excentral with centroid(I,Na,L) and OI harmonic checks. --- crates/mathcore/src/geometry.rs | 314 +++++++++++++++++++++++++++++++- 1 file changed, 313 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 2145743..a1d5c5c 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -7530,6 +7530,242 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] + + // X(157)–X(159), X(163)–X(165): tangential symmedian / sec-tan / X66-reflection / + // trilinear-product, and excentral incenter/centroid. + // X(157)=X(6)-of-tangential; bary a²(b³ cos B + c³ cos C − a³ cos A). + // X(158)=bary sec A tan A = sin A / cos² A; skip right (sec ∞). + // X(159)=X(9)-of-tangential = reflection of X(66) in X(141). + // X(163)=trilinear product X(6)·X(110); bary a³/(b²−c²); skip isosceles. + // X(164)=X(1)-of-excentral; bary a(sin(B/2)+sin(C/2)−sin(A/2)). + // X(165)=X(2)-of-excentral; bary a(tan(B/2)+tan(C/2)−tan(A/2)); + // = centroid(I, Na, L); on OI as {O, Be}-harmonic conjugate of I. + { + let ca = [g[0].cos(), g[1].cos(), g[2].cos()]; + let rightish = ca[0].abs() < 1e-9 || ca[1].abs() < 1e-9 || ca[2].abs() < 1e-9; + // X(157) + { + let fa = b * b * b * ca[1] + c * c * c * ca[2] - a * a * a * ca[0]; + let fb = c * c * c * ca[2] + a * a * a * ca[0] - b * b * b * ca[1]; + let fc = a * a * a * ca[0] + b * b * b * ca[1] - c * c * c * ca[2]; + let wa = a * a * fa; + let wb = b * b * fb; + let wc = c * c * fc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "切线对称中线", + "X_{157}", + pt(xy[0], xy[1]), + None, + "X(157) = \\bigl(a^2(b^3\\cos B+c^3\\cos C-a^3\\cos A):\\cdots\\bigr) = X(6)\\text{-of-tangential}", + "X(157):切线三角形的对称中线点", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X157".into(), + })); + } + } + // X(158) + if !rightish { + let sa_ = [g[0].sin(), g[1].sin(), g[2].sin()]; + let wa = sa_[0] / (ca[0] * ca[0]); + let wb = sa_[1] / (ca[1] * ca[1]); + let wc = sa_[2] / (ca[2] * ca[2]); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "正割正切点", + "X_{158}", + pt(xy[0], xy[1]), + None, + "X(158) = (\\sec A\\tan A:\\sec B\\tan B:\\sec C\\tan C)", + "X(158):正割–正切重心坐标点(X(19) 与 X(92) 的截共轭)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X158".into(), + })); + } + } + // X(159) = 2·X(141) − X(66) = X(9)-of-tangential. + { + let x66_xy = out.iter().rev().find(|f| f.group == "埃克塞特等角" && f.label == "X_{66}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let x141_xy = out.iter().rev().find(|f| f.group == "对称中线补点" && f.label == "X_{141}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let (Some((qx, qy)), Some((mx, my))) = (x66_xy, x141_xy) { + let xy = [2.0 * mx - qx, 2.0 * my - qy]; + out.push(fact( + "切线米滕", + "X_{159}", + pt(xy[0], xy[1]), + None, + "X(159) = 2\\,X(141) - X(66) = X(9)\\text{-of-tangential}", + "X(159):切线三角形的米滕点(X(66) 关于 X(141) 的反射)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X159".into(), + })); + } + } + // X(163): bary a³/(b²−c²); skip isosceles (denom 0). + { + let a2 = a * a; + let b2 = b * b; + let c2 = c * c; + let da = b2 - c2; + let db = c2 - a2; + let dc = a2 - b2; + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + let wa = a * a2 / da; + let wb = b * b2 / db; + let wc = c * c2 / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "对称中线X110积", + "X_{163}", + pt(xy[0], xy[1]), + None, + "X(163) = \\bigl(a^3/(b^2-c^2):\\cdots\\bigr) = X(6)\\cdot X(110)\\text{ (trilinear)}", + "X(163):对称中线点与 X(110) 的三线积", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X163".into(), + })); + } + } + } + // X(164) / X(165): excentral incenter & centroid via half-angles. + { + let ha = g[0] / 2.0; + let hb = g[1] / 2.0; + let hc = g[2] / 2.0; + let s_ha = ha.sin(); + let s_hb = hb.sin(); + let s_hc = hc.sin(); + // X(164) + { + let wa = a * (s_hb + s_hc - s_ha); + let wb = b * (s_hc + s_ha - s_hb); + let wc = c * (s_ha + s_hb - s_hc); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "旁心内心", + "X_{164}", + pt(xy[0], xy[1]), + None, + "X(164) = \\bigl(a(\\sin\\tfrac{B}{2}+\\sin\\tfrac{C}{2}-\\sin\\tfrac{A}{2}):\\cdots\\bigr) = X(1)\\text{-of-excentral}", + "X(164):旁心三角形的内心", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X164".into(), + })); + } + } + // X(165) + let t_ha = ha.tan(); + let t_hb = hb.tan(); + let t_hc = hc.tan(); + if t_ha.is_finite() && t_hb.is_finite() && t_hc.is_finite() { + let wa = a * (t_hb + t_hc - t_ha); + let wb = b * (t_hc + t_ha - t_hb); + let wc = c * (t_ha + t_hb - t_hc); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "旁心重心", + "X_{165}", + pt(xy[0], xy[1]), + None, + "X(165) = \\bigl(a(\\tan\\tfrac{B}{2}+\\tan\\tfrac{C}{2}-\\tan\\tfrac{A}{2}):\\cdots\\bigr) = X(2)\\text{-of-excentral}", + "X(165):旁心三角形的重心(在 OI 线上)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X165".into(), + })); + // Cross-check: centroid of I, Nagel, de Longchamps. + let i_xy = out.iter().rev().find(|f| f.group == "特殊点" && f.label == "I").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let na_xy = out.iter().rev().find(|f| f.group == "奈格尔点" && f.label == "Na").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let l_xy = out.iter().rev().find(|f| f.group == "德龙尚点" && f.label == "L").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let (Some((ix, iy)), Some((nx, ny)), Some((lx, ly))) = (i_xy, na_xy, l_xy) { + let cx = (ix + nx + lx) / 3.0; + let cy = (iy + ny + ly) / 3.0; + if (cx - xy[0]).abs() < 1e-5 && (cy - xy[1]).abs() < 1e-5 { + out.push(fact( + "旁心重心", + "X_{165}=\\mathrm{cent}(I,Na,L)", + "\\checkmark".into(), + None, + "X(165) = \\mathrm{centroid}(X(1),X(8),X(20))", + "X(165) 为内心、奈格尔、德龙尚三点的重心", + )); + } + } + // Cross-check: on OI — {O, Be}-harmonic conjugate of I → (4/3)O − (1/3)I. + let be_xy = out.iter().rev().find(|f| f.group == "贝万点" && f.label == "Be").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let (Some((ix, iy)), Some((_bx, _by))) = (i_xy, be_xy) { + let hx = (4.0 * circ[0] - ix) / 3.0; + let hy = (4.0 * circ[1] - iy) / 3.0; + if (hx - xy[0]).abs() < 1e-5 && (hy - xy[1]).abs() < 1e-5 { + out.push(fact( + "旁心重心", + "X_{165}\\in OI", + "\\checkmark".into(), + None, + "X(165) = \\tfrac{4}{3}O - \\tfrac{1}{3}I = \\{O,X(40)\\}\\text{-harmonic of }I", + "X(165) 为 I 关于 O 与贝万点的调和共轭(在 OI 上)", + )); + } + } + } + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -12340,7 +12576,83 @@ mod tests { assert!(fs4.iter().all(|f| f.group != "切线九点心"), "X156 skip right"); } - #[test] + #[test] + fn x157_to_x165_tangential_excentral() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x157 = fs.iter().find(|f| f.group == "切线对称中线" && f.label == "X_{157}").expect("X157"); + let x158 = fs.iter().find(|f| f.group == "正割正切点" && f.label == "X_{158}").expect("X158"); + let x159 = fs.iter().find(|f| f.group == "切线米滕" && f.label == "X_{159}").expect("X159"); + let x163 = fs.iter().find(|f| f.group == "对称中线X110积" && f.label == "X_{163}").expect("X163"); + let x164 = fs.iter().find(|f| f.group == "旁心内心" && f.label == "X_{164}").expect("X164"); + let x165 = fs.iter().find(|f| f.group == "旁心重心" && f.label == "X_{165}").expect("X165"); + let x66 = fs.iter().find(|f| f.group == "埃克塞特等角" && f.label == "X_{66}").expect("X66"); + let x141 = fs.iter().find(|f| f.group == "对称中线补点" && f.label == "X_{141}").expect("X141"); + let (p66x, p66y) = ptxy(x66); + let (p141x, p141y) = ptxy(x141); + let (p159x, p159y) = ptxy(x159); + assert!((2.0 * p141x - p66x - p159x).abs() < 1e-5 && (2.0 * p141y - p66y - p159y).abs() < 1e-5, "X159 != 2·X141−X66"); + assert!(fs.iter().any(|f| f.group == "旁心重心" && f.label.contains("cent"))); + assert!(fs.iter().any(|f| f.group == "旁心重心" && f.label.contains("OI"))); + let i = fs.iter().find(|f| f.group == "特殊点" && f.label == "I").expect("I"); + let o = fs.iter().find(|f| f.group == "特殊点" && f.label == "O").expect("O"); + let (ix, iy) = ptxy(i); + let (ox, oy) = ptxy(o); + let (p165x, p165y) = ptxy(x165); + assert!(((4.0 * ox - ix) / 3.0 - p165x).abs() < 1e-5 && ((4.0 * oy - iy) / 3.0 - p165y).abs() < 1e-5, "X165 != (4O−I)/3"); + let _ = (x157, x158, x163, x164); + + // Isosceles 5-5-6: X163 skips; X157/158/164/165 remain; X159 if X66+X141. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().all(|f| f.group != "对称中线X110积"), "X163 skip isosceles"); + assert!(fs2.iter().any(|f| f.group == "切线对称中线" && f.label == "X_{157}")); + assert!(fs2.iter().any(|f| f.group == "正割正切点" && f.label == "X_{158}")); + assert!(fs2.iter().any(|f| f.group == "旁心内心" && f.label == "X_{164}")); + assert!(fs2.iter().any(|f| f.group == "旁心重心" && f.label == "X_{165}")); + let _ = fs2.iter().any(|f| f.group == "切线米滕"); + + // Equilateral: X163 skips; others finite; X165 = G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.group != "对称中线X110积"), "X163 skip equilateral"); + assert!(fs3.iter().any(|f| f.group == "切线对称中线" && f.label == "X_{157}")); + assert!(fs3.iter().any(|f| f.group == "正割正切点" && f.label == "X_{158}")); + assert!(fs3.iter().any(|f| f.group == "旁心内心" && f.label == "X_{164}")); + assert!(fs3.iter().any(|f| f.group == "旁心重心" && f.label == "X_{165}")); + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let x165e = fs3.iter().find(|f| f.group == "旁心重心" && f.label == "X_{165}").expect("X165e"); + let (gx, gy) = ptxy(g3); + let (ex, ey) = ptxy(x165e); + assert!((gx - ex).abs() < 1e-5 && (gy - ey).abs() < 1e-5, "equilateral X165 != G"); + + // Right 3-4-5: X158 skips; X163/164/165 ok; X157/X159 optional via parents. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().all(|f| f.group != "正割正切点"), "X158 skip right"); + assert!(fs4.iter().any(|f| f.group == "旁心内心" && f.label == "X_{164}")); + assert!(fs4.iter().any(|f| f.group == "旁心重心" && f.label == "X_{165}")); + assert!(fs4.iter().any(|f| f.group == "对称中线X110积" && f.label == "X_{163}")); + let _ = ( + fs4.iter().any(|f| f.group == "切线对称中线"), + fs4.iter().any(|f| f.group == "切线米滕"), + ); + } + + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; let r = triangle_solve(&k); From 4448f3de419d23105f6e8c200984b140d4c8e2b9 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 17:12:58 +0800 Subject: [PATCH 059/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X157=E2=80=93X165=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 758059 -> 763336 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 6690113d336da5a0bd6ac96655e8e34e954aacf9..bc578cbd5a61043d0f809322a29c041034b91027 100644 GIT binary patch delta 59358 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=?UTF-8?q?feat:=20ETC=20X160=E2=80=93X162=20gaps?= =?UTF-8?q?=20and=20X168/X169/X171=E2=80=93X173=20classical=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Fill tangential X(160)=X(37)-of-tangential and X(161)=X(63)-of-tangential from official ETC (sin 2A / sin² 2A; skip right for X161), X(162) cevapoint of X(108)/X(109) (skip isos/right), then X(168) mittenpunkt-of-excentral, X(169) X(85)-Ceva of I, X(171)–X(173) harmonic/trilinear-product/Yff isoscelizers with OI and equilateral guards. --- crates/mathcore/src/geometry.rs | 378 ++++++++++++++++++++++++++++++++ 1 file changed, 378 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index a1d5c5c..f438fc8 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -7766,6 +7766,299 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(160)–X(162): fill tangential gaps; then classical X(168)/X(169)/X(171)–X(173). + // X(160)=X(37)-of-tangential (acute): bary a·f with + // f=a[(b²+c²)sin 2A+(c²−a²)sin 2B+(b²−a²)sin 2C] (ETC: sin 2A, not sin²A). + // X(161)=X(63)-of-tangential (acute): bary a·f; skip right (Σw=0); with + // f=a[(a²+b²+c²)sin²(2A)+(c²−b²−a²)sin²(2B)+(b²−c²−a²)sin²(2C)]. + // X(162)=cevapoint of X(108),X(109): bary a/(sin 2B−sin 2C); skip isos/right (denom 0; right ⇒ sin 2A=sin 2B). + // X(168)=X(9)-of-excentral (mittenpunkt): trilinear b/(1−sin(B/2))+c/(1−sin(C/2))−a/(1−sin(A/2)). + // X(169)=X(85)-Ceva conjugate of X(1): bary a·(a³−a²(b+c)+a(b²+c²)−(b−c)²(b+c)). + // X(171)={X(2),X(31)}-harmonic of X(238): bary a³+abc; on OI. + // X(172)=trilinear product X(6)·X(171): bary a⁴+bc a². + // X(173)=congruent isoscelizers: bary a(cos(B/2)+cos(C/2)−cos(A/2)). + { + let a2 = a * a; + let b2 = b * b; + let c2 = c * c; + let s2a = (2.0 * g[0]).sin(); + let s2b = (2.0 * g[1]).sin(); + let s2c = (2.0 * g[2]).sin(); + // X(160) + { + let fa = a * ((b2 + c2) * s2a + (c2 - a2) * s2b + (b2 - a2) * s2c); + let fb = b * ((c2 + a2) * s2b + (a2 - b2) * s2c + (c2 - b2) * s2a); + let fc = c * ((a2 + b2) * s2c + (b2 - c2) * s2a + (a2 - c2) * s2b); + let wa = a * fa; + let wb = b * fb; + let wc = c * fc; + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push(fact( + "切线格林伯格", + "X_{160}", + pt(xy[0], xy[1]), + None, + "X(160) = X(37)\\text{-of-tangential (acute)};\\ f=a[(b^2+c^2)\\sin 2A+(c^2-a^2)\\sin 2B+(b^2-a^2)\\sin 2C]", + "X(160):切线三角形的格林伯格点(锐角时)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X160".into(), + })); + } + } + } + // X(161): skip right (Σweights → 0 when one angle is 90°). + let rightish = g[0].cos().abs() < 1e-9 || g[1].cos().abs() < 1e-9 || g[2].cos().abs() < 1e-9; + if !rightish { + let ss2a = s2a * s2a; + let ss2b = s2b * s2b; + let ss2c = s2c * s2c; + let s2 = a2 + b2 + c2; + let fa = a * (s2 * ss2a + (c2 - b2 - a2) * ss2b + (b2 - c2 - a2) * ss2c); + let fb = b * (s2 * ss2b + (a2 - c2 - b2) * ss2c + (c2 - a2 - b2) * ss2a); + let fc = c * (s2 * ss2c + (b2 - a2 - c2) * ss2a + (a2 - b2 - c2) * ss2b); + let wa = a * fa; + let wb = b * fb; + let wc = c * fc; + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push(fact( + "切线X63", + "X_{161}", + pt(xy[0], xy[1]), + None, + "X(161) = X(63)\\text{-of-tangential (acute)};\\ f=a[(a^2+b^2+c^2)\\sin^2 2A+\\cdots]", + "X(161):切线三角形的 X(63)(锐角时)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X161".into(), + })); + } + } + } + // X(162): skip isosceles / when sin 2B ≈ sin 2C. + { + let da = s2b - s2c; + let db = s2c - s2a; + let dc = s2a - s2b; + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + let wa = a / da; + let wb = b / db; + let wc = c / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push(fact( + "X108X109截点", + "X_{162}", + pt(xy[0], xy[1]), + None, + "X(162) = \\bigl(a/(\\sin 2B-\\sin 2C):\\cdots\\bigr) = \\text{cevapoint of }X(108),X(109)", + "X(162):X(108) 与 X(109) 的截点", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X162".into(), + })); + } + } + } + } + // X(168) mittenpunkt of excentral + { + let s_ha = (g[0] / 2.0).sin(); + let s_hb = (g[1] / 2.0).sin(); + let s_hc = (g[2] / 2.0).sin(); + let d_a = 1.0 - s_ha; + let d_b = 1.0 - s_hb; + let d_c = 1.0 - s_hc; + if d_a.abs() > 1e-12 && d_b.abs() > 1e-12 && d_c.abs() > 1e-12 { + let fa = b / d_b + c / d_c - a / d_a; + let fb = c / d_c + a / d_a - b / d_b; + let fc = a / d_a + b / d_b - c / d_c; + let wa = a * fa; + let wb = b * fb; + let wc = c * fc; + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push(fact( + "旁心米滕", + "X_{168}", + pt(xy[0], xy[1]), + None, + "X(168) = X(9)\\text{-of-excentral};\\ f=b/(1-\\sin\\tfrac{B}{2})+c/(1-\\sin\\tfrac{C}{2})-a/(1-\\sin\\tfrac{A}{2})", + "X(168):旁心三角形的米滕点", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X168".into(), + })); + } + } + } + } + // X(169): X(85)-Ceva conjugate of I; polynomial trilinear × a. + { + let t169 = |aa: f64, bb: f64, cc: f64| -> f64 { + aa * aa * aa - aa * aa * (bb + cc) + aa * (bb * bb + cc * cc) - (bb - cc) * (bb - cc) * (bb + cc) + }; + let fa = t169(a, b, c); + let fb = t169(b, c, a); + let fc = t169(c, a, b); + let wa = a * fa; + let wb = b * fb; + let wc = c * fc; + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push(fact( + "X85截共轭I", + "X_{169}", + pt(xy[0], xy[1]), + None, + "X(169) = X(85)\\text{-Ceva conjugate of }X(1);\\ a^3-a^2(b+c)+a(b^2+c^2)-(b-c)^2(b+c)", + "X(169):X(85) 关于内心的截共轭", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X169".into(), + })); + } + } + } + // X(171) / X(172) / X(173) + { + let abc = a * b * c; + let wa = a * a * a + abc; + let wb = b * b * b + abc; + let wc = c * c * c + abc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "调和X238", + "X_{171}", + pt(xy[0], xy[1]), + None, + "X(171) = (a^3+abc:b^3+abc:c^3+abc) = \\{X(2),X(31)\\}\\text{-harmonic of }X(238)", + "X(171):{X(2),X(31)} 关于 X(238) 的调和共轭(在 OI 上)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X171".into(), + })); + // Cross-check collinear with O,I (lines 1,3). + let i_xy = out.iter().rev().find(|f| f.group == "特殊点" && f.label == "I").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((ix, iy)) = i_xy { + let ox = circ[0]; + let oy = circ[1]; + let cross = (ix - ox) * (xy[1] - oy) - (iy - oy) * (xy[0] - ox); + let scale = ((ix - ox).hypot(iy - oy) + (xy[0] - ox).hypot(xy[1] - oy)).max(1.0); + if cross.abs() < 1e-5 * scale { + out.push(fact( + "调和X238", + "X_{171}\\in OI", + "\\checkmark".into(), + None, + "X(171)\\in OI", + "X(171) 在 OI 线上", + )); + } + } + } + // X(172) + { + let wa = a2 * a2 + b * c * a2; + let wb = b2 * b2 + c * a * b2; + let wc = c2 * c2 + a * b * c2; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "对称中线X171积", + "X_{172}", + pt(xy[0], xy[1]), + None, + "X(172) = (a^4+bca^2:\\cdots) = X(6)\\cdot X(171)\\text{ (trilinear)}", + "X(172):对称中线点与 X(171) 的三线积", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X172".into(), + })); + } + } + // X(173) + { + let ha = g[0] / 2.0; + let hb = g[1] / 2.0; + let hc = g[2] / 2.0; + let fa = hb.cos() + hc.cos() - ha.cos(); + let fb = hc.cos() + ha.cos() - hb.cos(); + let fc = ha.cos() + hb.cos() - hc.cos(); + let wa = a * fa; + let wb = b * fb; + let wc = c * fc; + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push(fact( + "等腰等化器", + "X_{173}", + pt(xy[0], xy[1]), + None, + "X(173) = \\bigl(a(\\cos\\tfrac{B}{2}+\\cos\\tfrac{C}{2}-\\cos\\tfrac{A}{2}):\\cdots\\bigr)", + "X(173):全等等腰等化器点(Yff)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X173".into(), + })); + } + } + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -12652,6 +12945,91 @@ mod tests { ); } + #[test] + fn x160_to_x173_tangential_gaps_classical() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8: all centers finite. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x160 = fs.iter().find(|f| f.group == "切线格林伯格" && f.label == "X_{160}").expect("X160"); + let x161 = fs.iter().find(|f| f.group == "切线X63" && f.label == "X_{161}").expect("X161"); + let x162 = fs.iter().find(|f| f.group == "X108X109截点" && f.label == "X_{162}").expect("X162"); + let x168 = fs.iter().find(|f| f.group == "旁心米滕" && f.label == "X_{168}").expect("X168"); + let x169 = fs.iter().find(|f| f.group == "X85截共轭I" && f.label == "X_{169}").expect("X169"); + let x171 = fs.iter().find(|f| f.group == "调和X238" && f.label == "X_{171}").expect("X171"); + let x172 = fs.iter().find(|f| f.group == "对称中线X171积" && f.label == "X_{172}").expect("X172"); + let x173 = fs.iter().find(|f| f.group == "等腰等化器" && f.label == "X_{173}").expect("X173"); + assert!(fs.iter().any(|f| f.group == "调和X238" && f.label.contains("OI"))); + let i = fs.iter().find(|f| f.group == "特殊点" && f.label == "I").expect("I"); + let o = fs.iter().find(|f| f.group == "特殊点" && f.label == "O").expect("O"); + let (ix, iy) = ptxy(i); + let (ox, oy) = ptxy(o); + let (p171x, p171y) = ptxy(x171); + let cross = (ix - ox) * (p171y - oy) - (iy - oy) * (p171x - ox); + assert!(cross.abs() < 1e-5, "X171 not on OI: cross={}", cross); + // Numeric spot-check vs ETC side formula for X162 / X171. + let (p162x, p162y) = ptxy(x162); + assert!((p162x - 3.4398888116747757).abs() < 1e-6 && (p162y - 5.032994341492612).abs() < 1e-6, "X162 xy {:?}", (p162x, p162y)); + let (p171nx, p171ny) = ptxy(x171); + assert!((p171nx - 4.575757575757576).abs() < 1e-6 && (p171ny - 2.073415326757506).abs() < 1e-6, "X171 xy {:?}", (p171nx, p171ny)); + let _ = (x160, x161, x168, x169, x172, x173); + + // Isosceles 5-5-6: X162 skips; others remain. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().all(|f| f.group != "X108X109截点"), "X162 skip isosceles"); + assert!(fs2.iter().any(|f| f.group == "切线格林伯格" && f.label == "X_{160}")); + assert!(fs2.iter().any(|f| f.group == "切线X63" && f.label == "X_{161}")); + assert!(fs2.iter().any(|f| f.group == "旁心米滕" && f.label == "X_{168}")); + assert!(fs2.iter().any(|f| f.group == "X85截共轭I" && f.label == "X_{169}")); + assert!(fs2.iter().any(|f| f.group == "调和X238" && f.label == "X_{171}")); + assert!(fs2.iter().any(|f| f.group == "对称中线X171积" && f.label == "X_{172}")); + assert!(fs2.iter().any(|f| f.group == "等腰等化器" && f.label == "X_{173}")); + + // Equilateral: X162 skips; X160/161/168/169/171/172/173 = G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.group != "X108X109截点"), "X162 skip equilateral"); + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (gx, gy) = ptxy(g3); + for (grp, lab) in [ + ("切线格林伯格", "X_{160}"), + ("切线X63", "X_{161}"), + ("旁心米滕", "X_{168}"), + ("X85截共轭I", "X_{169}"), + ("调和X238", "X_{171}"), + ("对称中线X171积", "X_{172}"), + ("等腰等化器", "X_{173}"), + ] { + let f = fs3.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!((x - gx).abs() < 1e-5 && (y - gy).abs() < 1e-5, "equilateral {} != G", lab); + } + + // Right 3-4-5: X161/X162 skip; X160/168/169/171–173 finite. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().any(|f| f.group == "切线格林伯格" && f.label == "X_{160}")); + assert!(fs4.iter().all(|f| f.group != "切线X63"), "X161 skip right"); + assert!(fs4.iter().all(|f| f.group != "X108X109截点"), "X162 skip right"); + assert!(fs4.iter().any(|f| f.group == "旁心米滕" && f.label == "X_{168}")); + assert!(fs4.iter().any(|f| f.group == "X85截共轭I" && f.label == "X_{169}")); + assert!(fs4.iter().any(|f| f.group == "调和X238" && f.label == "X_{171}")); + assert!(fs4.iter().any(|f| f.group == "对称中线X171积" && f.label == "X_{172}")); + assert!(fs4.iter().any(|f| f.group == "等腰等化器" && f.label == "X_{173}")); + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 079ac07293798b7d125c3d3dbb1d462ebd5bd441 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 17:16:55 +0800 Subject: [PATCH 061/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X160=E2=80=93X173=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 763336 -> 768780 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index bc578cbd5a61043d0f809322a29c041034b91027..94af0030be7816bb365669155f1174814a7c1b3a 100644 GIT binary patch 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z1Y7C*H8rXhxTh^L;$p(?u}4^XKAmbTY8aNtl%uIeRb1FvyZcvI8?C?is&QDnsA?QG z8(#>Eq{OgNKQw>1-A@Gz}G2jDkb@Ew|oC{I|tvM$4D<_XI#4Qmr)n}TOr8!>uG zSi7>U7~3g4Kj68EC#qG9Efr5&JU#IA!!sJsOg!aymf-Q@c?HiwJRjlt22Xf)jIBGK z5qR#yQ-)_Tp4E6N@w|rT2%dl7Ig964Jb&P6)wp$xtr?z Date: Mon, 2 Nov 2026 18:16:04 +0800 Subject: [PATCH 062/123] =?UTF-8?q?feat:=20ETC=20X166/X167/X170=20gaps=20a?= =?UTF-8?q?nd=20X177=E2=80=93X180=20mid-arc/Malfatti?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Fill excentral Gergonne X(166), Nagel X(167), and X(9)-aleph X(170) (=X(76)-of-excentral, on IG) from official ETC half-angle trilinears, with X165–X168 / X164–X165 / IG collinearity guards. Then classical X(177)/X(178) mid-arc, X(179)/X(180) Ajima-Malfatti (sec⁴ A/4 and t_a=1+2(sec A/4 cos B/4 cos C/4)²). Acute/right/equilateral/isosceles coverage; prefer centers not already in geometry.rs. --- crates/mathcore/src/geometry.rs | 409 ++++++++++++++++++++++++++++++++ 1 file changed, 409 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index f438fc8..e97d3ea 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -8059,6 +8059,320 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(166)/X(167)/X(170): fill excentral gaps; then X(177)–X(180) mid-arc / Ajima-Malfatti. + // X(166)=X(7)-of-excentral (Gergonne): trilinear + // f = tan(A/2)/d_a − tan(B/2)/d_b − tan(C/2)/d_c, + // d_a = cos(B/2)+cos(C/2)−cos(A/2); bary a·f. On line X(165)X(168). + // X(167)=X(8)-of-excentral (Nagel): f = s_b t_b + s_c t_c − s_a t_a with + // s_a=sin(A/2), t_a=d_a sec(A/2); on line X(164)X(165). + // X(170)=X(9)-aleph conjugate of X(9)=X(76)-of-excentral: trilinear + // f = −tan(A/2)sec²(A/2)+tan(B/2)sec²(B/2)+tan(C/2)sec²(C/2); on IG. + // X(177)=1st mid-arc: bary a(cos(B/2)+cos(C/2))sec(A/2); =X(1)-of-intouch. + // X(178)=2nd mid-arc: bary cos(B/2)+cos(C/2). + // X(179)=1st Ajima-Malfatti: bary a sec⁴(A/4). + // X(180)=2nd Ajima-Malfatti: f=1/t_b+1/t_c−1/t_a, + // t_a=1+2(sec(A/4)cos(B/4)cos(C/4))². + { + let ha = g[0] / 2.0; + let hb = g[1] / 2.0; + let hc = g[2] / 2.0; + let (s_ha, s_hb, s_hc) = (ha.sin(), hb.sin(), hc.sin()); + let (c_ha, c_hb, c_hc) = (ha.cos(), hb.cos(), hc.cos()); + let (t_ha, t_hb, t_hc) = (ha.tan(), hb.tan(), hc.tan()); + let d_a = c_hb + c_hc - c_ha; + let d_b = c_hc + c_ha - c_hb; + let d_c = c_ha + c_hb - c_hc; + // X(166) + if d_a.abs() > 1e-12 && d_b.abs() > 1e-12 && d_c.abs() > 1e-12 { + let fa = t_ha / d_a - t_hb / d_b - t_hc / d_c; + let fb = t_hb / d_b - t_hc / d_c - t_ha / d_a; + let fc = t_hc / d_c - t_ha / d_a - t_hb / d_b; + let wa = a * fa; + let wb = b * fb; + let wc = c * fc; + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push(fact( + "旁心格尔巩", + "X_{166}", + pt(xy[0], xy[1]), + None, + "X(166) = X(7)\\text{-of-excentral};\\ f=\\tan\\tfrac{A}{2}/d_A-\\tan\\tfrac{B}{2}/d_B-\\tan\\tfrac{C}{2}/d_C", + "X(166):旁心三角形的格尔巩点", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X166".into(), + })); + // Cross-check collinear with X165, X168 when both present. + let x165 = out.iter().rev().find(|f| f.label == "X_{165}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let x168 = out.iter().rev().find(|f| f.label == "X_{168}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let (Some((x1, y1)), Some((x8, y8))) = (x165, x168) { + let cross = (x8 - x1) * (xy[1] - y1) - (y8 - y1) * (xy[0] - x1); + let scale = (x8 - x1).abs() + (y8 - y1).abs() + (xy[0] - x1).abs() + (xy[1] - y1).abs() + 1e-12; + if cross.abs() / scale < 1e-5 { + out.push(fact( + "旁心格尔巩", + "X_{166}\\in X_{165}X_{168}", + "\\text{共线}".into(), + None, + "X(166)\\in X(165)X(168)", + "X(166) 在旁心重心与旁心米滕的连线上", + )); + } + } + } + } + } + // X(167) + if c_ha.abs() > 1e-12 && c_hb.abs() > 1e-12 && c_hc.abs() > 1e-12 + && d_a.abs() > 1e-12 && d_b.abs() > 1e-12 && d_c.abs() > 1e-12 + { + let ta = d_a / c_ha; + let tb = d_b / c_hb; + let tc = d_c / c_hc; + let fa = s_hb * tb + s_hc * tc - s_ha * ta; + let fb = s_hc * tc + s_ha * ta - s_hb * tb; + let fc = s_ha * ta + s_hb * tb - s_hc * tc; + let wa = a * fa; + let wb = b * fb; + let wc = c * fc; + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push(fact( + "旁心奈格尔", + "X_{167}", + pt(xy[0], xy[1]), + None, + "X(167) = X(8)\\text{-of-excentral};\\ f=s_B t_B+s_C t_C-s_A t_A", + "X(167):旁心三角形的奈格尔点", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X167".into(), + })); + let x164 = out.iter().rev().find(|f| f.label == "X_{164}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let x165 = out.iter().rev().find(|f| f.label == "X_{165}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let (Some((x4, y4)), Some((x5, y5))) = (x164, x165) { + let cross = (x5 - x4) * (xy[1] - y4) - (y5 - y4) * (xy[0] - x4); + let scale = (x5 - x4).abs() + (y5 - y4).abs() + (xy[0] - x4).abs() + (xy[1] - y4).abs() + 1e-12; + if cross.abs() / scale < 1e-5 { + out.push(fact( + "旁心奈格尔", + "X_{167}\\in X_{164}X_{165}", + "\\text{共线}".into(), + None, + "X(167)\\in X(164)X(165)", + "X(167) 在旁心内心与旁心重心的连线上", + )); + } + } + } + } + } + // X(170) + if c_ha.abs() > 1e-12 && c_hb.abs() > 1e-12 && c_hc.abs() > 1e-12 { + let ua = t_ha / (c_ha * c_ha); + let ub = t_hb / (c_hb * c_hb); + let uc = t_hc / (c_hc * c_hc); + let fa = -ua + ub + uc; + let fb = -ub + uc + ua; + let fc = -uc + ua + ub; + let wa = a * fa; + let wb = b * fb; + let wc = c * fc; + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push(fact( + "米滕阿列夫自共轭", + "X_{170}", + pt(xy[0], xy[1]), + None, + "X(170) = X(9)\\text{-aleph of }X(9)=X(76)\\text{-of-excentral};\\ f=-\\tan\\tfrac{A}{2}\\sec^2\\tfrac{A}{2}+\\cdots", + "X(170):米滕点的 X(9)-阿列夫共轭(在 IG 上)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X170".into(), + })); + let i_xy = out.iter().rev().find(|f| f.group == "特殊点" && f.label == "I").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let ge_xy = out.iter().rev().find(|f| f.label == "X_{7}" || f.label == "Ge").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let (Some((ix, iy)), Some((gx, gy))) = (i_xy, ge_xy) { + let cross = (gx - ix) * (xy[1] - iy) - (gy - iy) * (xy[0] - ix); + let scale = (gx - ix).abs() + (gy - iy).abs() + (xy[0] - ix).abs() + (xy[1] - iy).abs() + 1e-12; + if cross.abs() / scale < 1e-5 { + out.push(fact( + "米滕阿列夫自共轭", + "X_{170}\\in IG", + "\\text{共线}".into(), + None, + "X(170)\\in IG", + "X(170) 在内心与格尔巩点的连线上", + )); + } + } + } + } + } + // X(177) / X(178) + if c_ha.abs() > 1e-12 && c_hb.abs() > 1e-12 && c_hc.abs() > 1e-12 { + let fa = (c_hb + c_hc) / c_ha; + let fb = (c_hc + c_ha) / c_hb; + let fc = (c_ha + c_hb) / c_hc; + let wa = a * fa; + let wb = b * fb; + let wc = c * fc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "第一中弧点", + "X_{177}", + pt(xy[0], xy[1]), + None, + "X(177) = \\bigl(a(\\cos\\tfrac{B}{2}+\\cos\\tfrac{C}{2})\\sec\\tfrac{A}{2}:\\cdots\\bigr) = X(1)\\text{-of-intouch}", + "X(177):第一中弧点(接触三角形的内心)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X177".into(), + })); + } + // X(178): bary cos(B/2)+cos(C/2) (no side factor) + let wa = c_hb + c_hc; + let wb = c_hc + c_ha; + let wc = c_ha + c_hb; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "第二中弧点", + "X_{178}", + pt(xy[0], xy[1]), + None, + "X(178) = \\bigl(\\cos\\tfrac{B}{2}+\\cos\\tfrac{C}{2}:\\cdots\\bigr)", + "X(178):第二中弧点", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X178".into(), + })); + } + } + // X(179) + { + let c_qa = (g[0] / 4.0).cos(); + let c_qb = (g[1] / 4.0).cos(); + let c_qc = (g[2] / 4.0).cos(); + if c_qa.abs() > 1e-12 && c_qb.abs() > 1e-12 && c_qc.abs() > 1e-12 { + let wa = a / (c_qa * c_qa * c_qa * c_qa); + let wb = b / (c_qb * c_qb * c_qb * c_qb); + let wc = c / (c_qc * c_qc * c_qc * c_qc); + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push(fact( + "第一阿吉马-马尔法蒂", + "X_{179}", + pt(xy[0], xy[1]), + None, + "X(179) = \\bigl(a\\sec^4\\tfrac{A}{4}:\\cdots\\bigr)", + "X(179):第一阿吉马-马尔法蒂点", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X179".into(), + })); + } + } + } + } + // X(180) + { + let qa = g[0] / 4.0; + let qb = g[1] / 4.0; + let qc = g[2] / 4.0; + let (c_qa, c_qb, c_qc) = (qa.cos(), qb.cos(), qc.cos()); + if c_qa.abs() > 1e-12 && c_qb.abs() > 1e-12 && c_qc.abs() > 1e-12 { + let t_a = 1.0 + 2.0 * (c_qb * c_qc / c_qa).powi(2); + let t_b = 1.0 + 2.0 * (c_qc * c_qa / c_qb).powi(2); + let t_c = 1.0 + 2.0 * (c_qa * c_qb / c_qc).powi(2); + if t_a.abs() > 1e-12 && t_b.abs() > 1e-12 && t_c.abs() > 1e-12 { + let fa = 1.0 / t_b + 1.0 / t_c - 1.0 / t_a; + let fb = 1.0 / t_c + 1.0 / t_a - 1.0 / t_b; + let fc = 1.0 / t_a + 1.0 / t_b - 1.0 / t_c; + let wa = a * fa; + let wb = b * fb; + let wc = c * fc; + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push(fact( + "第二阿吉马-马尔法蒂", + "X_{180}", + pt(xy[0], xy[1]), + None, + "X(180) = 2\\text{nd Ajima-Malfatti};\\ f=1/t_B+1/t_C-1/t_A", + "X(180):第二阿吉马-马尔法蒂点", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X180".into(), + })); + } + } + } + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -13030,6 +13344,101 @@ mod tests { assert!(fs4.iter().any(|f| f.group == "等腰等化器" && f.label == "X_{173}")); } + #[test] + fn x166_x167_x170_gaps_and_x177_to_x180() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x166 = fs.iter().find(|f| f.group == "旁心格尔巩" && f.label == "X_{166}").expect("X166"); + let x167 = fs.iter().find(|f| f.group == "旁心奈格尔" && f.label == "X_{167}").expect("X167"); + let x170 = fs.iter().find(|f| f.group == "米滕阿列夫自共轭" && f.label == "X_{170}").expect("X170"); + let x177 = fs.iter().find(|f| f.group == "第一中弧点" && f.label == "X_{177}").expect("X177"); + let x178 = fs.iter().find(|f| f.group == "第二中弧点" && f.label == "X_{178}").expect("X178"); + let x179 = fs.iter().find(|f| f.group == "第一阿吉马-马尔法蒂" && f.label == "X_{179}").expect("X179"); + let x180 = fs.iter().find(|f| f.group == "第二阿吉马-马尔法蒂" && f.label == "X_{180}").expect("X180"); + assert!(fs.iter().any(|f| f.group == "旁心格尔巩" && f.label.contains("165"))); + assert!(fs.iter().any(|f| f.group == "旁心奈格尔" && f.label.contains("164"))); + assert!(fs.iter().any(|f| f.group == "米滕阿列夫自共轭" && f.label.contains("IG"))); + let (p166x, p166y) = ptxy(x166); + assert!((p166x - 4.116074059198164).abs() < 1e-6 && (p166y - 1.3875764592887037).abs() < 1e-6, "X166 {:?}", (p166x, p166y)); + let (p167x, p167y) = ptxy(x167); + assert!((p167x - 3.586801781111747).abs() < 1e-6 && (p167y - 0.024620487649944494).abs() < 1e-6, "X167 {:?}", (p167x, p167y)); + let (p170x, p170y) = ptxy(x170); + assert!((p170x - 3.612326337570204).abs() < 1e-6 && (p170y + 0.017134392772165687).abs() < 1e-6, "X170 {:?}", (p170x, p170y)); + let (p177x, p177y) = ptxy(x177); + assert!((p177x - 4.607015416275967).abs() < 1e-6 && (p177y - 2.1605390776490716).abs() < 1e-6, "X177 {:?}", (p177x, p177y)); + let (p178x, p178y) = ptxy(x178); + assert!((p178x - 4.315677276217948).abs() < 1e-6 && (p178y - 1.7640727698612098).abs() < 1e-6, "X178 {:?}", (p178x, p178y)); + let (p179x, p179y) = ptxy(x179); + assert!((p179x - 4.567591551964102).abs() < 1e-6 && (p179y - 2.0737600520097113).abs() < 1e-6, "X179 {:?}", (p179x, p179y)); + let (p180x, p180y) = ptxy(x180); + assert!((p180x - 4.591012676125583).abs() < 1e-6 && (p180y - 2.1107123730916184).abs() < 1e-6, "X180 {:?}", (p180x, p180y)); + // IG collinearity for X170. + let i = fs.iter().find(|f| f.group == "特殊点" && f.label == "I").expect("I"); + let ge = fs.iter().find(|f| f.label == "X_{7}" || f.label == "Ge").expect("Ge"); + let (ix, iy) = ptxy(i); + let (gx, gy) = ptxy(ge); + let cross = (gx - ix) * (p170y - iy) - (gy - iy) * (p170x - ix); + assert!(cross.abs() < 1e-5, "X170 not on IG: cross={}", cross); + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab) in [ + ("旁心格尔巩", "X_{166}"), + ("旁心奈格尔", "X_{167}"), + ("米滕阿列夫自共轭", "X_{170}"), + ("第一中弧点", "X_{177}"), + ("第二中弧点", "X_{178}"), + ("第一阿吉马-马尔法蒂", "X_{179}"), + ("第二阿吉马-马尔法蒂", "X_{180}"), + ] { + assert!(fs2.iter().any(|f| f.group == grp && f.label == lab), "isos missing {} {}", grp, lab); + } + + // Equilateral: all coincide with G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (gx, gy) = ptxy(g3); + for (grp, lab) in [ + ("旁心格尔巩", "X_{166}"), + ("旁心奈格尔", "X_{167}"), + ("米滕阿列夫自共轭", "X_{170}"), + ("第一中弧点", "X_{177}"), + ("第二中弧点", "X_{178}"), + ("第一阿吉马-马尔法蒂", "X_{179}"), + ("第二阿吉马-马尔法蒂", "X_{180}"), + ] { + let f = fs3.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!((x - gx).abs() < 1e-5 && (y - gy).abs() < 1e-5, "equilateral {} != G", lab); + } + + // Right 3-4-5: all finite (half-angle formulas stay defined). + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().any(|f| f.group == "旁心格尔巩" && f.label == "X_{166}")); + assert!(fs4.iter().any(|f| f.group == "旁心奈格尔" && f.label == "X_{167}")); + assert!(fs4.iter().any(|f| f.group == "米滕阿列夫自共轭" && f.label == "X_{170}")); + assert!(fs4.iter().any(|f| f.group == "第一中弧点" && f.label == "X_{177}")); + assert!(fs4.iter().any(|f| f.group == "第二中弧点" && f.label == "X_{178}")); + assert!(fs4.iter().any(|f| f.group == "第一阿吉马-马尔法蒂" && f.label == "X_{179}")); + assert!(fs4.iter().any(|f| f.group == "第二阿吉马-马尔法蒂" && f.label == "X_{180}")); + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From f994d3b4194d68781531f55d8a3a0994388aa841 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 18:16:04 +0800 Subject: [PATCH 063/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X166=E2=80=93X170=20/=20X177=E2=80=93X180=20ETC=20centers?= 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zh3g=$d|c;o{fx`@7&5_C7gtMMU2u)TwGr2TT&HmTh^q+KEnK2akgX=JhjF#W)d^Q` zTm#w!J#3qf$lJIG*LGZ=;rbHSC0xb0{=(&a9KQpnhKoLJY4jj$x!!0?>jtTv90hHI zsM27JdA*TJ+LCjy+DN$DQOm*V(tr=z1?hMH7sB8wQqW)(KZMv;RfErg&i1t)7uy~9 z9}HF_d(~)UVCeZx>&BpF2#=3ZJG5-l zHAr_@Gr{E7wh$~L$4n)n0T2FQ}5|&WXP14jCuD>gqRO(ZzJSN(Mz;> zI!+Jv0khjajF8K94I$6pHxWV=^HrRIV;7Up{c@1LM; z*zyOxtSz0PUX;Unz8a*TmOcj}7u>{s5wE6KycV|W&4-K{fk5A}r$B<&BHN(fuA7$j zb-Y@!p~#y@7q_D0O6F1hZE94bHuG_k0>76$fA_(B?Z7rQ*(uH^zujk-N_}?urT>3%0ae@p From 1ff01878bca0cc240706ba9df783f6a18f2497d3 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 16:55:34 +0800 Subject: [PATCH 050/123] =?UTF-8?q?feat:=20NPC=20complements=20X122/X123/X?= =?UTF-8?q?124/X126/X127=20(medial=20of=20=CE=A8/Parry)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit X(122)=complement(X107), X(123)=complement(X108), X(124)=complement(X109)=mid(H,X102), X(126)=complement(Parry X111), X(127)=complement(X112); on nine-point circle via G-homothety −1/2. --- crates/mathcore/src/geometry.rs | 252 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 700928 -> 707064 bytes 2 files changed, 252 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index f5afc63..67c26d9 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -6349,6 +6349,169 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(122)/X(123)/X(124)/X(126)/X(127): complements of circumcircle Ψ/Parry points + // (= X(n)-of-medial). Homothety at G with factor −1/2 maps (O) → NPC. + // Q = (3G − P)/2. Skip when the parent point was skipped (isos/equil/right). + { + let n9 = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; + let r9 = rr / 2.0; + let p107 = out.iter().rev().find(|f| f.group == "Ψ对称中线垂心" && f.label == "X_{107}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let p108 = out.iter().rev().find(|f| f.group == "Ψ外心垂心" && f.label == "X_{108}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let p109 = out.iter().rev().find(|f| f.group == "Ψ内心外心" && f.label == "X_{109}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let p102 = out.iter().rev().find(|f| f.group == "Λ内心垂心" && f.label == "X_{102}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let p111 = out.iter().rev().find(|f| f.group == "帕里点" && f.label == "Py").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let p112 = out.iter().rev().find(|f| f.group == "Ψ垂心对称中线" && f.label == "X_{112}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + + if let Some((px, py)) = p107 { + let xy = [(3.0 * centroid[0] - px) / 2.0, (3.0 * centroid[1] - py) / 2.0]; + out.push(fact( + "中点X107", + "X_{122}", + pt(xy[0], xy[1]), + None, + "X(122) = \\mathrm{complement}(X(107)) = X(107)\\text{-of-medial}", + "X(122):X(107) 关于重心的补点(中点三角形的 X(107);九点圆上)", + ).with(Shape::Point { x: xy[0], y: xy[1], label: "X122".into() })); + if (dist2(xy, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "中点X107", + "X_{122}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(122)) = R/2", + "X(122) 在九点圆上", + )); + } + let cross = (px - centroid[0]) * (xy[1] - centroid[1]) - (py - centroid[1]) * (xy[0] - centroid[0]); + if cross.abs() < 1e-6 { + out.push(fact( + "中点X107", + "G,X_{107},X_{122}", + "\\text{共线}".into(), + None, + "G, X(107), X(122) \\text{ collinear}", + "重心、X(107)、X(122) 共线", + )); + } + } + if let Some((px, py)) = p108 { + let xy = [(3.0 * centroid[0] - px) / 2.0, (3.0 * centroid[1] - py) / 2.0]; + out.push(fact( + "中点X108", + "X_{123}", + pt(xy[0], xy[1]), + None, + "X(123) = \\mathrm{complement}(X(108)) = X(108)\\text{-of-medial}", + "X(123):X(108) 关于重心的补点(中点三角形的 X(108);九点圆上)", + ).with(Shape::Point { x: xy[0], y: xy[1], label: "X123".into() })); + if (dist2(xy, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "中点X108", + "X_{123}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(123)) = R/2", + "X(123) 在九点圆上", + )); + } + } + if let Some((px, py)) = p109 { + let xy = [(3.0 * centroid[0] - px) / 2.0, (3.0 * centroid[1] - py) / 2.0]; + out.push(fact( + "中点X109", + "X_{124}", + pt(xy[0], xy[1]), + None, + "X(124) = \\mathrm{complement}(X(109)) = \\mathrm{mid}(H,X(102))", + "X(124):X(109) 的补点 = mid(H,X(102))(九点圆上)", + ).with(Shape::Point { x: xy[0], y: xy[1], label: "X124".into() })); + if (dist2(xy, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "中点X109", + "X_{124}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(124)) = R/2", + "X(124) 在九点圆上", + )); + } + if let Some((qx, qy)) = p102 { + let mx = (orth[0] + qx) / 2.0; + let my = (orth[1] + qy) / 2.0; + if (mx - xy[0]).abs() < 1e-5 && (my - xy[1]).abs() < 1e-5 { + out.push(fact( + "中点X109", + "X_{124}=\\mathrm{mid}(H,X_{102})", + "\\checkmark".into(), + None, + "X(124) = \\text{midpoint}(H, X(102))", + "X(124) 为垂心与 X(102) 的中点", + )); + } + } + } + if let Some((px, py)) = p111 { + let xy = [(3.0 * centroid[0] - px) / 2.0, (3.0 * centroid[1] - py) / 2.0]; + out.push(fact( + "中点X111", + "X_{126}", + pt(xy[0], xy[1]), + None, + "X(126) = \\mathrm{complement}(X(111)) = X(111)\\text{-of-medial}", + "X(126):帕里点关于重心的补点(中点三角形的 X(111);九点圆上)", + ).with(Shape::Point { x: xy[0], y: xy[1], label: "X126".into() })); + if (dist2(xy, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "中点X111", + "X_{126}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(126)) = R/2", + "X(126) 在九点圆上", + )); + } + } + if let Some((px, py)) = p112 { + let xy = [(3.0 * centroid[0] - px) / 2.0, (3.0 * centroid[1] - py) / 2.0]; + out.push(fact( + "中点X112", + "X_{127}", + pt(xy[0], xy[1]), + None, + "X(127) = \\mathrm{complement}(X(112)) = X(112)\\text{-of-medial}", + "X(127):X(112) 关于重心的补点(中点三角形的 X(112);九点圆上)", + ).with(Shape::Point { x: xy[0], y: xy[1], label: "X127".into() })); + if (dist2(xy, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "中点X112", + "X_{127}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(127)) = R/2", + "X(127) 在九点圆上", + )); + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -10781,6 +10944,95 @@ mod tests { assert!(fs4.iter().any(|f| f.group == "中点X106" && f.label == "X_{121}")); } + #[test] + fn x122_x123_x124_x126_x127() { + // Scalene acute 6-7-9: complements of Ψ/Parry on NPC. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(9.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let h = fs.iter().find(|f| f.group == "特殊点" && f.label == "H").expect("H"); + let x107 = fs.iter().find(|f| f.group == "Ψ对称中线垂心" && f.label == "X_{107}").expect("X107"); + let x108 = fs.iter().find(|f| f.group == "Ψ外心垂心" && f.label == "X_{108}").expect("X108"); + let x109 = fs.iter().find(|f| f.group == "Ψ内心外心" && f.label == "X_{109}").expect("X109"); + let x102 = fs.iter().find(|f| f.group == "Λ内心垂心" && f.label == "X_{102}").expect("X102"); + let py = fs.iter().find(|f| f.group == "帕里点" && f.label == "Py").expect("Py"); + let x112 = fs.iter().find(|f| f.group == "Ψ垂心对称中线" && f.label == "X_{112}").expect("X112"); + let x122 = fs.iter().find(|f| f.group == "中点X107" && f.label == "X_{122}").expect("X122"); + let x123 = fs.iter().find(|f| f.group == "中点X108" && f.label == "X_{123}").expect("X123"); + let x124 = fs.iter().find(|f| f.group == "中点X109" && f.label == "X_{124}").expect("X124"); + let x126 = fs.iter().find(|f| f.group == "中点X111" && f.label == "X_{126}").expect("X126"); + let x127 = fs.iter().find(|f| f.group == "中点X112" && f.label == "X_{127}").expect("X127"); + let (gx, gy) = ptxy(g); + let (hx, hy) = ptxy(h); + let check_comp = |parent: &Fact, child: &Fact, tag: &str| { + let (px, py) = ptxy(parent); + let (cx, cy) = ptxy(child); + let qx = (3.0 * gx - px) / 2.0; + let qy = (3.0 * gy - py) / 2.0; + assert!((cx - qx).abs() < 1e-5 && (cy - qy).abs() < 1e-5, "{} not complement", tag); + }; + check_comp(x107, x122, "X122"); + check_comp(x108, x123, "X123"); + check_comp(x109, x124, "X124"); + check_comp(py, x126, "X126"); + check_comp(x112, x127, "X127"); + // X124 = mid(H, X102) + let (p102x, p102y) = ptxy(x102); + let (p124x, p124y) = ptxy(x124); + assert!(((hx + p102x) / 2.0 - p124x).abs() < 1e-5 && ((hy + p102y) / 2.0 - p124y).abs() < 1e-5, "X124 != mid(H,X102)"); + assert!(fs.iter().any(|f| f.group == "中点X107" && f.label.contains("NPC"))); + assert!(fs.iter().any(|f| f.group == "中点X108" && f.label.contains("NPC"))); + assert!(fs.iter().any(|f| f.group == "中点X109" && f.label.contains("NPC"))); + assert!(fs.iter().any(|f| f.group == "中点X111" && f.label.contains("NPC"))); + assert!(fs.iter().any(|f| f.group == "中点X112" && f.label.contains("NPC"))); + assert!(fs.iter().any(|f| f.group == "中点X109" && f.label.contains("mid"))); + + // Isosceles 5-5-6: parents Ψ skipped → children skipped; Parry may remain. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().all(|f| f.group != "中点X107"), "X122 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "中点X108"), "X123 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "中点X109"), "X124 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "中点X112"), "X127 skip isosceles"); + // Parry / X126: denom 2a²−b²−c² may be nonzero on 5-5-6. + let _ = fs2.iter().any(|f| f.group == "中点X111"); + + // Equilateral: all skip with parents. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.group != "中点X107"), "X122 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "中点X108"), "X123 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "中点X109"), "X124 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "中点X111"), "X126 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "中点X112"), "X127 skip equilateral"); + + // Right 3-4-5: X107 skips (b²+c²−a²=0 on hypotenuse); X108 skips (sec of right ∠). + // X109/X112/Parry and their complements remain. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + let has = |g: &str, lab: &str| fs4.iter().any(|f| f.group == g && f.label == lab); + // Parents that survive 3-4-5: X109 (cos diffs), Parry; X107/X108/X112 typically skip. + assert!(has("中点X109", "X_{124}"), "X124 on 3-4-5"); + assert!(has("中点X111", "X_{126}"), "X126 on 3-4-5"); + assert!(fs4.iter().all(|f| f.group != "中点X107"), "X122 skip right"); + assert!(fs4.iter().all(|f| f.group != "中点X108"), "X123 skip right"); + // X112 / X127: sin2B−sin2C may vanish on right — accept either skip or present. + let _ = has("中点X112", "X_{127}"); + assert!(fs4.iter().any(|f| f.group == "中点X109" && f.label.contains("mid")), "mid(H,X102)"); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index e6055e71eab5b899d32c48fb946e072870f83349..e535c50343cbcd1fbe374da1a5d0be04e936d46f 100644 GIT binary patch delta 50105 zcmb@v30zi1_c+eXz4u{<2V_wYxIBu2f@@kpE;pAlcQf~`Oe@SS%eJ>b#Y9C#A9O%b z9~Ki86$QPNWT;f6lvq@lR8(kGq*zpxsK0aO-e-|XU?2CGk5M| zQhm1;bN9lpCAa*8?>V_AIw@%fi++$=sn?gE$g7=enw*8eMEctLqF-HN4751kZ1P@2 zEArWq6U2`Veve4z1KzLFs(f=d<6)s}%^7p8F({xR|BRF3ZQM^}Ng@4dvKy2-jal~j zkhbKr@XI8ssJ*X3Xw_cMtY~q&R|sv~Yi{(L%^8jH4+==X3nLw06VCh((>#rvd1=7A zwE7Ls%)Gdr!OR|LXPy^mp>;Z}Zf*zjJ?-z~%on#03TS!*w2W!1Wxl428F4Gyub_o{ zi^g_vBeW#1XnN2MLTmHPQ##J2>3hs?cMPVMJ?1YuMna=m45_3gd(2}y_?y?s0Yx`M z1_16J^Zj9ebxGd?Vm#z_vJtFMLK7Y!a+EAZ(poBeDaoiqH_(9%{GJ5T!Z(mb(K>mR 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00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 16:58:44 +0800 Subject: [PATCH 051/123] feat: orthic NPC centers X128/X129/X130/X137 + mid(H) X132/X133 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit X(132)=mid(H,X112)=2N−X127; X(133)=mid(H,X107)=2N−X122. X(130)=Steiner-of-orthic; X(129)=Tarry-of-orthic=2N−X130. X(128)=X(74)-of-orthic; X(137)=2N−X128. Skip right/isos/equil guards. --- crates/mathcore/src/geometry.rs | 342 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 707064 -> 713652 bytes 2 files changed, 342 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 67c26d9..24ec31a 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -6512,6 +6512,264 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(132)/X(133): mid(H, X(112))/mid(H, X(107)) on the nine-point circle. + // Also NPC antipodes of medial complements: X(132)=2N−X(127), X(133)=2N−X(122). + // Skip when the circumcircle parent was skipped (isos/equil/right as applicable). + { + let n9 = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; + let r9 = rr / 2.0; + let p112 = out.iter().rev().find(|f| f.group == "Ψ垂心对称中线" && f.label == "X_{112}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let p107 = out.iter().rev().find(|f| f.group == "Ψ对称中线垂心" && f.label == "X_{107}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let p127 = out.iter().rev().find(|f| f.group == "中点X112" && f.label == "X_{127}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let p122 = out.iter().rev().find(|f| f.group == "中点X107" && f.label == "X_{122}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + + if let Some((px, py)) = p112 { + let xy = [(orth[0] + px) / 2.0, (orth[1] + py) / 2.0]; + out.push(fact( + "垂心X112中点", + "X_{132}", + pt(xy[0], xy[1]), + None, + "X(132) = \\mathrm{mid}(H,X(112)) = X(105)\\text{-of-orthic}", + "X(132):H 与 X(112) 的中点(垂足三角形的 X(105);九点圆上)", + ).with(Shape::Point { x: xy[0], y: xy[1], label: "X132".into() })); + if (dist2(xy, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "垂心X112中点", + "X_{132}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(132)) = R/2", + "X(132) 在九点圆上", + )); + } + if let Some((qx, qy)) = p127 { + let rx = 2.0 * n9[0] - qx; + let ry = 2.0 * n9[1] - qy; + if (rx - xy[0]).abs() < 1e-5 && (ry - xy[1]).abs() < 1e-5 { + out.push(fact( + "垂心X112中点", + "X_{132}=2N-X_{127}", + "\\checkmark".into(), + None, + "X(132) = 2N - X(127)", + "X(132) 与 X(127) 互为九点圆对径点", + )); + } + } + } + if let Some((px, py)) = p107 { + let xy = [(orth[0] + px) / 2.0, (orth[1] + py) / 2.0]; + out.push(fact( + "垂心X107中点", + "X_{133}", + pt(xy[0], xy[1]), + None, + "X(133) = \\mathrm{mid}(H,X(107)) = X(106)\\text{-of-orthic}", + "X(133):H 与 X(107) 的中点(垂足三角形的 X(106);九点圆上)", + ).with(Shape::Point { x: xy[0], y: xy[1], label: "X133".into() })); + if (dist2(xy, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "垂心X107中点", + "X_{133}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(133)) = R/2", + "X(133) 在九点圆上", + )); + } + if let Some((qx, qy)) = p122 { + let rx = 2.0 * n9[0] - qx; + let ry = 2.0 * n9[1] - qy; + if (rx - xy[0]).abs() < 1e-5 && (ry - xy[1]).abs() < 1e-5 { + out.push(fact( + "垂心X107中点", + "X_{133}=2N-X_{122}", + "\\checkmark".into(), + None, + "X(133) = 2N - X(122)", + "X(133) 与 X(122) 互为九点圆对径点", + )); + } + } + } + } + + // X(128)/X(129)/X(130)/X(137): centers of the orthic triangle that lie on NPC. + // X(130)=Steiner-of-orthic; X(129)=Tarry-of-orthic=2N−X(130); + // X(128)=X(74)-of-orthic; X(137)=NPC antipode of X(128)=2N−X(128). + // Skip right/near-right (orthic degenerates) and isosceles (Steiner denoms vanish; + // X74-of-orthic may still emit when denoms are safe). + { + let n9 = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; + let r9 = rr / 2.0; + let ca = g[0].cos(); + let cb = g[1].cos(); + let cc = g[2].cos(); + let rightish = ca.abs() < 1e-9 || cb.abs() < 1e-9 || cc.abs() < 1e-9; + if !rightish { + let mut feet = [[0.0f64; 2]; 3]; + let mut ok = true; + for i in 0..3 { + let p0 = v[i]; + let q1 = v[(i + 1) % 3]; + let q2 = v[(i + 2) % 3]; + let dx = q2[0] - q1[0]; + let dy = q2[1] - q1[1]; + let den = dx * dx + dy * dy; + if den < 1e-18 { + ok = false; + break; + } + let t = ((p0[0] - q1[0]) * dx + (p0[1] - q1[1]) * dy) / den; + feet[i] = [q1[0] + t * dx, q1[1] + t * dy]; + } + if ok { + // Orthic side lengths opposite Ha, Hb, Hc. + let oa = dist2(feet[1], feet[2]); + let ob = dist2(feet[2], feet[0]); + let oc = dist2(feet[0], feet[1]); + if oa > 1e-10 && ob > 1e-10 && oc > 1e-10 { + // Steiner X(99)-of-orthic = X(130): bary 1/(b'²−c'²) at Ha:Hb:Hc. + let dbc = ob * ob - oc * oc; + let dca = oc * oc - oa * oa; + let dab = oa * oa - ob * ob; + if dbc.abs() > 1e-10 && dca.abs() > 1e-10 && dab.abs() > 1e-10 { + let wa = 1.0 / dbc; + let wb = 1.0 / dca; + let wc = 1.0 / dab; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let st = [ + (wa * feet[0][0] + wb * feet[1][0] + wc * feet[2][0]) / den, + (wa * feet[0][1] + wb * feet[1][1] + wc * feet[2][1]) / den, + ]; + if (dist2(st, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "垂足施泰纳", + "X_{130}", + pt(st[0], st[1]), + None, + "X(130) = \\mathrm{Steiner}\\text{-of-orthic}", + "X(130):垂足三角形的施泰纳点(九点圆上)", + ).with(Shape::Point { + x: st[0], + y: st[1], + label: "X130".into(), + })); + out.push(fact( + "垂足施泰纳", + "X_{130}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(130)) = R/2", + "X(130) 在九点圆上", + )); + // Tarry-of-orthic = NPC antipode of Steiner-of-orthic. + let ty = [2.0 * n9[0] - st[0], 2.0 * n9[1] - st[1]]; + out.push(fact( + "垂足塔里", + "X_{129}", + pt(ty[0], ty[1]), + None, + "X(129) = 2N - X(130) = \\mathrm{Tarry}\\text{-of-orthic}", + "X(129):垂足三角形的塔里点(九点圆上)", + ).with(Shape::Point { + x: ty[0], + y: ty[1], + label: "X129".into(), + })); + out.push(fact( + "垂足塔里", + "X_{129}=2N-X_{130}", + "\\text{九点圆对径}".into(), + None, + "X(129) = 2N - X(130)", + "X(129) 与 X(130) 互为九点圆对径点", + )); + } + } + } + + // X(74)-of-orthic = X(128): bary a'/(cos A' − 2 cos B' cos C'). + let cos_a = ((ob * ob + oc * oc - oa * oa) / (2.0 * ob * oc)).clamp(-1.0, 1.0); + let cos_b = ((oc * oc + oa * oa - ob * ob) / (2.0 * oc * oa)).clamp(-1.0, 1.0); + let cos_c = ((oa * oa + ob * ob - oc * oc) / (2.0 * oa * ob)).clamp(-1.0, 1.0); + let da = cos_a - 2.0 * cos_b * cos_c; + let db = cos_b - 2.0 * cos_c * cos_a; + let dc = cos_c - 2.0 * cos_a * cos_b; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = oa / da; + let wb = ob / db; + let wc = oc / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x128 = [ + (wa * feet[0][0] + wb * feet[1][0] + wc * feet[2][0]) / den, + (wa * feet[0][1] + wb * feet[1][1] + wc * feet[2][1]) / den, + ]; + if (dist2(x128, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "垂足X74", + "X_{128}", + pt(x128[0], x128[1]), + None, + "X(128) = X(74)\\text{-of-orthic}", + "X(128):垂足三角形的 X(74)(九点圆上)", + ).with(Shape::Point { + x: x128[0], + y: x128[1], + label: "X128".into(), + })); + out.push(fact( + "垂足X74", + "X_{128}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(128)) = R/2", + "X(128) 在九点圆上", + )); + let x137 = [2.0 * n9[0] - x128[0], 2.0 * n9[1] - x128[1]]; + out.push(fact( + "垂足X74对径", + "X_{137}", + pt(x137[0], x137[1]), + None, + "X(137) = 2N - X(128) = X(110)\\text{-of-orthic}", + "X(137):X(128) 的九点圆对径点(垂足三角形的 X(110))", + ).with(Shape::Point { + x: x137[0], + y: x137[1], + label: "X137".into(), + })); + out.push(fact( + "垂足X74对径", + "X_{137}=2N-X_{128}", + "\\text{九点圆对径}".into(), + None, + "X(137) = 2N - X(128)", + "X(137) 与 X(128) 互为九点圆对径点", + )); + } + } + } + } + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -11033,6 +11291,90 @@ mod tests { assert!(fs4.iter().any(|f| f.group == "中点X109" && f.label.contains("mid")), "mid(H,X102)"); } + #[test] + fn x128_x129_x130_x132_x133_x137() { + // Scalene acute 6-7-8: orthic Steiner/Tarry/X74 and mid(H, Ψ) on NPC. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + let h = fs.iter().find(|f| f.group == "特殊点" && f.label == "H").expect("H"); + let n = fs.iter().find(|f| f.group == "欧拉线" && f.label == "N").expect("N"); + let x112 = fs.iter().find(|f| f.group == "Ψ垂心对称中线" && f.label == "X_{112}").expect("X112"); + let x107 = fs.iter().find(|f| f.group == "Ψ对称中线垂心" && f.label == "X_{107}").expect("X107"); + let x122 = fs.iter().find(|f| f.group == "中点X107" && f.label == "X_{122}").expect("X122"); + let x127 = fs.iter().find(|f| f.group == "中点X112" && f.label == "X_{127}").expect("X127"); + let x132 = fs.iter().find(|f| f.group == "垂心X112中点" && f.label == "X_{132}").expect("X132"); + let x133 = fs.iter().find(|f| f.group == "垂心X107中点" && f.label == "X_{133}").expect("X133"); + let x130 = fs.iter().find(|f| f.group == "垂足施泰纳" && f.label == "X_{130}").expect("X130"); + let x129 = fs.iter().find(|f| f.group == "垂足塔里" && f.label == "X_{129}").expect("X129"); + let x128 = fs.iter().find(|f| f.group == "垂足X74" && f.label == "X_{128}").expect("X128"); + let x137 = fs.iter().find(|f| f.group == "垂足X74对径" && f.label == "X_{137}").expect("X137"); + let (hx, hy) = ptxy(h); + let (nx, ny) = ptxy(n); + let (p112x, p112y) = ptxy(x112); + let (p107x, p107y) = ptxy(x107); + let (p132x, p132y) = ptxy(x132); + let (p133x, p133y) = ptxy(x133); + assert!(((hx + p112x) / 2.0 - p132x).abs() < 1e-5 && ((hy + p112y) / 2.0 - p132y).abs() < 1e-5, "X132 != mid(H,X112)"); + assert!(((hx + p107x) / 2.0 - p133x).abs() < 1e-5 && ((hy + p107y) / 2.0 - p133y).abs() < 1e-5, "X133 != mid(H,X107)"); + let (p127x, p127y) = ptxy(x127); + let (p122x, p122y) = ptxy(x122); + assert!((2.0 * nx - p127x - p132x).abs() < 1e-5 && (2.0 * ny - p127y - p132y).abs() < 1e-5, "X132 != 2N-X127"); + assert!((2.0 * nx - p122x - p133x).abs() < 1e-5 && (2.0 * ny - p122y - p133y).abs() < 1e-5, "X133 != 2N-X122"); + let (p130x, p130y) = ptxy(x130); + let (p129x, p129y) = ptxy(x129); + let (p128x, p128y) = ptxy(x128); + let (p137x, p137y) = ptxy(x137); + assert!((2.0 * nx - p130x - p129x).abs() < 1e-5 && (2.0 * ny - p130y - p129y).abs() < 1e-5, "X129 != 2N-X130"); + assert!((2.0 * nx - p128x - p137x).abs() < 1e-5 && (2.0 * ny - p128y - p137y).abs() < 1e-5, "X137 != 2N-X128"); + assert!(fs.iter().any(|f| f.group == "垂心X112中点" && f.label.contains("NPC"))); + assert!(fs.iter().any(|f| f.group == "垂心X107中点" && f.label.contains("NPC"))); + assert!(fs.iter().any(|f| f.group == "垂足施泰纳" && f.label.contains("NPC"))); + assert!(fs.iter().any(|f| f.group == "垂足X74" && f.label.contains("NPC"))); + assert!(fs.iter().any(|f| f.group == "垂足塔里" && f.label.contains("2N"))); + assert!(fs.iter().any(|f| f.group == "垂足X74对径" && f.label.contains("2N"))); + + // Isosceles 5-5-6: Steiner/Tarry of orthic skip; mid(H,X107) skips with X107; + // mid(H,X112) may skip with X112; X74-of-orthic may remain (orthic isos). + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().all(|f| f.group != "垂足施泰纳"), "X130 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "垂足塔里"), "X129 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "垂心X107中点"), "X133 skip isosceles"); + + // Equilateral: all skip. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.group != "垂心X112中点"), "X132 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "垂心X107中点"), "X133 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "垂足施泰纳"), "X130 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "垂足塔里"), "X129 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "垂足X74"), "X128 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "垂足X74对径"), "X137 skip equilateral"); + + // Right 3-4-5: orthic degenerates → X128/129/130/137 skip; mid parents also skip. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().all(|f| f.group != "垂足施泰纳"), "X130 skip right"); + assert!(fs4.iter().all(|f| f.group != "垂足塔里"), "X129 skip right"); + assert!(fs4.iter().all(|f| f.group != "垂足X74"), "X128 skip right"); + assert!(fs4.iter().all(|f| f.group != "垂足X74对径"), "X137 skip right"); + assert!(fs4.iter().all(|f| f.group != "垂心X107中点"), "X133 skip right"); + // X112 / X132: may skip on right. + let _ = fs4.iter().any(|f| f.group == "垂心X112中点"); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index e535c50343cbcd1fbe374da1a5d0be04e936d46f..93b7b83eef112cc0e19f6cb1131456517866e495 100644 GIT binary patch delta 50676 zcmce<3tSb&7dXz$?q1#x6%avTxrl;_?=h&jV`k1db7pq# z+T!S0a;j(XdBvyc;7JePWDo7!!F}HBvJ zyKhSPAB-35b==c=Ca>M=INUjcH|%wM+&K;_9def{p7OfmmQEp#6>8|dKf4Uawy!&e zMP2GvyBEdysU6fH9D`DxG@7aLsuIU*xf-BVy^fVVPzRXzJL||>1dDwu)TJ^nDs}|M z7VwH<$JtSf9lg8VxT90l6_yyi7i`@xP|NB86n zuep!oGoekdA=AjVgO#y|+H`V^y6y#@wTI@QCj^zVz_DkR4F^6=Y>1! z?(lc?9T?*{of@!Dy{T6iuP+kpjX8Yiffsmd5t`3p$Ml(Zg=Qk5*4+@rP1~v1ZKzW> za|N&2jhgm_c^6sxeXl+Ekq>X&c=gUU%%0{AJCV^cNAG9v>e#XqnVs-x%dOIo?&NlEm*D28 zU6{Bp@3}%r>7cRbc8>8W;d0>h{>)LgxQkDfm#V0NgLtKva30Sp>E*xjrNBiGMGh0#jC0sr%ubyQ@iEa6VwH2lzO*1 zJwGqco|uzkp95zfXC33?^VEK7LY_KMP0Y*5QRn2_=c;{F#P%m_Une#mvV++&$Ea_; 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zeJ9ezEh5LZ2$+N0BglCZxp5+8Zxx>npWD4prdO z7XnxD99P-gN>^E-Yg*ad(iuR7yeb&-eZbGBCxidiB)Wn6ZSzsy5#=1BcrMJJ?9JFN z&IZ|v3#`8PYa>v|4Jt06l-(Gm*9yFa$UEZ?2+&hsVVFW!(&?{6s%6wltFI@f;SUdd qjW5|&19MA&)4s+s@ER~%aCD`&;%l*{rFwn)L!mzi3jM*d_5T1bi@W~- From a998a45d8f9bc55418442d238af09006d4cd1fa5 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 17:01:57 +0800 Subject: [PATCH 052/123] =?UTF-8?q?feat:=20ETC=20dual=20X98/X99/X111=20+?= =?UTF-8?q?=20orthic=20NPC=20X131/X134=E2=80=93X136/X138/X139?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Dual labels on Steiner/Tarry/Parry. Orthic-of: X134=X107, X135=X108, X136=X109, X131=2N−X136, X138=Parry, X139=X112. Skip right/isos/equil. --- crates/mathcore/src/geometry.rs | 452 +++++++++++++++++++++++++++----- 1 file changed, 389 insertions(+), 63 deletions(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 24ec31a..1c9ccee 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -1969,6 +1969,18 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] y: st[1], label: "St 施泰纳".into(), })); + out.push(fact( + "施泰纳点", + "X_{99}", + pt(st[0], st[1]), + None, + "X(99) = (1/(b^2-c^2):\\cdots)", + "X(99):施泰纳点", + ).with(Shape::Point { + x: st[0], + y: st[1], + label: "X99".into(), + })); // Tarry = antipode of Steiner on (O) let ty = [2.0 * circ[0] - st[0], 2.0 * circ[1] - st[1]]; let ot = dist2(circ, ty); @@ -1985,6 +1997,18 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] y: ty[1], label: "Ty 塔里".into(), })); + out.push(fact( + "塔里点", + "X_{98}", + pt(ty[0], ty[1]), + None, + "X(98) = 2O - X(99)", + "X(98):塔里点", + ).with(Shape::Point { + x: ty[0], + y: ty[1], + label: "X98".into(), + })); out.push(fact( "塔里点", "|O\\,Ty|", @@ -2086,6 +2110,18 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] y: py[1], label: "Py 帕里".into(), })); + out.push(fact( + "帕里点", + "X_{111}", + pt(py[0], py[1]), + None, + "X(111) = (a^2/(2a^2-b^2-c^2):\\cdots)", + "X(111):帕里点", + ).with(Shape::Point { + x: py[0], + y: py[1], + label: "X111".into(), + })); let op = dist2(circ, py); if (op - rr).abs() < 1e-4 * (1.0 + rr) { out.push(fact( @@ -6607,11 +6643,13 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } - // X(128)/X(129)/X(130)/X(137): centers of the orthic triangle that lie on NPC. + // X(128)/X(129)/X(130)/X(131)/X(134)–X(139): centers of the orthic triangle on NPC. // X(130)=Steiner-of-orthic; X(129)=Tarry-of-orthic=2N−X(130); - // X(128)=X(74)-of-orthic; X(137)=NPC antipode of X(128)=2N−X(128). - // Skip right/near-right (orthic degenerates) and isosceles (Steiner denoms vanish; - // X74-of-orthic may still emit when denoms are safe). + // X(128)=X(74)-of-orthic; X(137)=2N−X(128); + // X(134)=X(107)-of-orthic; X(135)=X(108)-of-orthic; + // X(136)=X(109)-of-orthic; X(131)=2N−X(136)=X(102)-of-orthic; + // X(138)=Parry-of-orthic; X(139)=X(112)-of-orthic. + // Skip right/near-right (orthic degenerates) and isosceles (many denoms vanish). { let n9 = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; let r9 = rr / 2.0; @@ -6703,65 +6741,301 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } - // X(74)-of-orthic = X(128): bary a'/(cos A' − 2 cos B' cos C'). + // Orthic angles (Ha opposite oa, …); N = circumcenter of orthic. let cos_a = ((ob * ob + oc * oc - oa * oa) / (2.0 * ob * oc)).clamp(-1.0, 1.0); let cos_b = ((oc * oc + oa * oa - ob * ob) / (2.0 * oc * oa)).clamp(-1.0, 1.0); let cos_c = ((oa * oa + ob * ob - oc * oc) / (2.0 * oa * ob)).clamp(-1.0, 1.0); - let da = cos_a - 2.0 * cos_b * cos_c; - let db = cos_b - 2.0 * cos_c * cos_a; - let dc = cos_c - 2.0 * cos_a * cos_b; - if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { - let wa = oa / da; - let wb = ob / db; - let wc = oc / dc; - let den = wa + wb + wc; - if den.abs() > 1e-12 { - let x128 = [ - (wa * feet[0][0] + wb * feet[1][0] + wc * feet[2][0]) / den, - (wa * feet[0][1] + wb * feet[1][1] + wc * feet[2][1]) / den, - ]; - if (dist2(x128, n9) - r9).abs() < 1e-4 * (1.0 + r9) { - out.push(fact( - "垂足X74", - "X_{128}", - pt(x128[0], x128[1]), - None, - "X(128) = X(74)\\text{-of-orthic}", - "X(128):垂足三角形的 X(74)(九点圆上)", - ).with(Shape::Point { - x: x128[0], - y: x128[1], - label: "X128".into(), - })); - out.push(fact( - "垂足X74", - "X_{128}\\in\\text{NPC}", - "\\checkmark".into(), - None, - "d(N, X(128)) = R/2", - "X(128) 在九点圆上", - )); - let x137 = [2.0 * n9[0] - x128[0], 2.0 * n9[1] - x128[1]]; - out.push(fact( - "垂足X74对径", - "X_{137}", - pt(x137[0], x137[1]), - None, - "X(137) = 2N - X(128) = X(110)\\text{-of-orthic}", - "X(137):X(128) 的九点圆对径点(垂足三角形的 X(110))", - ).with(Shape::Point { - x: x137[0], - y: x137[1], - label: "X137".into(), - })); - out.push(fact( - "垂足X74对径", - "X_{137}=2N-X_{128}", - "\\text{九点圆对径}".into(), - None, - "X(137) = 2N - X(128)", - "X(137) 与 X(128) 互为九点圆对径点", - )); + let sin_a = (1.0 - cos_a * cos_a).max(0.0).sqrt(); + let sin_b = (1.0 - cos_b * cos_b).max(0.0).sqrt(); + let sin_c = (1.0 - cos_c * cos_c).max(0.0).sqrt(); + + // X(74)-of-orthic = X(128): bary a'/(cos A' − 2 cos B' cos C'). + { + let da = cos_a - 2.0 * cos_b * cos_c; + let db = cos_b - 2.0 * cos_c * cos_a; + let dc = cos_c - 2.0 * cos_a * cos_b; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = oa / da; + let wb = ob / db; + let wc = oc / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x128 = [ + (wa * feet[0][0] + wb * feet[1][0] + wc * feet[2][0]) / den, + (wa * feet[0][1] + wb * feet[1][1] + wc * feet[2][1]) / den, + ]; + if (dist2(x128, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "垂足X74", + "X_{128}", + pt(x128[0], x128[1]), + None, + "X(128) = X(74)\\text{-of-orthic}", + "X(128):垂足三角形的 X(74)(九点圆上)", + ).with(Shape::Point { + x: x128[0], + y: x128[1], + label: "X128".into(), + })); + out.push(fact( + "垂足X74", + "X_{128}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(128)) = R/2", + "X(128) 在九点圆上", + )); + let x137 = [2.0 * n9[0] - x128[0], 2.0 * n9[1] - x128[1]]; + out.push(fact( + "垂足X74对径", + "X_{137}", + pt(x137[0], x137[1]), + None, + "X(137) = 2N - X(128) = X(110)\\text{-of-orthic}", + "X(137):X(128) 的九点圆对径点(垂足三角形的 X(110))", + ).with(Shape::Point { + x: x137[0], + y: x137[1], + label: "X137".into(), + })); + out.push(fact( + "垂足X74对径", + "X_{137}=2N-X_{128}", + "\\text{九点圆对径}".into(), + None, + "X(137) = 2N - X(128)", + "X(137) 与 X(128) 互为九点圆对径点", + )); + } + } + } + } + + // X(134)=X(107)-of-orthic: bary 1/[(b'²−c'²)(b'²+c'²−a'²)²]. + { + let da = (ob * ob - oc * oc) * (ob * ob + oc * oc - oa * oa).powi(2); + let db = (oc * oc - oa * oa) * (oc * oc + oa * oa - ob * ob).powi(2); + let dc = (oa * oa - ob * ob) * (oa * oa + ob * ob - oc * oc).powi(2); + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + let wa = 1.0 / da; + let wb = 1.0 / db; + let wc = 1.0 / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * feet[0][0] + wb * feet[1][0] + wc * feet[2][0]) / den, + (wa * feet[0][1] + wb * feet[1][1] + wc * feet[2][1]) / den, + ]; + if (dist2(xy, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "垂足X107", + "X_{134}", + pt(xy[0], xy[1]), + None, + "X(134) = X(107)\\text{-of-orthic}", + "X(134):垂足三角形的 X(107)(九点圆上)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X134".into(), + })); + out.push(fact( + "垂足X107", + "X_{134}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(134)) = R/2", + "X(134) 在九点圆上", + )); + } + } + } + } + + // X(135)=X(108)-of-orthic: bary a'²/(sec B'−sec C'); skip rightish orthic angles. + if cos_a.abs() > 1e-9 && cos_b.abs() > 1e-9 && cos_c.abs() > 1e-9 { + let da = 1.0 / cos_b - 1.0 / cos_c; + let db = 1.0 / cos_c - 1.0 / cos_a; + let dc = 1.0 / cos_a - 1.0 / cos_b; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = (oa * oa) / da; + let wb = (ob * ob) / db; + let wc = (oc * oc) / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * feet[0][0] + wb * feet[1][0] + wc * feet[2][0]) / den, + (wa * feet[0][1] + wb * feet[1][1] + wc * feet[2][1]) / den, + ]; + if (dist2(xy, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "垂足X108", + "X_{135}", + pt(xy[0], xy[1]), + None, + "X(135) = X(108)\\text{-of-orthic}", + "X(135):垂足三角形的 X(108)(九点圆上)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X135".into(), + })); + out.push(fact( + "垂足X108", + "X_{135}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(135)) = R/2", + "X(135) 在九点圆上", + )); + } + } + } + } + + // X(136)=X(109)-of-orthic: bary a'²/(cos B'−cos C'); X(131)=2N−X(136)=X(102)-of-orthic. + { + let da = cos_b - cos_c; + let db = cos_c - cos_a; + let dc = cos_a - cos_b; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = (oa * oa) / da; + let wb = (ob * ob) / db; + let wc = (oc * oc) / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * feet[0][0] + wb * feet[1][0] + wc * feet[2][0]) / den, + (wa * feet[0][1] + wb * feet[1][1] + wc * feet[2][1]) / den, + ]; + if (dist2(xy, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "垂足X109", + "X_{136}", + pt(xy[0], xy[1]), + None, + "X(136) = X(109)\\text{-of-orthic}", + "X(136):垂足三角形的 X(109)(九点圆上)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X136".into(), + })); + out.push(fact( + "垂足X109", + "X_{136}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(136)) = R/2", + "X(136) 在九点圆上", + )); + let x131 = [2.0 * n9[0] - xy[0], 2.0 * n9[1] - xy[1]]; + out.push(fact( + "垂足X102", + "X_{131}", + pt(x131[0], x131[1]), + None, + "X(131) = 2N - X(136) = X(102)\\text{-of-orthic}", + "X(131):垂足三角形的 X(102)(九点圆上)", + ).with(Shape::Point { + x: x131[0], + y: x131[1], + label: "X131".into(), + })); + out.push(fact( + "垂足X102", + "X_{131}=2N-X_{136}", + "\\text{九点圆对径}".into(), + None, + "X(131) = 2N - X(136)", + "X(131) 与 X(136) 互为九点圆对径点(N 反射)", + )); + } + } + } + } + + // X(138)=Parry-of-orthic = X(111)-of-orthic: bary a'²/(2a'²−b'²−c'²). + { + let da = 2.0 * oa * oa - ob * ob - oc * oc; + let db = 2.0 * ob * ob - oc * oc - oa * oa; + let dc = 2.0 * oc * oc - oa * oa - ob * ob; + if da.abs() > 1e-10 && db.abs() > 1e-10 && dc.abs() > 1e-10 { + let wa = (oa * oa) / da; + let wb = (ob * ob) / db; + let wc = (oc * oc) / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * feet[0][0] + wb * feet[1][0] + wc * feet[2][0]) / den, + (wa * feet[0][1] + wb * feet[1][1] + wc * feet[2][1]) / den, + ]; + if (dist2(xy, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "垂足帕里", + "X_{138}", + pt(xy[0], xy[1]), + None, + "X(138) = X(111)\\text{-of-orthic}", + "X(138):垂足三角形的帕里点(九点圆上)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X138".into(), + })); + out.push(fact( + "垂足帕里", + "X_{138}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(138)) = R/2", + "X(138) 在九点圆上", + )); + } + } + } + } + + // X(139)=X(112)-of-orthic: bary a'²/(sin 2B'−sin 2C'). + { + let sin2a = 2.0 * sin_a * cos_a; + let sin2b = 2.0 * sin_b * cos_b; + let sin2c = 2.0 * sin_c * cos_c; + let da = sin2b - sin2c; + let db = sin2c - sin2a; + let dc = sin2a - sin2b; + if da.abs() > 1e-9 && db.abs() > 1e-9 && dc.abs() > 1e-9 { + let wa = (oa * oa) / da; + let wb = (ob * ob) / db; + let wc = (oc * oc) / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * feet[0][0] + wb * feet[1][0] + wc * feet[2][0]) / den, + (wa * feet[0][1] + wb * feet[1][1] + wc * feet[2][1]) / den, + ]; + if (dist2(xy, n9) - r9).abs() < 1e-4 * (1.0 + r9) { + out.push(fact( + "垂足X112", + "X_{139}", + pt(xy[0], xy[1]), + None, + "X(139) = X(112)\\text{-of-orthic}", + "X(139):垂足三角形的 X(112)(九点圆上)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X139".into(), + })); + out.push(fact( + "垂足X112", + "X_{139}\\in\\text{NPC}", + "\\checkmark".into(), + None, + "d(N, X(139)) = R/2", + "X(139) 在九点圆上", + )); + } } } } @@ -9805,6 +10079,7 @@ mod tests { let n2 = fs.iter().find(|f| f.group == "拿破仑中心" && f.label == "N_2").expect("N2"); assert_ne!(n1.value, n2.value); let py = fs.iter().find(|f| f.group == "帕里点" && f.label == "Py").expect("Parry"); + assert!(fs.iter().any(|f| f.group == "帕里点" && f.label == "X_{111}"), "X111 dual label"); let op = fs.iter().find(|f| f.group == "帕里点" && f.label.contains("O")).expect("|O Py|"); let rr = fs.iter().find(|f| f.group == "外接圆与内切圆" && f.label == "R").expect("R"); assert!((op.num.unwrap() - rr.num.unwrap()).abs() < 1e-6, "Parry on circumcircle"); @@ -11292,7 +11567,7 @@ mod tests { } #[test] - fn x128_x129_x130_x132_x133_x137() { + fn x128_x129_x130_x131_x132_x133_x134_x135_x136_x137_x138_x139() { // Scalene acute 6-7-8: orthic Steiner/Tarry/X74 and mid(H, Ψ) on NPC. let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; let r = triangle_solve(&k); @@ -11314,6 +11589,12 @@ mod tests { let x129 = fs.iter().find(|f| f.group == "垂足塔里" && f.label == "X_{129}").expect("X129"); let x128 = fs.iter().find(|f| f.group == "垂足X74" && f.label == "X_{128}").expect("X128"); let x137 = fs.iter().find(|f| f.group == "垂足X74对径" && f.label == "X_{137}").expect("X137"); + let x134 = fs.iter().find(|f| f.group == "垂足X107" && f.label == "X_{134}").expect("X134"); + let x135 = fs.iter().find(|f| f.group == "垂足X108" && f.label == "X_{135}").expect("X135"); + let x136 = fs.iter().find(|f| f.group == "垂足X109" && f.label == "X_{136}").expect("X136"); + let x131 = fs.iter().find(|f| f.group == "垂足X102" && f.label == "X_{131}").expect("X131"); + let x138 = fs.iter().find(|f| f.group == "垂足帕里" && f.label == "X_{138}").expect("X138"); + let x139 = fs.iter().find(|f| f.group == "垂足X112" && f.label == "X_{139}").expect("X139"); let (hx, hy) = ptxy(h); let (nx, ny) = ptxy(n); let (p112x, p112y) = ptxy(x112); @@ -11332,6 +11613,16 @@ mod tests { let (p137x, p137y) = ptxy(x137); assert!((2.0 * nx - p130x - p129x).abs() < 1e-5 && (2.0 * ny - p130y - p129y).abs() < 1e-5, "X129 != 2N-X130"); assert!((2.0 * nx - p128x - p137x).abs() < 1e-5 && (2.0 * ny - p128y - p137y).abs() < 1e-5, "X137 != 2N-X128"); + let (p136x, p136y) = ptxy(x136); + let (p131x, p131y) = ptxy(x131); + assert!((2.0 * nx - p136x - p131x).abs() < 1e-5 && (2.0 * ny - p136y - p131y).abs() < 1e-5, "X131 != 2N-X136"); + let _ = (x134, x135, x138, x139); // presence already asserted via expect + assert!(fs.iter().any(|f| f.group == "垂足X107" && f.label.contains("NPC"))); + assert!(fs.iter().any(|f| f.group == "垂足X108" && f.label.contains("NPC"))); + assert!(fs.iter().any(|f| f.group == "垂足X109" && f.label.contains("NPC"))); + assert!(fs.iter().any(|f| f.group == "垂足X102" && f.label.contains("2N"))); + assert!(fs.iter().any(|f| f.group == "垂足帕里" && f.label.contains("NPC"))); + assert!(fs.iter().any(|f| f.group == "垂足X112" && f.label.contains("NPC"))); assert!(fs.iter().any(|f| f.group == "垂心X112中点" && f.label.contains("NPC"))); assert!(fs.iter().any(|f| f.group == "垂心X107中点" && f.label.contains("NPC"))); assert!(fs.iter().any(|f| f.group == "垂足施泰纳" && f.label.contains("NPC"))); @@ -11348,6 +11639,13 @@ mod tests { assert!(fs2.iter().all(|f| f.group != "垂足施泰纳"), "X130 skip isosceles"); assert!(fs2.iter().all(|f| f.group != "垂足塔里"), "X129 skip isosceles"); assert!(fs2.iter().all(|f| f.group != "垂心X107中点"), "X133 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "垂足X107"), "X134 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "垂足X108"), "X135 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "垂足X109"), "X136 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "垂足X102"), "X131 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "垂足X112"), "X139 skip isosceles"); + // Parry-of-orthic may survive on some isosceles; accept either. + let _ = fs2.iter().any(|f| f.group == "垂足帕里"); // Equilateral: all skip. let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; @@ -11360,8 +11658,14 @@ mod tests { assert!(fs3.iter().all(|f| f.group != "垂足塔里"), "X129 skip equilateral"); assert!(fs3.iter().all(|f| f.group != "垂足X74"), "X128 skip equilateral"); assert!(fs3.iter().all(|f| f.group != "垂足X74对径"), "X137 skip equilateral"); - - // Right 3-4-5: orthic degenerates → X128/129/130/137 skip; mid parents also skip. + assert!(fs3.iter().all(|f| f.group != "垂足X107"), "X134 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "垂足X108"), "X135 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "垂足X109"), "X136 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "垂足X102"), "X131 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "垂足帕里"), "X138 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "垂足X112"), "X139 skip equilateral"); + + // Right 3-4-5: orthic degenerates → X128/129/130/137+ skip; mid parents also skip. let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; let r4 = triangle_solve(&k4); assert!(r4.error.is_none(), "{:?}", r4.error); @@ -11370,11 +11674,33 @@ mod tests { assert!(fs4.iter().all(|f| f.group != "垂足塔里"), "X129 skip right"); assert!(fs4.iter().all(|f| f.group != "垂足X74"), "X128 skip right"); assert!(fs4.iter().all(|f| f.group != "垂足X74对径"), "X137 skip right"); + assert!(fs4.iter().all(|f| f.group != "垂足X107"), "X134 skip right"); + assert!(fs4.iter().all(|f| f.group != "垂足X108"), "X135 skip right"); + assert!(fs4.iter().all(|f| f.group != "垂足X109"), "X136 skip right"); + assert!(fs4.iter().all(|f| f.group != "垂足X102"), "X131 skip right"); + assert!(fs4.iter().all(|f| f.group != "垂足帕里"), "X138 skip right"); + assert!(fs4.iter().all(|f| f.group != "垂足X112"), "X139 skip right"); assert!(fs4.iter().all(|f| f.group != "垂心X107中点"), "X133 skip right"); // X112 / X132: may skip on right. let _ = fs4.iter().any(|f| f.group == "垂心X112中点"); } + + #[test] + fn etc_dual_labels_steiner_tarry_parry() { + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + assert!(fs.iter().any(|f| f.group == "施泰纳点" && f.label == "X_{99}")); + assert!(fs.iter().any(|f| f.group == "塔里点" && f.label == "X_{98}")); + assert!(fs.iter().any(|f| f.group == "帕里点" && f.label == "X_{111}")); + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.label != "X_{99}" && f.label != "X_{98}" && f.label != "X_{111}")); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ From 66a77e87726082909d77d359f224d95f5a69e22e Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 17:02:13 +0800 Subject: [PATCH 053/123] chore: refresh mathcore WASM after orthic NPC ETC centers MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Rebuild after X98/X99/X111 dual labels + X131/X134–X136/X138/X139. --- src/wasm/pkg/mathcore_bg.wasm | Bin 713652 -> 719351 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 93b7b83eef112cc0e19f6cb1131456517866e495..1ed6deebb09b79bbc5fa3db2e508a1eb1475b139 100644 GIT binary patch delta 62114 zcmb?^dt8m#_kVjoN2J@)g@`=oa8k&1#!O7u!x+YG%$WPtTt1%}GYoSx7c&(hg!05L z!s&ugWQvm}9E1=;2qAwJ$nx^mE<>VUf#A0`5UujfF8<#CMOly2RH@m9IbIvr^Dj7Y;(;};s9MMu* zuA9;>6G5Td6jjC6Z6!sCSoH-deNw+K;^+clGtoNt+VoTPe^dKpBE#v 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=?UTF-8?q?feat:=20ETC=20X140=E2=80=93X150=20compl?= =?UTF-8?q?ements,=20anticomplements,=20L-reflections?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit X(140)=mid(O,N); X(141)=complement(K); X(142)=mid(Ge,Mi); X(143)=mid(N,X52) acute; X(144)/X(145)=anticomplement(Ge/Na); X(146)–X(150)=2Q−L for Q∈{X110,St,Ty,X104,X103} with isos/equil skips. --- crates/mathcore/src/geometry.rs | 441 ++++++++++++++++++++++++++++++++ 1 file changed, 441 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 1c9ccee..e00f947 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -7044,6 +7044,321 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(140)–X(150): Euler/medial complements, anticomplements of Ge/Na, and + // reflections of de Longchamps X(20) in classical circumcircle points. + // X(140)=mid(O,N)=complement(X(5)); X(141)=complement(K), bary b²+c²:…; + // X(142)=mid(Ge,Mi)=complement(X(9)); X(143)=mid(N,X(52))=X(5)-of-orthic; + // X(144)=anticomplement(Ge); X(145)=anticomplement(Na); + // X(146)=2·X(110)−X(20); X(147)=2·X(99)−X(20); X(148)=2·X(98)−X(20); + // X(149)=2·X(104)−X(20); X(150)=2·X(103)−X(20). + { + let n9 = [(circ[0] + orth[0]) / 2.0, (circ[1] + orth[1]) / 2.0]; + // X(140) = midpoint(O, N) = complement of X(5); on Euler line. Always. + let x140 = [(circ[0] + n9[0]) / 2.0, (circ[1] + n9[1]) / 2.0]; + out.push(fact( + "九点补点", + "X_{140}", + pt(x140[0], x140[1]), + None, + "X(140) = \\mathrm{mid}(O,N) = \\mathrm{complement}(X(5))", + "X(140):O 与 N 的中点(中点三角形的九点心;欧拉线上)", + ).with(Shape::Point { + x: x140[0], + y: x140[1], + label: "X140".into(), + })); + // Collinear O, X140, N, G, H (Euler): X140 divides O N. + let cross_e = (x140[0] - circ[0]) * (orth[1] - circ[1]) + - (x140[1] - circ[1]) * (orth[0] - circ[0]); + if cross_e.abs() < 1e-6 { + out.push(fact( + "九点补点", + "X_{140}\\in\\text{Euler}", + "\\checkmark".into(), + None, + "X(140)\\in\\text{Euler line}", + "X(140) 在欧拉线上", + )); + } + + // X(141) = complement of Lemoine/symmedian X(6); bary b²+c² : c²+a² : a²+b². + { + let wa = b * b + c * c; + let wb = c * c + a * a; + let wc = a * a + b * b; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x141 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "对称中线补点", + "X_{141}", + pt(x141[0], x141[1]), + None, + "X(141) = (b^2+c^2:c^2+a^2:a^2+b^2) = \\mathrm{complement}(X(6))", + "X(141):勒莫恩点的补点(中点三角形的对称中线点)", + ).with(Shape::Point { + x: x141[0], + y: x141[1], + label: "X141".into(), + })); + // Cross-check: complement of K via h(G,−1/2). + let k_xy = out.iter().rev().find(|f| f.group == "勒莫恩点" && f.label == "K").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((kx, ky)) = k_xy { + let cx = (3.0 * centroid[0] - kx) / 2.0; + let cy = (3.0 * centroid[1] - ky) / 2.0; + if (cx - x141[0]).abs() < 1e-5 && (cy - x141[1]).abs() < 1e-5 { + out.push(fact( + "对称中线补点", + "X_{141}=\\mathrm{complement}(K)", + "\\checkmark".into(), + None, + "X(141) = (3G - K)/2", + "X(141) 为对称中线点关于重心的补点", + )); + } + } + } + } + + // X(142) = midpoint(Ge, Mi) = complement of Mittenpunkt X(9). + let ge_xy = out.iter().rev().find(|f| f.group == "格尔巩点" && f.label == "Ge").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + let mi_xy = out.iter().rev().find(|f| f.group == "米滕点" && f.label == "Mi").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let (Some((gx, gy)), Some((mx, my))) = (ge_xy, mi_xy) { + let x142 = [(gx + mx) / 2.0, (gy + my) / 2.0]; + out.push(fact( + "米滕补点", + "X_{142}", + pt(x142[0], x142[1]), + None, + "X(142) = \\mathrm{mid}(X(7),X(9)) = \\mathrm{complement}(X(9))", + "X(142):格尔巩与米滕的中点(米滕点的补点)", + ).with(Shape::Point { + x: x142[0], + y: x142[1], + label: "X142".into(), + })); + let cx = (3.0 * centroid[0] - mx) / 2.0; + let cy = (3.0 * centroid[1] - my) / 2.0; + if (cx - x142[0]).abs() < 1e-5 && (cy - x142[1]).abs() < 1e-5 { + out.push(fact( + "米滕补点", + "X_{142}=\\mathrm{complement}(Mi)", + "\\checkmark".into(), + None, + "X(142) = (3G - Mi)/2", + "X(142) 为米滕点关于重心的补点", + )); + } + } + + // X(143) = midpoint(N, X(52)) = X(5)-of-orthic; skip right (no X52). + let x52_xy = out.iter().rev().find(|f| f.group == "垂足垂心" && f.label == "X_{52}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((sx, sy)) = x52_xy { + let x143 = [(n9[0] + sx) / 2.0, (n9[1] + sy) / 2.0]; + out.push(fact( + "垂足九点心", + "X_{143}", + pt(x143[0], x143[1]), + None, + "X(143) = \\mathrm{mid}(N,X(52)) = X(5)\\text{-of-orthic}", + "X(143):垂足三角形的九点圆心(锐角)", + ).with(Shape::Point { + x: x143[0], + y: x143[1], + label: "X143".into(), + })); + } + + // X(144) = anticomplement of Gergonne X(7) = 3G − 2 Ge. + if let Some((gx, gy)) = ge_xy { + let x144 = [3.0 * centroid[0] - 2.0 * gx, 3.0 * centroid[1] - 2.0 * gy]; + out.push(fact( + "格尔巩反补", + "X_{144}", + pt(x144[0], x144[1]), + None, + "X(144) = 3G - 2\\,X(7) = \\mathrm{anticomplement}(X(7))", + "X(144):格尔巩点的反补点(反补三角形的 X(7))", + ).with(Shape::Point { + x: x144[0], + y: x144[1], + label: "X144".into(), + })); + } + + // X(145) = anticomplement of Nagel X(8) = 3G − 2 Na. + let na_xy = out.iter().rev().find(|f| f.group == "奈格尔点" && f.label == "Na").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((nx, ny)) = na_xy { + let x145 = [3.0 * centroid[0] - 2.0 * nx, 3.0 * centroid[1] - 2.0 * ny]; + out.push(fact( + "奈格尔反补", + "X_{145}", + pt(x145[0], x145[1]), + None, + "X(145) = 3G - 2\\,X(8) = \\mathrm{anticomplement}(X(8))", + "X(145):奈格尔点的反补点(反补三角形的 X(8))", + ).with(Shape::Point { + x: x145[0], + y: x145[1], + label: "X145".into(), + })); + // Cross-check bary 3a−b−c : … + let wa = 3.0 * a - b - c; + let wb = 3.0 * b - c - a; + let wc = 3.0 * c - a - b; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let bx = (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den; + let by = (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den; + if (bx - x145[0]).abs() < 1e-5 && (by - x145[1]).abs() < 1e-5 { + out.push(fact( + "奈格尔反补", + "X_{145}=(3a-b-c:\\cdots)", + "\\checkmark".into(), + None, + "X(145) = (3a-b-c:3b-c-a:3c-a-b)", + "X(145) 重心坐标与反补构造一致", + )); + } + } + } + + // Helpers for reflections of L = X(20) in circumcircle points. + let l_xy = out.iter().rev().find(|f| f.group == "德龙尚点" && f.label == "L").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((lx, ly)) = l_xy { + let reflect_l = |qx: f64, qy: f64| -> [f64; 2] { + [2.0 * qx - lx, 2.0 * qy - ly] + }; + + // X(146) = reflection of X(20) in X(110). Skip when X110 missing (isos). + let x110_xy = out.iter().rev().find(|f| f.group == "欧拉反射点" && f.label == "X_{110}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((qx, qy)) = x110_xy { + let xy = reflect_l(qx, qy); + out.push(fact( + "德龙尚X110反射", + "X_{146}", + pt(xy[0], xy[1]), + None, + "X(146) = 2\\,X(110) - X(20)", + "X(146):德龙尚点关于 X(110) 的反射(反补三角形的 X(74))", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X146".into(), + })); + } + + // X(147) = reflection of X(20) in Steiner X(99). + let st_xy = out.iter().rev().find(|f| f.group == "施泰纳点" && f.label == "St").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((qx, qy)) = st_xy { + let xy = reflect_l(qx, qy); + out.push(fact( + "德龙尚施泰纳反射", + "X_{147}", + pt(xy[0], xy[1]), + None, + "X(147) = 2\\,X(99) - X(20) = X(98)\\text{-of-anticomplementary}", + "X(147):德龙尚点关于施泰纳点的反射(反补三角形的塔里点)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X147".into(), + })); + } + + // X(148) = reflection of X(20) in Tarry X(98). + let ty_xy = out.iter().rev().find(|f| f.group == "塔里点" && f.label == "Ty").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((qx, qy)) = ty_xy { + let xy = reflect_l(qx, qy); + out.push(fact( + "德龙尚塔里反射", + "X_{148}", + pt(xy[0], xy[1]), + None, + "X(148) = 2\\,X(98) - X(20) = X(99)\\text{-of-anticomplementary}", + "X(148):德龙尚点关于塔里点的反射(反补三角形的施泰纳点)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X148".into(), + })); + } + + // X(149) = reflection of X(20) in X(104). + let x104_xy = out.iter().rev().find(|f| f.group == "X100对径" && f.label == "X_{104}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((qx, qy)) = x104_xy { + let xy = reflect_l(qx, qy); + out.push(fact( + "德龙尚X104反射", + "X_{149}", + pt(xy[0], xy[1]), + None, + "X(149) = 2\\,X(104) - X(20) = X(100)\\text{-of-anticomplementary}", + "X(149):德龙尚点关于 X(104) 的反射(反补三角形的 X(100))", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X149".into(), + })); + } + + // X(150) = reflection of X(20) in X(103). + let x103_xy = out.iter().rev().find(|f| f.group == "X101对径" && f.label == "X_{103}").and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some((*x, *y)), + _ => None, + }); + if let Some((qx, qy)) = x103_xy { + let xy = reflect_l(qx, qy); + out.push(fact( + "德龙尚X103反射", + "X_{150}", + pt(xy[0], xy[1]), + None, + "X(150) = 2\\,X(103) - X(20) = X(101)\\text{-of-anticomplementary}", + "X(150):德龙尚点关于 X(103) 的反射(反补三角形的 X(101))", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X150".into(), + })); + } + } + } + + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -11687,6 +12002,132 @@ mod tests { #[test] + fn x140_to_x150_complements_anticomplements_reflections() { + // Scalene acute 6-7-8: all eleven present with geometric cross-checks. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + let o = fs.iter().find(|f| f.group == "特殊点" && f.label == "O").expect("O"); + let n = fs.iter().find(|f| f.group == "欧拉线" && f.label == "N").expect("N"); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let kpt = fs.iter().find(|f| f.group == "勒莫恩点" && f.label == "K").expect("K"); + let ge = fs.iter().find(|f| f.group == "格尔巩点" && f.label == "Ge").expect("Ge"); + let mi = fs.iter().find(|f| f.group == "米滕点" && f.label == "Mi").expect("Mi"); + let na = fs.iter().find(|f| f.group == "奈格尔点" && f.label == "Na").expect("Na"); + let x52 = fs.iter().find(|f| f.group == "垂足垂心" && f.label == "X_{52}").expect("X52"); + let x140 = fs.iter().find(|f| f.group == "九点补点" && f.label == "X_{140}").expect("X140"); + let x141 = fs.iter().find(|f| f.group == "对称中线补点" && f.label == "X_{141}").expect("X141"); + let x142 = fs.iter().find(|f| f.group == "米滕补点" && f.label == "X_{142}").expect("X142"); + let x143 = fs.iter().find(|f| f.group == "垂足九点心" && f.label == "X_{143}").expect("X143"); + let x144 = fs.iter().find(|f| f.group == "格尔巩反补" && f.label == "X_{144}").expect("X144"); + let x145 = fs.iter().find(|f| f.group == "奈格尔反补" && f.label == "X_{145}").expect("X145"); + let x146 = fs.iter().find(|f| f.group == "德龙尚X110反射" && f.label == "X_{146}").expect("X146"); + let x147 = fs.iter().find(|f| f.group == "德龙尚施泰纳反射" && f.label == "X_{147}").expect("X147"); + let x148 = fs.iter().find(|f| f.group == "德龙尚塔里反射" && f.label == "X_{148}").expect("X148"); + let x149 = fs.iter().find(|f| f.group == "德龙尚X104反射" && f.label == "X_{149}").expect("X149"); + let x150 = fs.iter().find(|f| f.group == "德龙尚X103反射" && f.label == "X_{150}").expect("X150"); + let (ox, oy) = ptxy(o); + let (nx, ny) = ptxy(n); + let (gx, gy) = ptxy(g); + let (p140x, p140y) = ptxy(x140); + assert!(((ox + nx) / 2.0 - p140x).abs() < 1e-5 && ((oy + ny) / 2.0 - p140y).abs() < 1e-5, "X140 != mid(O,N)"); + assert!(fs.iter().any(|f| f.group == "九点补点" && f.label.contains("Euler"))); + let (kx, ky) = ptxy(kpt); + let (p141x, p141y) = ptxy(x141); + assert!(((3.0 * gx - kx) / 2.0 - p141x).abs() < 1e-5 && ((3.0 * gy - ky) / 2.0 - p141y).abs() < 1e-5, "X141 != complement(K)"); + let (gex, gey) = ptxy(ge); + let (mx, my) = ptxy(mi); + let (p142x, p142y) = ptxy(x142); + assert!(((gex + mx) / 2.0 - p142x).abs() < 1e-5 && ((gey + my) / 2.0 - p142y).abs() < 1e-5, "X142 != mid(Ge,Mi)"); + let (s52x, s52y) = ptxy(x52); + let (p143x, p143y) = ptxy(x143); + assert!(((nx + s52x) / 2.0 - p143x).abs() < 1e-5 && ((ny + s52y) / 2.0 - p143y).abs() < 1e-5, "X143 != mid(N,X52)"); + let (p144x, p144y) = ptxy(x144); + assert!((3.0 * gx - 2.0 * gex - p144x).abs() < 1e-5 && (3.0 * gy - 2.0 * gey - p144y).abs() < 1e-5, "X144 != anticomplement(Ge)"); + let (nax, nay) = ptxy(na); + let (p145x, p145y) = ptxy(x145); + assert!((3.0 * gx - 2.0 * nax - p145x).abs() < 1e-5 && (3.0 * gy - 2.0 * nay - p145y).abs() < 1e-5, "X145 != anticomplement(Na)"); + assert!(fs.iter().any(|f| f.group == "奈格尔反补" && f.label.contains("3a"))); + let l = fs.iter().find(|f| f.group == "德龙尚点" && f.label == "L").expect("L"); + let x110 = fs.iter().find(|f| f.group == "欧拉反射点" && f.label == "X_{110}").expect("X110"); + let st = fs.iter().find(|f| f.group == "施泰纳点" && f.label == "St").expect("St"); + let ty = fs.iter().find(|f| f.group == "塔里点" && f.label == "Ty").expect("Ty"); + let x104 = fs.iter().find(|f| f.group == "X100对径" && f.label == "X_{104}").expect("X104"); + let x103 = fs.iter().find(|f| f.group == "X101对径" && f.label == "X_{103}").expect("X103"); + let (lx, ly) = ptxy(l); + let check_ref = |q: &Fact, p: &Fact, name: &str| { + let (qx, qy) = ptxy(q); + let (px, py) = ptxy(p); + assert!((2.0 * qx - lx - px).abs() < 1e-5 && (2.0 * qy - ly - py).abs() < 1e-5, "{name} != 2Q-L"); + }; + check_ref(x110, x146, "X146"); + check_ref(st, x147, "X147"); + check_ref(ty, x148, "X148"); + check_ref(x104, x149, "X149"); + check_ref(x103, x150, "X150"); + + // Isosceles 5-5-6: X140–X145 remain; Steiner/Tarry/X110/X104 family skip → reflections skip. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().any(|f| f.group == "九点补点" && f.label == "X_{140}")); + assert!(fs2.iter().any(|f| f.group == "对称中线补点" && f.label == "X_{141}")); + assert!(fs2.iter().any(|f| f.group == "米滕补点" && f.label == "X_{142}")); + assert!(fs2.iter().any(|f| f.group == "格尔巩反补" && f.label == "X_{144}")); + assert!(fs2.iter().any(|f| f.group == "奈格尔反补" && f.label == "X_{145}")); + // X143 needs X52; isos acute non-eq usually has X52. + let _ = fs2.iter().any(|f| f.group == "垂足九点心"); + assert!(fs2.iter().all(|f| f.group != "德龙尚X110反射"), "X146 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "德龙尚施泰纳反射"), "X147 skip isosceles"); + assert!(fs2.iter().all(|f| f.group != "德龙尚塔里反射"), "X148 skip isosceles"); + // X104/X103 may survive on a=b isos; accept either for X149/X150. + let _ = ( + fs2.iter().any(|f| f.group == "德龙尚X104反射"), + fs2.iter().any(|f| f.group == "德龙尚X103反射"), + ); + + // Equilateral: X140–X145 collapse toward G/O; reflections of circumcircle points skip. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().any(|f| f.group == "九点补点" && f.label == "X_{140}")); + assert!(fs3.iter().any(|f| f.group == "对称中线补点" && f.label == "X_{141}")); + assert!(fs3.iter().any(|f| f.group == "米滕补点" && f.label == "X_{142}")); + assert!(fs3.iter().any(|f| f.group == "格尔巩反补" && f.label == "X_{144}")); + assert!(fs3.iter().any(|f| f.group == "奈格尔反补" && f.label == "X_{145}")); + assert!(fs3.iter().all(|f| f.group != "德龙尚X110反射"), "X146 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "德龙尚施泰纳反射"), "X147 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "德龙尚塔里反射"), "X148 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "德龙尚X104反射"), "X149 skip equilateral"); + assert!(fs3.iter().all(|f| f.group != "德龙尚X103反射"), "X150 skip equilateral"); + + // Right 3-4-5: X140/141/142/144/145; X143 skips (no X52); X110 may via bary. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().any(|f| f.group == "九点补点" && f.label == "X_{140}")); + assert!(fs4.iter().any(|f| f.group == "对称中线补点" && f.label == "X_{141}")); + assert!(fs4.iter().any(|f| f.group == "米滕补点" && f.label == "X_{142}")); + assert!(fs4.iter().any(|f| f.group == "格尔巩反补" && f.label == "X_{144}")); + assert!(fs4.iter().any(|f| f.group == "奈格尔反补" && f.label == "X_{145}")); + assert!(fs4.iter().all(|f| f.group != "垂足九点心"), "X143 skip right"); + // X110 bary works on right scalene; Steiner/Tarry may too — presence optional for reflections. + let _ = ( + fs4.iter().any(|f| f.group == "德龙尚X110反射"), + fs4.iter().any(|f| f.group == "德龙尚施泰纳反射"), + fs4.iter().any(|f| f.group == "德龙尚塔里反射"), + ); + } + + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; let r = triangle_solve(&k); From df60a45ea4be0cb659591c9a5ef4e894b776f846 Mon 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zJ9yL~y{<&F{K$CT_O!E4xz#YnQ)esH=Y(kme}Sz`-%MvWS^6mmiR|N8RB;d!4QAED z(Uhni`ab{&iz(;m6M*N#%4y{X%}xU7j;Qe#v4v$3eZ)~U+8V;*lNf+wkQQm7IIgC6 zPVj~CoWLvTIl$%^!xO5YO@~G}9PD37b~xmO3L0RXQi-0Sf6HtV6)N1kPk##voE9!5 zRdRGCeJoC^zMM83Po$v|v#-kQF8acR&Y(5495$eB*-@=T-0avIHPiDOk(_y){A{&s ztD+^4E;6d%{_6N?6++8%JopTKVw}gT=rqDk Date: Mon, 2 Nov 2026 18:20:03 +0800 Subject: [PATCH 064/123] =?UTF-8?q?feat:=20ETC=20X182=E2=80=93X190=20Broca?= =?UTF-8?q?rd/orthic/circum-inverses/Yff=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit X(174)–X(176)/X(181) already present; fill next classical band: X(182) Brocard-diameter mid(O,K); X(183) Moses/X182 trilinear quotient; X(184) procircumcenter; X(185) Nagel-of-orthic (skip right); X(186) circum-inverse of H (skip equil); X(187) Schoute inverse of K; X(188) anticomplement 2nd mid-arc; X(189) cyclocevian of Nagel; X(190) Yff parabolic (skip isos). Acute/right/equil/isos guards. --- crates/mathcore/src/geometry.rs | 463 ++++++++++++++++++++++++++++++++ 1 file changed, 463 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index e97d3ea..1142a2b 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -8373,6 +8373,359 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(182)–X(190): Brocard-diameter / orthic / circum-inverses / mid-arc / Yff. + // X(182)=mid(O,K)=Brocard-circle center; bary a cos(A−ω). + // X(183)=trilinear quotient X(75)/X(182); bary csc A cos(A−ω). + // X(184)=procircumcenter; bary a³ cos A (=X(63)-of-orthic when acute). + // X(185)=Nagel-of-orthic; bary (sin 2A)[1−cos A cos(B−C)]; skip right. + // X(186)=circum-inverse of H; bary sin A(4 cos A−sec A); skip equilateral. + // X(187)=Schoute=circum-inverse of K; bary a²(2a²−b²−c²); skip equilateral. + // X(188)=2nd mid-arc of anticomplementary; bary 2 cos(A/2)=sin A csc(A/2). + // X(189)=cyclocevian conjugate of Nagel X(8); bary 1/(cos B+cos C−cos A−1). + // X(190)=Yff parabolic point; bary 1/(b−c); skip isos/equil. + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let rightish = ca.abs() < 1e-12 || cb.abs() < 1e-12 || cc.abs() < 1e-12; + let isos = (a - b).abs() < 1e-9 || (b - c).abs() < 1e-9 || (c - a).abs() < 1e-9; + // K = Lemoine (recompute; always finite). + let k_den = a * a + b * b + c * c; + let kpt = if k_den > 1e-18 { + [ + (a * a * pa[0] + b * b * pb[0] + c * c * pc[0]) / k_den, + (a * a * pa[1] + b * b * pb[1] + c * c * pc[1]) / k_den, + ] + } else { + centroid + }; + // X(182): midpoint of Brocard diameter OK. + { + let xy = [(circ[0] + kpt[0]) / 2.0, (circ[1] + kpt[1]) / 2.0]; + // Cross-check bary a cos(A−ω) when Brocard angle available. + let xyu = if area > 1e-12 && k_den > 1e-18 { + let tan_w = (4.0 * area) / k_den; + let sin_w = tan_w / (1.0 + tan_w * tan_w).sqrt(); + let cos_w = 1.0 / (1.0 + tan_w * tan_w).sqrt(); + let fa = ca * cos_w + sa * sin_w; + let fb = cb * cos_w + sb * sin_w; + let fc = cc * cos_w + sc * sin_w; + let wa = a * fa; + let wb = b * fb; + let wc = c * fc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xb = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if dist2(xb, xy) < 1e-5 * (1.0 + rr) { xb } else { xy } + } else { + xy + } + } else { + xy + }; + out.push(fact( + "布罗卡直径中点", + "X_{182}", + pt(xyu[0], xyu[1]), + None, + "X(182) = \\text{mid}(O,K);\\ \\text{bary }a\\cos(A-\\omega)", + "X(182):布罗卡直径中点(布罗卡圆圆心)", + ).with(Shape::Point { + x: xyu[0], + y: xyu[1], + label: "X182".into(), + })); + // On OK + let cross = (kpt[0] - circ[0]) * (xyu[1] - circ[1]) - (kpt[1] - circ[1]) * (xyu[0] - circ[0]); + let scale = (kpt[0] - circ[0]).abs() + (kpt[1] - circ[1]).abs() + + (xyu[0] - circ[0]).abs() + (xyu[1] - circ[1]).abs() + 1e-12; + if cross.abs() / scale < 1e-5 { + out.push(fact( + "布罗卡直径中点", + "X_{182}\\in OK", + "\\text{共线}".into(), + None, + "X(182)\\in OK", + "X(182) 在外心与勒莫恩点的连线上", + )); + } + } + // X(183): bary csc A cos(A−ω) + if area > 1e-12 && k_den > 1e-18 && sa.abs() > 1e-12 && sb.abs() > 1e-12 && sc.abs() > 1e-12 { + let tan_w = (4.0 * area) / k_den; + let sin_w = tan_w / (1.0 + tan_w * tan_w).sqrt(); + let cos_w = 1.0 / (1.0 + tan_w * tan_w).sqrt(); + let fa = (ca * cos_w + sa * sin_w) / sa; + let fb = (cb * cos_w + sb * sin_w) / sb; + let fc = (cc * cos_w + sc * sin_w) / sc; + let den = fa + fb + fc; + if den.abs() > 1e-12 && fa.is_finite() && fb.is_finite() && fc.is_finite() { + let xy = [ + (fa * pa[0] + fb * pb[0] + fc * pc[0]) / den, + (fa * pa[1] + fb * pb[1] + fc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push(fact( + "摩西布罗卡商", + "X_{183}", + pt(xy[0], xy[1]), + None, + "X(183) = X(75)/X(182)\\text{ trilinear quotient};\\ \\text{bary }\\csc A\\cos(A-\\omega)", + "X(183):摩西点与布罗卡直径中点的三线商", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X183".into(), + })); + } + } + } + // X(184): bary a³ cos A + { + let wa = a * a * a * ca; + let wb = b * b * b * cb; + let wc = c * c * c * cc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "准外心", + "X_{184}", + pt(xy[0], xy[1]), + None, + "X(184) = \\bigl(a^3\\cos A:\\cdots\\bigr)", + "X(184):准外心(垂足三角形的 X(63))", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X184".into(), + })); + } + } + // X(185): Nagel of orthic; skip right + if !rightish { + let wa = (2.0 * g[0]).sin() * (1.0 - ca * (g[1] - g[2]).cos()); + let wb = (2.0 * g[1]).sin() * (1.0 - cb * (g[2] - g[0]).cos()); + let wc = (2.0 * g[2]).sin() * (1.0 - cc * (g[0] - g[1]).cos()); + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push(fact( + "垂足奈格尔", + "X_{185}", + pt(xy[0], xy[1]), + None, + "X(185) = X(8)\\text{-of-orthic};\\ \\text{bary }(\\sin 2A)[1-\\cos A\\cos(B-C)]", + "X(185):垂足三角形的奈格尔点", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X185".into(), + })); + } + } + } + // X(186): circum-inverse of H; skip equilateral (H=O) + { + let oh2 = { + let dx = orth[0] - circ[0]; + let dy = orth[1] - circ[1]; + dx * dx + dy * dy + }; + if oh2 > 1e-12 { + let scale = (rr * rr) / oh2; + let mut xy = [ + circ[0] + scale * (orth[0] - circ[0]), + circ[1] + scale * (orth[1] - circ[1]), + ]; + // Prefer ETC bary when sec finite (non-right) + if !rightish { + let wa = sa * (4.0 * ca - 1.0 / ca); + let wb = sb * (4.0 * cb - 1.0 / cb); + let wc = sc * (4.0 * cc - 1.0 / cc); + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xb = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if dist2(xb, xy) < 1e-4 * (1.0 + rr) { + xy = xb; + } + } + } + out.push(fact( + "反演垂心", + "X_{186}", + pt(xy[0], xy[1]), + None, + "X(186) = O + R^2(H-O)/|OH|^2", + "X(186):垂心关于外接圆的反演点", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X186".into(), + })); + let cross = (orth[0] - circ[0]) * (xy[1] - circ[1]) - (orth[1] - circ[1]) * (xy[0] - circ[0]); + if cross.abs() < 1e-5 * (1.0 + oh2) * (1.0 + dist2(circ, xy)) { + out.push(fact( + "反演垂心", + "X_{186}\\in OH", + "\\text{共线}".into(), + None, + "X(186)\\in OH", + "X(186) 在欧拉线 OH 上", + )); + } + } + } + // X(187): Schoute = circum-inverse of K; skip equilateral (K=O → weights 0) + { + let wa = a * a * (2.0 * a * a - b * b - c * c); + let wb = b * b * (2.0 * b * b - c * c - a * a); + let wc = c * c * (2.0 * c * c - a * a - b * b); + let den = wa + wb + wc; + let ok2 = { + let dx = kpt[0] - circ[0]; + let dy = kpt[1] - circ[1]; + dx * dx + dy * dy + }; + if den.abs() > 1e-12 && ok2 > 1e-12 { + let xb = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + let scale = (rr * rr) / ok2; + let xg = [ + circ[0] + scale * (kpt[0] - circ[0]), + circ[1] + scale * (kpt[1] - circ[1]), + ]; + let xy = if dist2(xb, xg) < 1e-4 * (1.0 + rr) { xb } else { xg }; + out.push(fact( + "肖特中心", + "X_{187}", + pt(xy[0], xy[1]), + None, + "X(187) = O + R^2(K-O)/|OK|^2;\\ \\text{bary }a^2(2a^2-b^2-c^2)", + "X(187):肖特中心(勒莫恩点关于外接圆的反演)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X187".into(), + })); + let cross = (kpt[0] - circ[0]) * (xy[1] - circ[1]) - (kpt[1] - circ[1]) * (xy[0] - circ[0]); + let scale_c = (kpt[0] - circ[0]).abs() + (kpt[1] - circ[1]).abs() + + (xy[0] - circ[0]).abs() + (xy[1] - circ[1]).abs() + 1e-12; + if cross.abs() / scale_c < 1e-5 { + out.push(fact( + "肖特中心", + "X_{187}\\in OK", + "\\text{共线}".into(), + None, + "X(187)\\in OK", + "X(187) 在外心与勒莫恩点的连线上", + )); + } + } + } + // X(188): bary 2 cos(A/2) + { + let wa = 2.0 * (g[0] / 2.0).cos(); + let wb = 2.0 * (g[1] / 2.0).cos(); + let wc = 2.0 * (g[2] / 2.0).cos(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "反补第二中弧", + "X_{188}", + pt(xy[0], xy[1]), + None, + "X(188) = \\bigl(2\\cos\\tfrac{A}{2}:\\cdots\\bigr) = \\text{anticomplement of }X(178)", + "X(188):反补三角形的第二中弧点", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X188".into(), + })); + } + } + // X(189): cyclocevian conjugate of Nagel + { + let da = cb + cc - ca - 1.0; + let db = cc + ca - cb - 1.0; + let dc = ca + cb - cc - 1.0; + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + let wa = 1.0 / da; + let wb = 1.0 / db; + let wc = 1.0 / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push(fact( + "奈格尔圆塞瓦共轭", + "X_{189}", + pt(xy[0], xy[1]), + None, + "X(189) = \\text{cyclocevian of }X(8);\\ \\text{bary }1/(\\cos B+\\cos C-\\cos A-1)", + "X(189):奈格尔点的圆塞瓦共轭", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X189".into(), + })); + } + } + } + } + // X(190): Yff parabolic; skip isos/equil + if !isos { + let da = b - c; + let db = c - a; + let dc = a - b; + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + let wa = 1.0 / da; + let wb = 1.0 / db; + let wc = 1.0 / dc; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "伊夫抛物点", + "X_{190}", + pt(xy[0], xy[1]), + None, + "X(190) = \\bigl(1/(b-c):\\cdots\\bigr)", + "X(190):伊夫抛物点(切 BC/CA/AB 且焦点为 X(101) 的抛物线的切点塞瓦交点)", + ).with(Shape::Point { + x: xy[0], + y: xy[1], + label: "X190".into(), + })); + } + } + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -13439,6 +13792,116 @@ mod tests { assert!(fs4.iter().any(|f| f.group == "第二阿吉马-马尔法蒂" && f.label == "X_{180}")); } + #[test] + fn x182_to_x190_brocard_orthic_inverses() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x182 = fs.iter().find(|f| f.group == "布罗卡直径中点" && f.label == "X_{182}").expect("X182"); + let x183 = fs.iter().find(|f| f.group == "摩西布罗卡商" && f.label == "X_{183}").expect("X183"); + let x184 = fs.iter().find(|f| f.group == "准外心" && f.label == "X_{184}").expect("X184"); + let x185 = fs.iter().find(|f| f.group == "垂足奈格尔" && f.label == "X_{185}").expect("X185"); + let x186 = fs.iter().find(|f| f.group == "反演垂心" && f.label == "X_{186}").expect("X186"); + let x187 = fs.iter().find(|f| f.group == "肖特中心" && f.label == "X_{187}").expect("X187"); + let x188 = fs.iter().find(|f| f.group == "反补第二中弧" && f.label == "X_{188}").expect("X188"); + let x189 = fs.iter().find(|f| f.group == "奈格尔圆塞瓦共轭" && f.label == "X_{189}").expect("X189"); + let x190 = fs.iter().find(|f| f.group == "伊夫抛物点" && f.label == "X_{190}").expect("X190"); + assert!(fs.iter().any(|f| f.group == "布罗卡直径中点" && f.label.contains("OK"))); + assert!(fs.iter().any(|f| f.group == "反演垂心" && f.label.contains("OH"))); + assert!(fs.iter().any(|f| f.group == "肖特中心" && f.label.contains("OK"))); + let (p182x, p182y) = ptxy(x182); + assert!((p182x - 4.348993288590604).abs() < 1e-6 && (p182y - 1.6081112059420504).abs() < 1e-6, "X182 {:?}", (p182x, p182y)); + let (p183x, p183y) = ptxy(x183); + assert!((p183x - 3.819745041145412).abs() < 1e-6 && (p183y - 1.1780332020797852).abs() < 1e-6, "X183 {:?}", (p183x, p183y)); + let (p184x, p184y) = ptxy(x184); + assert!((p184x - 4.52074391988555).abs() < 1e-6 && (p184y - 1.41843166899728).abs() < 1e-6, "X184 {:?}", (p184x, p184y)); + let (p185x, p185y) = ptxy(x185); + assert!((p185x - 4.7109375).abs() < 1e-6 && (p185y - 1.5592792326137148).abs() < 1e-6, "X185 {:?}", (p185x, p185y)); + let (p186x, p186y) = ptxy(x186); + assert!((p186x - 7.014492753623188).abs() < 1e-6 && (p186y - 8.397076936125066).abs() < 1e-6, "X186 {:?}", (p186x, p186y)); + let (p187x, p187y) = ptxy(x187); + assert!((p187x - 10.577249575551782).abs() < 1e-6 && (p187y - 11.875395455433948).abs() < 1e-6, "X187 {:?}", (p187x, p187y)); + let (p188x, p188y) = ptxy(x188); + assert!((p188x - 4.181145447564104).abs() < 1e-6 && (p188y - 1.5551451021748157).abs() < 1e-6, "X188 {:?}", (p188x, p188y)); + let (p189x, p189y) = ptxy(x189); + assert!((p189x - 4.8141694490818026).abs() < 1e-6 && (p189y - 4.675948486953883).abs() < 1e-6, "X189 {:?}", (p189x, p189y)); + let (p190x, p190y) = ptxy(x190); + assert!((p190x - 0.5416666666666666).abs() < 1e-6 && (p190y - 3.38886042793149).abs() < 1e-6, "X190 {:?}", (p190x, p190y)); + // mid(O,K) for X182 + let o = fs.iter().find(|f| f.group == "特殊点" && f.label == "O").or_else(|| fs.iter().find(|f| f.label == "O")).expect("O"); + let kk = fs.iter().find(|f| f.group == "勒莫恩点" && f.label == "K").expect("K"); + let (ox, oy) = ptxy(o); + let (kx, ky) = ptxy(kk); + assert!((p182x - (ox + kx) / 2.0).abs() < 1e-6 && (p182y - (oy + ky) / 2.0).abs() < 1e-6); + + // Isosceles 5-5-6: X190 skips; others finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab) in [ + ("布罗卡直径中点", "X_{182}"), + ("摩西布罗卡商", "X_{183}"), + ("准外心", "X_{184}"), + ("垂足奈格尔", "X_{185}"), + ("反演垂心", "X_{186}"), + ("肖特中心", "X_{187}"), + ("反补第二中弧", "X_{188}"), + ("奈格尔圆塞瓦共轭", "X_{189}"), + ] { + assert!(fs2.iter().any(|f| f.group == grp && f.label == lab), "isos missing {} {}", grp, lab); + } + assert!(fs2.iter().all(|f| f.group != "伊夫抛物点"), "X190 skip isos"); + + // Equilateral: X182/183/184/185/188/189 → G; X186/187/190 skip. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (gx, gy) = ptxy(g3); + for (grp, lab) in [ + ("布罗卡直径中点", "X_{182}"), + ("摩西布罗卡商", "X_{183}"), + ("准外心", "X_{184}"), + ("垂足奈格尔", "X_{185}"), + ("反补第二中弧", "X_{188}"), + ("奈格尔圆塞瓦共轭", "X_{189}"), + ] { + let f = fs3.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!((x - gx).abs() < 1e-5 && (y - gy).abs() < 1e-5, "equilateral {} != G", lab); + } + assert!(fs3.iter().all(|f| f.group != "反演垂心"), "X186 skip equil"); + assert!(fs3.iter().all(|f| f.group != "肖特中心"), "X187 skip equil"); + assert!(fs3.iter().all(|f| f.group != "伊夫抛物点"), "X190 skip equil"); + + // Right 3-4-5: X185 skips; X186 = H (on circumcircle); others finite; X190 ok. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().any(|f| f.group == "布罗卡直径中点" && f.label == "X_{182}")); + assert!(fs4.iter().any(|f| f.group == "摩西布罗卡商" && f.label == "X_{183}")); + assert!(fs4.iter().any(|f| f.group == "准外心" && f.label == "X_{184}")); + assert!(fs4.iter().all(|f| f.group != "垂足奈格尔"), "X185 skip right"); + let x186r = fs4.iter().find(|f| f.group == "反演垂心" && f.label == "X_{186}").expect("X186 right"); + let h4 = fs4.iter().find(|f| f.group == "特殊点" && f.label == "H").or_else(|| fs4.iter().find(|f| f.label == "H")).expect("H"); + let (hx, hy) = ptxy(h4); + let (x6, y6) = ptxy(x186r); + assert!((x6 - hx).abs() < 1e-5 && (y6 - hy).abs() < 1e-5, "right X186 should = H"); + assert!(fs4.iter().any(|f| f.group == "肖特中心" && f.label == "X_{187}")); + assert!(fs4.iter().any(|f| f.group == "反补第二中弧" && f.label == "X_{188}")); + assert!(fs4.iter().any(|f| f.group == "奈格尔圆塞瓦共轭" && f.label == "X_{189}")); + assert!(fs4.iter().any(|f| f.group == "伊夫抛物点" && f.label == "X_{190}")); + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From c96208c446a64aa9aa0a6027d09da626274a2e2b Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 18:20:27 +0800 Subject: [PATCH 065/123] 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zNp10b5qMxLJf#)>nFDWw{Pb3Mb}Rf}4!k{5J|GdpS%9#!z(rsq*uyeLJIQd{AntuUOGaEJccLz0~NgvYkZ9}~j8K-5DZ zDZ~h3;)j-`z6U?@u+eQuubz^0i<1xRY`CEn-rj?Eonxd29z2dxZN(<--F4{{`Td8J2oT9E{xN{MRduehFpZzv+-K>%%t^ z|BY7sH~LtoS7NVAs6@sCjslf^xI53dE-NXVtu}r$qz3uU5fgS!+3$dzGxWPY)}K}z z{ao_EKK%WBe{=#tbJRIk7eKc$be;r zTOy3F^*Jzqcf0YVJg1j6Vu$e|8@B<{53v>j!jHAWpE@d_{PPi*PyDknbKHyI|I$&8 z@FT78Sw}g_zZ!w9&;M-fWYhkN3`|eB$Aq0jB|O2AU)oBZuv5OYxAp1k#&6eI2eRCA zTx~)dvdd?Ux!s+_+@EfZ>K4!9ey}aJbk4<)G%VWLPm?`ePNZePDYfxpSYCwu^S zpGT7BD=j0xmSTN6!#yOs%`>Cor4>l4M)A&j+(QC28S&CpB=wefsUuP!qzt4xknTg8 zgY-C3KGFuH%}BeEjv!Sdok#i}smF+TX*SX#q%}zR Date: Mon, 2 Nov 2026 18:24:43 +0800 Subject: [PATCH 066/123] =?UTF-8?q?feat:=20ETC=20X191=E2=80=93X200=20class?= =?UTF-8?q?ical=20Ceva-conjugate=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Fill next contiguous classical band after X190: X(191) Spieker-Ceva of I; X(192) I-Ceva of G (=anti Moses); X(193) H-Ceva of G (=anti X69); X(194) K-Ceva of G (=anti X76); X(195) nine-point-Ceva of O; X(196) Gergonne-Ceva of H (skip right); X(197) Nagel-Ceva of K; X(198) Mittenpunkt-Ceva of K (=isog X189); X(199) Spieker-Ceva of K; X(200) a(b+c−a)² harmonic. Acute/right/ equilateral/isosceles guards; prefer centers not already in geometry.rs. --- crates/mathcore/src/geometry.rs | 390 ++++++++++++++++++++++++++++++++ 1 file changed, 390 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 1142a2b..f9c9801 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -8726,6 +8726,310 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(191)–X(200): classical Ceva-conjugate band (ETC). + // X(191)=X(10)-Ceva of I; bary a·f, f=(b+c−a)(bc+ca+ab)+b³+c³−a³. + // X(192)=X(1)-Ceva of G = anticomplement of Moses; bary ab+ac−bc. + // X(193)=X(4)-Ceva of G = anticomplement of X(69); bary 3a²−b²−c². + // X(194)=X(6)-Ceva of G = anticomplement of X(76); bary a²(b²+c²)−b²c². + // X(195)=X(5)-Ceva of O; bary 4 cos 2A + cot² A − cot A cot ω. + // X(196)=X(7)-Ceva of H; bary (cos B+cos C−cos A−1) tan A tan(A/2); skip right. + // X(197)=X(8)-Ceva of K; bary a²(S−2a² tan(A/2)), S=∑a² tan(A/2). + // X(198)=X(9)-Ceva of K (=isogonal of X(189)); bary a²(cos B+cos C−cos A−1). + // X(199)=X(10)-Ceva of K; bary a²[b⁴+c⁴−a⁴+(b²+c²−a²)(bc+ca+ab)]. + // X(200)={X(8),X(78)}-harmonic of I; bary a(b+c−a)². + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let rightish = ca.abs() < 1e-12 || cb.abs() < 1e-12 || cc.abs() < 1e-12; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(191) + { + let f = |aa: f64, bb: f64, cc: f64| { + (bb + cc - aa) * (bb * cc + cc * aa + aa * bb) + bb * bb * bb + cc * cc * cc + - aa * aa * aa + }; + let wa = a * f(a, b, c); + let wb = b * f(b, c, a); + let wc = c * f(c, a, b); + push_bary( + &mut out, + "斯皮克内心塞瓦", + "X_{191}", + "X(191) = X(10)\\text{-Ceva of }X(1);\\ f=(b+c-a)(\\Sigma bc)+b^3+c^3-a^3", + "X(191):斯皮克点对内心的塞瓦共轭", + "X191", + wa, + wb, + wc, + ); + } + // X(192): anticomplement of Moses + { + let wa = a * b + a * c - b * c; + let wb = b * c + b * a - c * a; + let wc = c * a + c * b - a * b; + push_bary( + &mut out, + "内心重心塞瓦", + "X_{192}", + "X(192) = X(1)\\text{-Ceva of }X(2) = \\text{anticomplement of }X(75)", + "X(192):内心对重心的塞瓦共轭(摩西点的反补)", + "X192", + wa, + wb, + wc, + ); + if let Some(mo) = out.iter().rev().find(|f| f.group == "摩西点" && f.label == "Mo") { + if let Some(Shape::Point { x, y, .. }) = mo.shape.as_ref() { + let aq = [3.0 * centroid[0] - 2.0 * *x, 3.0 * centroid[1] - 2.0 * *y]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if dist2(xy, aq) < 1e-6 * (1.0 + rr) { + out.push(fact( + "内心重心塞瓦", + "X_{192}=\\mathrm{anti}(X_{75})", + "\\text{反补}".into(), + None, + "X(192) = 3G - 2\\,X(75)", + "X(192) 是摩西点关于重心的反补", + )); + } + } + } + } + } + // X(193): anticomplement of X(69) + { + let wa = 3.0 * a * a - b * b - c * c; + let wb = 3.0 * b * b - c * c - a * a; + let wc = 3.0 * c * c - a * a - b * b; + push_bary( + &mut out, + "垂心重心塞瓦", + "X_{193}", + "X(193) = X(4)\\text{-Ceva of }X(2);\\ \\text{bary }3a^2-b^2-c^2", + "X(193):垂心对重心的塞瓦共轭(余切点 X(69) 的反补)", + "X193", + wa, + wb, + wc, + ); + if let Some(x69) = out.iter().rev().find(|f| f.group == "余切点" && f.label == "X_{69}") { + if let Some(Shape::Point { x, y, .. }) = x69.shape.as_ref() { + let aq = [3.0 * centroid[0] - 2.0 * *x, 3.0 * centroid[1] - 2.0 * *y]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if dist2(xy, aq) < 1e-6 * (1.0 + rr) { + out.push(fact( + "垂心重心塞瓦", + "X_{193}=\\mathrm{anti}(X_{69})", + "\\text{反补}".into(), + None, + "X(193) = 3G - 2\\,X(69)", + "X(193) 是余切点关于重心的反补", + )); + } + } + } + } + } + // X(194): anticomplement of X(76) + { + let wa = a * a * b * b + a * a * c * c - b * b * c * c; + let wb = b * b * c * c + b * b * a * a - c * c * a * a; + let wc = c * c * a * a + c * c * b * b - a * a * b * b; + push_bary( + &mut out, + "勒莫恩重心塞瓦", + "X_{194}", + "X(194) = X(6)\\text{-Ceva of }X(2);\\ \\text{bary }a^2(b^2+c^2)-b^2c^2", + "X(194):勒莫恩点对重心的塞瓦共轭(第三布罗卡点的反补)", + "X194", + wa, + wb, + wc, + ); + if let Some(x76) = out + .iter() + .rev() + .find(|f| f.group == "第三布罗卡点" && f.label == "X_{76}") + { + if let Some(Shape::Point { x, y, .. }) = x76.shape.as_ref() { + let aq = [3.0 * centroid[0] - 2.0 * *x, 3.0 * centroid[1] - 2.0 * *y]; + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if dist2(xy, aq) < 1e-6 * (1.0 + rr) { + out.push(fact( + "勒莫恩重心塞瓦", + "X_{194}=\\mathrm{anti}(X_{76})", + "\\text{反补}".into(), + None, + "X(194) = 3G - 2\\,X(76)", + "X(194) 是第三布罗卡点关于重心的反补", + )); + } + } + } + } + } + // X(195): Iliev form with Brocard cot ω = (a²+b²+c²)/(4Δ) + if sa.abs() > 1e-12 && sb.abs() > 1e-12 && sc.abs() > 1e-12 && area > 1e-12 { + let cot_w = (a * a + b * b + c * c) / (4.0 * area); + let cot_a = ca / sa; + let cot_b = cb / sb; + let cot_c = cc / sc; + let wa = 4.0 * (2.0 * g[0]).cos() + cot_a * cot_a - cot_a * cot_w; + let wb = 4.0 * (2.0 * g[1]).cos() + cot_b * cot_b - cot_b * cot_w; + let wc = 4.0 * (2.0 * g[2]).cos() + cot_c * cot_c - cot_c * cot_w; + push_bary( + &mut out, + "九点外心塞瓦", + "X_{195}", + "X(195) = X(5)\\text{-Ceva of }X(3);\\ 4\\cos 2A+\\cot^2 A-\\cot A\\cot\\omega", + "X(195):九点中心对外心的塞瓦共轭", + "X195", + wa, + wb, + wc, + ); + } + // X(196): skip right (tan A → ∞) + if !rightish { + let g_a = (cb + cc - ca - 1.0) * g[0].tan() * (g[0] / 2.0).tan(); + let g_b = (cc + ca - cb - 1.0) * g[1].tan() * (g[1] / 2.0).tan(); + let g_c = (ca + cb - cc - 1.0) * g[2].tan() * (g[2] / 2.0).tan(); + push_bary( + &mut out, + "格尔巩垂心塞瓦", + "X_{196}", + "X(196) = X(7)\\text{-Ceva of }X(4);\\ (\\cos B+\\cos C-\\cos A-1)\\tan A\\tan\\tfrac{A}{2}", + "X(196):格尔巩点对垂心的塞瓦共轭", + "X196", + g_a, + g_b, + g_c, + ); + } + // X(197) + { + let t_a = (g[0] / 2.0).tan(); + let t_b = (g[1] / 2.0).tan(); + let t_c = (g[2] / 2.0).tan(); + let sum = a * a * t_a + b * b * t_b + c * c * t_c; + let wa = a * a * (sum - 2.0 * a * a * t_a); + let wb = b * b * (sum - 2.0 * b * b * t_b); + let wc = c * c * (sum - 2.0 * c * c * t_c); + push_bary( + &mut out, + "奈格尔勒莫恩塞瓦", + "X_{197}", + "X(197) = X(8)\\text{-Ceva of }X(6);\\ a^2(S-2a^2\\tan\\tfrac{A}{2})", + "X(197):奈格尔点对勒莫恩点的塞瓦共轭", + "X197", + wa, + wb, + wc, + ); + } + // X(198): isogonal of X(189) + { + let da = cb + cc - ca - 1.0; + let db = cc + ca - cb - 1.0; + let dc = ca + cb - cc - 1.0; + let wa = a * a * da; + let wb = b * b * db; + let wc = c * c * dc; + push_bary( + &mut out, + "米滕阿列夫勒莫恩塞瓦", + "X_{198}", + "X(198) = X(9)\\text{-Ceva of }X(6) = \\text{isogonal of }X(189)", + "X(198):米滕阿列夫点对勒莫恩点的塞瓦共轭(X(189) 的等角共轭)", + "X198", + wa, + wb, + wc, + ); + } + // X(199) + { + let f = |aa: f64, bb: f64, cc: f64| { + let b2 = bb * bb; + let c2 = cc * cc; + let a2 = aa * aa; + aa * (b2 * b2 + c2 * c2 - a2 * a2 + (b2 + c2 - a2) * (bb * cc + cc * aa + aa * bb)) + }; + let wa = a * f(a, b, c); + let wb = b * f(b, c, a); + let wc = c * f(c, a, b); + push_bary( + &mut out, + "斯皮克莱莫恩塞瓦", + "X_{199}", + "X(199) = X(10)\\text{-Ceva of }X(6);\\ a[b^4+c^4-a^4+(b^2+c^2-a^2)\\Sigma bc]", + "X(199):斯皮克点对勒莫恩点的塞瓦共轭", + "X199", + wa, + wb, + wc, + ); + } + // X(200) + { + let wa = a * (b + c - a) * (b + c - a); + let wb = b * (c + a - b) * (c + a - b); + let wc = c * (a + b - c) * (a + b - c); + push_bary( + &mut out, + "半周长平方点", + "X_{200}", + "X(200) = \\bigl(a(b+c-a)^2:\\cdots\\bigr) = \\{X(8),X(78)\\}\\text{-harmonic of }X(1)", + "X(200):半周长平方点(奈格尔与 X(78) 关于内心的调和共轭)", + "X200", + wa, + wb, + wc, + ); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -13902,6 +14206,92 @@ mod tests { assert!(fs4.iter().any(|f| f.group == "伊夫抛物点" && f.label == "X_{190}")); } + #[test] + fn x191_to_x200_ceva_conjugates() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("斯皮克内心塞瓦", "X_{191}", 3.9126984126984126, 1.1373046334101145), + ("内心重心塞瓦", "X_{192}", 4.783390410958904, 2.1586576698467708), + ("垂心重心塞瓦", "X_{193}", 5.979446308724833, 3.6504167696845915), + ("勒莫恩重心塞瓦", "X_{194}", 5.3385272071071626, 2.5938612436999215), + ("九点外心塞瓦", "X_{195}", 5.197905759162303, 2.661476304367596), + ("格尔巩垂心塞瓦", "X_{196}", 4.508977844505761, 0.46286739978970115), + ("奈格尔勒莫恩塞瓦", "X_{197}", 3.52023988005997, -0.6271097472119954), + ("米滕阿列夫勒莫恩塞瓦", "X_{198}", 3.803825404610103, 0.15955399758775038), + ("斯皮克莱莫恩塞瓦", "X_{199}", 3.856005538248529, 0.681023032147237), + ("半周长平方点", "X_{200}", 3.6020408163265305, 0.9880059556651574), + ]; + for (grp, lab, ex, ey) in want { + let f = fs.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!((x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, "{} {:?} want {:?}", lab, (x, y), (ex, ey)); + } + assert!(fs.iter().any(|f| f.group == "内心重心塞瓦" && f.label.contains("anti"))); + assert!(fs.iter().any(|f| f.group == "垂心重心塞瓦" && f.label.contains("anti"))); + assert!(fs.iter().any(|f| f.group == "勒莫恩重心塞瓦" && f.label.contains("anti"))); + // Anticomplement Cartesian: 3G − 2P. + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let mo = fs.iter().find(|f| f.group == "摩西点" && f.label == "Mo").expect("Mo"); + let x69 = fs.iter().find(|f| f.group == "余切点" && f.label == "X_{69}").expect("X69"); + let x76 = fs.iter().find(|f| f.group == "第三布罗卡点" && f.label == "X_{76}").expect("X76"); + let (gx, gy) = ptxy(g); + let x192 = fs.iter().find(|f| f.group == "内心重心塞瓦" && f.label == "X_{192}").unwrap(); + let x193 = fs.iter().find(|f| f.group == "垂心重心塞瓦" && f.label == "X_{193}").unwrap(); + let x194 = fs.iter().find(|f| f.group == "勒莫恩重心塞瓦" && f.label == "X_{194}").unwrap(); + let (mox, moy) = ptxy(mo); + let (p69x, p69y) = ptxy(x69); + let (p76x, p76y) = ptxy(x76); + let (p192x, p192y) = ptxy(x192); + let (p193x, p193y) = ptxy(x193); + let (p194x, p194y) = ptxy(x194); + assert!((p192x - (3.0 * gx - 2.0 * mox)).abs() < 1e-6 && (p192y - (3.0 * gy - 2.0 * moy)).abs() < 1e-6); + assert!((p193x - (3.0 * gx - 2.0 * p69x)).abs() < 1e-6 && (p193y - (3.0 * gy - 2.0 * p69y)).abs() < 1e-6); + assert!((p194x - (3.0 * gx - 2.0 * p76x)).abs() < 1e-6 && (p194y - (3.0 * gy - 2.0 * p76y)).abs() < 1e-6); + + // Isosceles 5-5-6: all finite (incl. X196). + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!(fs2.iter().any(|f| f.group == grp && f.label == lab), "isos missing {} {}", grp, lab); + } + + // Equilateral: all → G; X196 present (not right). + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (gx3, gy3) = ptxy(g3); + for (grp, lab, ..) in want { + let f = fs3.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("equil missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!((x - gx3).abs() < 1e-5 && (y - gy3).abs() < 1e-5, "equilateral {} != G {:?}", lab, (x, y)); + } + + // Right 3-4-5: X196 skips; others finite. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for (grp, lab, ..) in want { + if grp == "格尔巩垂心塞瓦" { + assert!(fs4.iter().all(|f| f.group != grp), "X196 should skip right"); + } else { + assert!(fs4.iter().any(|f| f.group == grp && f.label == lab), "right missing {} {}", grp, lab); + } + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 183b6272d2b416bef3b9cac90c6bfba3708e1b98 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 18:24:43 +0800 Subject: [PATCH 067/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X191=E2=80=93X200=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 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=?UTF-8?q?12;=20X(202)=20I-Ceva=20of=201st=20isodynamic;=20X(203)=20I-Cev?= =?UTF-8?q?a=20of=202nd=20isodynamic=20(skip=20equil);=20X(204)=20I-Ceva?= =?UTF-8?q?=20of=20Clawson=20(skip=20right);=20X(205)=20Mittenpunkt-Ceva?= =?UTF-8?q?=20of=202nd=20power;=20X(206)=20G-Ceva=20of=203rd=20power=20(?= =?UTF-8?q?=3Dcomp=20X66;=20=E2=88=9E=20on=20right);=20X(207)/X(208)=20I/H?= =?UTF-8?q?-Ceva=20of=20X34=20(skip=20right);=20X(209)=20H-Ceva=20of=20Gre?= =?UTF-8?q?enberg;=20X(210)=20Spieker-Ceva=20of=20Greenberg.=20Acute/right?= =?UTF-8?q?/equilateral/isosceles=20guards;=20prefer=20centers=20not=20alr?= =?UTF-8?q?eady=20in=20geometry.rs.?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- crates/mathcore/src/geometry.rs | 388 ++++++++++++++++++++++++++++++++ 1 file changed, 388 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index f9c9801..a320d09 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -9030,6 +9030,310 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(201)–X(210): next classical Ceva-conjugate band (ETC). + // X(201)=X(10)-Ceva of X(12); bary (sin 2A)[1+cos(B−C)]. + // X(202)=X(1)-Ceva of X(15); bary sin A·u(v+w−u), u=sin(A+π/3). + // X(203)=X(1)-Ceva of X(16); same with u=sin(A−π/3); skip equil. + // X(204)=X(1)-Ceva of X(19); bary sin A·tan A(tan B+tan C−tan A); skip right. + // X(205)=X(9)-Ceva of X(31); bary a³[b²tan(B/2)+c²tan(C/2)−a²tan(A/2)]. + // X(206)=X(2)-Ceva of X(32)=complement of X(66)=mid(K,X159); bary a⁴(b⁴+c⁴−a⁴); ∞ on right. + // X(207)=X(1)-Ceva of X(34); bary sin A(1−sec A)(sec B+sec C−sec A−1); skip right. + // X(208)=X(4)-Ceva of X(34); bary sin A(1−sec A)(cos B+cos C−cos A−1); skip right. + // X(209)=X(4)-Ceva of X(37); bary sin A(sin B+sin C)[sin A+sin(A−B)+sin(A−C)]. + // X(210)=X(10)-Ceva of X(37); bary a(b+c)(b+c−a). + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let rightish = ca.abs() < 1e-12 || cb.abs() < 1e-12 || cc.abs() < 1e-12; + let equil = (a - b).abs() < 1e-12 && (b - c).abs() < 1e-12; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(201) + { + let wa = (2.0 * g[0]).sin() * (1.0 + (g[1] - g[2]).cos()); + let wb = (2.0 * g[1]).sin() * (1.0 + (g[2] - g[0]).cos()); + let wc = (2.0 * g[2]).sin() * (1.0 + (g[0] - g[1]).cos()); + push_bary( + &mut out, + "斯皮克费尔巴哈调和塞瓦", + "X_{201}", + "X(201) = X(10)\\text{-Ceva of }X(12);\\ (\\sin 2A)[1+\\cos(B-C)]", + "X(201):斯皮克点对费尔巴哈调和共轭点的塞瓦共轭", + "X201", + wa, + wb, + wc, + ); + } + // X(202): I-Ceva of 1st isodynamic + { + let ua = (g[0] + PI / 3.0).sin(); + let ub = (g[1] + PI / 3.0).sin(); + let uc = (g[2] + PI / 3.0).sin(); + let wa = sa * ua * (ub + uc - ua); + let wb = sb * ub * (uc + ua - ub); + let wc = sc * uc * (ua + ub - uc); + push_bary( + &mut out, + "内心第一等动力塞瓦", + "X_{202}", + "X(202) = X(1)\\text{-Ceva of }X(15);\\ u=\\sin(A+\\pi/3)", + "X(202):内心对第一等动力点的塞瓦共轭", + "X202", + wa, + wb, + wc, + ); + } + // X(203): skip equilateral (sin(A−π/3)=0) + if !equil { + let ua = (g[0] - PI / 3.0).sin(); + let ub = (g[1] - PI / 3.0).sin(); + let uc = (g[2] - PI / 3.0).sin(); + let wa = sa * ua * (ub + uc - ua); + let wb = sb * ub * (uc + ua - ub); + let wc = sc * uc * (ua + ub - uc); + push_bary( + &mut out, + "内心第二等动力塞瓦", + "X_{203}", + "X(203) = X(1)\\text{-Ceva of }X(16);\\ u=\\sin(A-\\pi/3)", + "X(203):内心对第二等动力点的塞瓦共轭", + "X203", + wa, + wb, + wc, + ); + } + // X(204): skip right (tan A → ∞) + if !rightish { + let ta = g[0].tan(); + let tb = g[1].tan(); + let tc = g[2].tan(); + let wa = sa * ta * (tb + tc - ta); + let wb = sb * tb * (tc + ta - tb); + let wc = sc * tc * (ta + tb - tc); + push_bary( + &mut out, + "内心克劳森塞瓦", + "X_{204}", + "X(204) = X(1)\\text{-Ceva of }X(19);\\ \\tan A(\\tan B+\\tan C-\\tan A)", + "X(204):内心对克劳森点的塞瓦共轭", + "X204", + wa, + wb, + wc, + ); + } + // X(205) + { + let t_a = (g[0] / 2.0).tan(); + let t_b = (g[1] / 2.0).tan(); + let t_c = (g[2] / 2.0).tan(); + let f = |aa: f64, bb: f64, cc: f64, ta: f64, tb: f64, tc: f64| { + aa * aa * (bb * bb * tb + cc * cc * tc - aa * aa * ta) + }; + let wa = a * f(a, b, c, t_a, t_b, t_c); + let wb = b * f(b, c, a, t_b, t_c, t_a); + let wc = c * f(c, a, b, t_c, t_a, t_b); + push_bary( + &mut out, + "米滕第二幂点塞瓦", + "X_{205}", + "X(205) = X(9)\\text{-Ceva of }X(31);\\ a^3[b^2\\tan\\tfrac{B}{2}+c^2\\tan\\tfrac{C}{2}-a^2\\tan\\tfrac{A}{2}]", + "X(205):米滕阿列夫点对第二幂点的塞瓦共轭", + "X205", + wa, + wb, + wc, + ); + } + // X(206): complement of X(66) = mid(K, X159) + { + let a2 = a * a; + let b2 = b * b; + let c2 = c * c; + let a4 = a2 * a2; + let b4 = b2 * b2; + let c4 = c2 * c2; + let wa = a4 * (b4 + c4 - a4); + let wb = b4 * (c4 + a4 - b4); + let wc = c4 * (a4 + b4 - c4); + push_bary( + &mut out, + "重心第三幂点塞瓦", + "X_{206}", + "X(206) = X(2)\\text{-Ceva of }X(32) = \\mathrm{comp}(X_{66});\\ a^4(b^4+c^4-a^4)", + "X(206):重心对第三幂点的塞瓦共轭(X(66) 的补点;K 与 X(159) 中点)", + "X206", + wa, + wb, + wc, + ); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if let Some(x66) = out + .iter() + .rev() + .find(|f| f.label == "X_{66}") + .and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some([*x, *y]), + _ => None, + }) + { + let comp = [ + (3.0 * centroid[0] - x66[0]) / 2.0, + (3.0 * centroid[1] - x66[1]) / 2.0, + ]; + if dist2(xy, comp) < 1e-6 * (1.0 + rr) { + out.push(fact( + "重心第三幂点塞瓦", + "X_{206}=\\mathrm{comp}(X_{66})", + "\\text{补点}".into(), + None, + "X(206) = (3G - X(66))/2", + "X(206) 是 X(66) 关于重心的补点", + )); + } + } + if let (Some(kxy), Some(x159)) = ( + out.iter() + .rev() + .find(|f| f.group == "勒莫恩点" && f.label == "K") + .and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some([*x, *y]), + _ => None, + }), + out.iter() + .rev() + .find(|f| f.label == "X_{159}") + .and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some([*x, *y]), + _ => None, + }), + ) { + let mid = [(kxy[0] + x159[0]) / 2.0, (kxy[1] + x159[1]) / 2.0]; + if dist2(xy, mid) < 1e-6 * (1.0 + rr) { + out.push(fact( + "重心第三幂点塞瓦", + "X_{206}=\\mathrm{mid}(K,X_{159})", + "\\text{中点}".into(), + None, + "X(206) = \\mathrm{mid}(X(6),X(159))", + "X(206) 是勒莫恩点与 X(159) 的中点", + )); + } + } + } + } + // X(207): skip right + if !rightish && ca.abs() > 1e-12 && cb.abs() > 1e-12 && cc.abs() > 1e-12 { + let seca = 1.0 / ca; + let secb = 1.0 / cb; + let secc = 1.0 / cc; + let wa = sa * (1.0 - seca) * (secb + secc - seca - 1.0); + let wb = sb * (1.0 - secb) * (secc + seca - secb - 1.0); + let wc = sc * (1.0 - secc) * (seca + secb - secc - 1.0); + push_bary( + &mut out, + "内心X34塞瓦", + "X_{207}", + "X(207) = X(1)\\text{-Ceva of }X(34);\\ (1-\\sec A)(\\sec B+\\sec C-\\sec A-1)", + "X(207):内心对 X(34) 的塞瓦共轭", + "X207", + wa, + wb, + wc, + ); + } + // X(208): skip right + if !rightish && ca.abs() > 1e-12 && cb.abs() > 1e-12 && cc.abs() > 1e-12 { + let seca = 1.0 / ca; + let secb = 1.0 / cb; + let secc = 1.0 / cc; + let wa = sa * (1.0 - seca) * (cb + cc - ca - 1.0); + let wb = sb * (1.0 - secb) * (cc + ca - cb - 1.0); + let wc = sc * (1.0 - secc) * (ca + cb - cc - 1.0); + push_bary( + &mut out, + "垂心X34塞瓦", + "X_{208}", + "X(208) = X(4)\\text{-Ceva of }X(34);\\ (1-\\sec A)(\\cos B+\\cos C-\\cos A-1)", + "X(208):垂心对 X(34) 的塞瓦共轭", + "X208", + wa, + wb, + wc, + ); + } + // X(209) + { + let fa = (sb + sc) * (sa + (g[0] - g[1]).sin() + (g[0] - g[2]).sin()); + let fb = (sc + sa) * (sb + (g[1] - g[2]).sin() + (g[1] - g[0]).sin()); + let fc = (sa + sb) * (sc + (g[2] - g[0]).sin() + (g[2] - g[1]).sin()); + let wa = sa * fa; + let wb = sb * fb; + let wc = sc * fc; + push_bary( + &mut out, + "垂心格林伯格塞瓦", + "X_{209}", + "X(209) = X(4)\\text{-Ceva of }X(37);\\ (\\sin B+\\sin C)[\\sin A+\\sin(A-B)+\\sin(A-C)]", + "X(209):垂心对格林伯格点的塞瓦共轭", + "X209", + wa, + wb, + wc, + ); + } + // X(210) + { + let wa = a * (b + c) * (b + c - a); + let wb = b * (c + a) * (c + a - b); + let wc = c * (a + b) * (a + b - c); + push_bary( + &mut out, + "斯皮克格林伯格塞瓦", + "X_{210}", + "X(210) = X(10)\\text{-Ceva of }X(37);\\ a(b+c)(b+c-a)", + "X(210):斯皮克点对格林伯格点的塞瓦共轭(X(8) 与 X(9) 的截点)", + "X210", + wa, + wb, + wc, + ); + } + } + + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -14292,6 +14596,90 @@ mod tests { } } + #[test] + fn x201_to_x210_ceva_conjugates() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("斯皮克费尔巴哈调和塞瓦", "X_{201}", 3.941144708423327, 1.0602605596798922), + ("内心第一等动力塞瓦", "X_{202}", 4.675197482892764, 2.1984959377388735), + ("内心第二等动力塞瓦", "X_{203}", 3.1297393021764734, 3.220416341963739), + ("内心克劳森塞瓦", "X_{204}", 4.230629739531817, -7.044283755144491), + ("米滕第二幂点塞瓦", "X_{205}", 3.836927177664627, -0.800458028153725), + ("重心第三幂点塞瓦", "X_{206}", 4.035459211140222, -0.6761005992159091), + ("内心X34塞瓦", "X_{207}", 4.427586630119051, 13.822429272105595), + ("垂心X34塞瓦", "X_{208}", 4.782730514518593, 0.553424263174315), + ("垂心格林伯格塞瓦", "X_{209}", 5.629901960784314, 3.578712552745579), + ("斯皮克格林伯格塞瓦", "X_{210}", 3.9635416666666665, 1.3111662369973027), + ]; + for (grp, lab, ex, ey) in want { + let f = fs.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!((x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, "{} {:?} want {:?}", lab, (x, y), (ex, ey)); + } + assert!(fs.iter().any(|f| f.group == "重心第三幂点塞瓦" && f.label.contains("comp"))); + assert!(fs.iter().any(|f| f.group == "重心第三幂点塞瓦" && f.label.contains("mid"))); + // Complement Cartesian: (3G − X66)/2. + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let x66 = fs.iter().find(|f| f.label == "X_{66}").expect("X66"); + let x206 = fs.iter().find(|f| f.group == "重心第三幂点塞瓦" && f.label == "X_{206}").unwrap(); + let (gx, gy) = ptxy(g); + let (p66x, p66y) = ptxy(x66); + let (p206x, p206y) = ptxy(x206); + assert!((p206x - (3.0 * gx - p66x) / 2.0).abs() < 1e-6 && (p206y - (3.0 * gy - p66y) / 2.0).abs() < 1e-6); + + // Isosceles 5-5-6: all finite (incl. X203/X204). + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!(fs2.iter().any(|f| f.group == grp && f.label == lab), "isos missing {} {}", grp, lab); + } + + // Equilateral: X203 skips; others → G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (gx3, gy3) = ptxy(g3); + assert!(fs3.iter().all(|f| f.group != "内心第二等动力塞瓦"), "X203 should skip equil"); + for (grp, lab, ..) in want { + if grp == "内心第二等动力塞瓦" { + continue; + } + let f = fs3.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("equil missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!((x - gx3).abs() < 1e-5 && (y - gy3).abs() < 1e-5, "equilateral {} != G {:?}", lab, (x, y)); + } + + // Right 3-4-5: X204/X207/X208 skip; others finite (X203 ok). + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for (grp, lab, ..) in want { + // X204/X207/X208: tan/sec → ∞. X206: bary sum vanishes (point at ∞). + if grp == "内心克劳森塞瓦" + || grp == "内心X34塞瓦" + || grp == "垂心X34塞瓦" + || grp == "重心第三幂点塞瓦" + { + assert!(fs4.iter().all(|f| !(f.group == grp && f.label == lab)), "{} should skip right", lab); + } else { + assert!(fs4.iter().any(|f| f.group == grp && f.label == lab), "right missing {} {}", grp, lab); + } + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From cd5f8822d1ca1d1df4824331053b4c152f42c4f8 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 18:27:55 +0800 Subject: [PATCH 069/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X201=E2=80=93X210=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 789021 -> 793650 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git 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076/123] =?UTF-8?q?feat:=20ETC=20X241=E2=80=93X250=20line?= =?UTF-8?q?=20conjugates=20and=20isogonals?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(241)–X(248) remaining line-conjugate band and X(249)/X(250) isogonals of X(115)/X(125) with acute/right/equilateral/isosceles guards. --- crates/mathcore/src/geometry.rs | 417 ++++++++++++++++++++++++++++++++ 1 file changed, 417 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 20ee323..d9b9957 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -10279,6 +10279,319 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(241)–X(250): finish line-conjugate band + first isogonals (ETC). + // X(241)=X(1)-line conjugate of X(55); f=cos⁴(B/2)−cos²(A/2)(cos²(B/2)+cos²(C/2))+cos⁴(C/2); skip equil. + // X(242)=X(4)-line conjugate of X(71); f=sec A(sin²A−sin B sin C); skip right/equil. + // X(243)=X(4)-line conjugate of X(73); f=sec A(cos²A−cos B cos C); skip right/equil. + // X(244)=X(1)-line conjugate of X(100); f=[1−cos(B−C)]sin²(A/2); skip equil. + // X(245)=X(1)-line conjugate of X(110); csc-diff form; skip isos (csc→∞). + // X(246)=X(3)-line conjugate of X(110); csc/cos form; skip isos. + // X(247)=X(4)-line conjugate of X(110); csc/sec form; skip isos/right. + // X(248)=X(4)-line conjugate of X(132); bary sin A sin 2A sec(A+ω); skip equil (A+ω→π/2). + // X(249)=isogonal of X(115); bary cos²(B−C); →G on equil. + // X(250)=isogonal of X(125); bary tan A csc²(B−C); skip right/isos. + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let equil = (a - b).abs() < 1e-12 && (b - c).abs() < 1e-12; + let isos = (a - b).abs() < 1e-12 || (b - c).abs() < 1e-12 || (c - a).abs() < 1e-12; + let right = ca.abs() < 1e-9 || cb.abs() < 1e-9 || cc.abs() < 1e-9; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(241): skip equilateral (weights→0); on IO + if !equil { + let f = |aa: f64, bb: f64, cc: f64| { + let cah2 = (aa * 0.5).cos().powi(2); + let cbh2 = (bb * 0.5).cos().powi(2); + let cch2 = (cc * 0.5).cos().powi(2); + cbh2 * cbh2 - cah2 * (cbh2 + cch2) + cch2 * cch2 + }; + let wa = sa * f(g[0], g[1], g[2]); + let wb = sb * f(g[1], g[2], g[0]); + let wc = sc * f(g[2], g[0], g[1]); + push_bary( + &mut out, + "内心X55线共轭", + "X_{241}", + "X(241) = X(1)\\text{-line conjugate of }X(55);\\ (\\sin A)f,\\ f=\\cos^4\\tfrac{B}{2}-\\cdots", + "X(241):内心对 X(55) 的线共轭", + "X241", + wa, + wb, + wc, + ); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if circ[0].is_finite() + && circ[1].is_finite() + && inc[0].is_finite() + && inc[1].is_finite() + { + let cross = (xy[0] - inc[0]) * (circ[1] - inc[1]) + - (xy[1] - inc[1]) * (circ[0] - inc[0]); + if cross.abs() < 1e-6 * (1.0 + rr) { + out.push(fact( + "内心X55线共轭", + "X_{241}\\in IO", + "\\text{共线}".into(), + None, + "X(241)\\in IO", + "X(241) 在内心–外心连线上", + )); + } + } + } + } + // X(242): skip right (sec) and equilateral + if !right && !equil { + let f = |aa: f64, bb: f64, cc: f64| { + let caa = aa.cos(); + if caa.abs() < 1e-12 { + return f64::NAN; + } + (aa.sin().powi(2) - bb.sin() * cc.sin()) / caa + }; + push_bary( + &mut out, + "垂心X71线共轭", + "X_{242}", + "X(242) = X(4)\\text{-line conjugate of }X(71);\\ (\\sin A)\\sec A(\\sin^2 A-\\sin B\\sin C)", + "X(242):垂心对 X(71) 的线共轭", + "X242", + sa * f(g[0], g[1], g[2]), + sb * f(g[1], g[2], g[0]), + sc * f(g[2], g[0], g[1]), + ); + } + // X(243): skip right/equilateral + if !right && !equil { + let f = |aa: f64, bb: f64, cc: f64| { + let caa = aa.cos(); + if caa.abs() < 1e-12 { + return f64::NAN; + } + (caa * caa - bb.cos() * cc.cos()) / caa + }; + push_bary( + &mut out, + "垂心X73线共轭", + "X_{243}", + "X(243) = X(4)\\text{-line conjugate of }X(73);\\ (\\sin A)\\sec A(\\cos^2 A-\\cos B\\cos C)", + "X(243):垂心对 X(73) 的线共轭", + "X243", + sa * f(g[0], g[1], g[2]), + sb * f(g[1], g[2], g[0]), + sc * f(g[2], g[0], g[1]), + ); + } + // X(244): skip equilateral + if !equil { + let f = |aa: f64, bb: f64, cc: f64| { + (1.0 - (bb - cc).cos()) * (aa * 0.5).sin().powi(2) + }; + push_bary( + &mut out, + "内心X100线共轭", + "X_{244}", + "X(244) = X(1)\\text{-line conjugate of }X(100);\\ (\\sin A)[1-\\cos(B-C)]\\sin^2\\tfrac{A}{2}", + "X(244):内心对 X(100) 的线共轭", + "X244", + sa * f(g[0], g[1], g[2]), + sb * f(g[1], g[2], g[0]), + sc * f(g[2], g[0], g[1]), + ); + } + // X(245): skip isosceles (angle-diff csc) + if !isos { + let f = |aa: f64, bb: f64, cc: f64| { + let d_ca = (cc - aa).sin(); + let d_cb = (cc - bb).sin(); + let d_ab = (aa - bb).sin(); + let d_ba = (bb - aa).sin(); + if d_ca.abs() < 1e-12 || d_cb.abs() < 1e-12 || d_ab.abs() < 1e-12 || d_ba.abs() < 1e-12 + { + return f64::NAN; + } + let csc_ca = 1.0 / d_ca; + let csc_cb = 1.0 / d_cb; + let csc_ab = 1.0 / d_ab; + let csc_ba = 1.0 / d_ba; + csc_ca * csc_ca + csc_cb * (csc_ca - csc_ba) + csc_ab * csc_ab + }; + push_bary( + &mut out, + "内心X110线共轭", + "X_{245}", + "X(245) = X(1)\\text{-line conjugate of }X(110);\\ \\csc\\text{-diff form}", + "X(245):内心对 X(110) 的线共轭", + "X245", + sa * f(g[0], g[1], g[2]), + sb * f(g[1], g[2], g[0]), + sc * f(g[2], g[0], g[1]), + ); + } + // X(246): skip isosceles + if !isos { + let f = |aa: f64, bb: f64, cc: f64| { + let d_ba = (bb - aa).sin(); + let d_bc = (bb - cc).sin(); + let d_ca = (cc - aa).sin(); + let d_cb = (cc - bb).sin(); + if d_ba.abs() < 1e-12 || d_bc.abs() < 1e-12 || d_ca.abs() < 1e-12 || d_cb.abs() < 1e-12 + { + return f64::NAN; + } + let csc_ba = 1.0 / d_ba; + let csc_bc = 1.0 / d_bc; + let csc_ca = 1.0 / d_ca; + let csc_cb = 1.0 / d_cb; + let u = aa.cos() * csc_ca + bb.cos() * csc_cb; + csc_ba * (aa.cos() * csc_ba + cc.cos() * csc_bc) - csc_ca * u + }; + push_bary( + &mut out, + "外心X110线共轭", + "X_{246}", + "X(246) = X(3)\\text{-line conjugate of }X(110);\\ \\csc/\\cos\\text{ form}", + "X(246):外心对 X(110) 的线共轭", + "X246", + sa * f(g[0], g[1], g[2]), + sb * f(g[1], g[2], g[0]), + sc * f(g[2], g[0], g[1]), + ); + } + // X(247): skip isosceles and right (sec) + if !isos && !right { + let f = |aa: f64, bb: f64, cc: f64| { + let caa = aa.cos(); + let cbb = bb.cos(); + let ccc = cc.cos(); + if caa.abs() < 1e-12 || cbb.abs() < 1e-12 || ccc.abs() < 1e-12 { + return f64::NAN; + } + let d_ba = (bb - aa).sin(); + let d_bc = (bb - cc).sin(); + let d_ca = (cc - aa).sin(); + let d_cb = (cc - bb).sin(); + if d_ba.abs() < 1e-12 || d_bc.abs() < 1e-12 || d_ca.abs() < 1e-12 || d_cb.abs() < 1e-12 + { + return f64::NAN; + } + let csc_ba = 1.0 / d_ba; + let csc_bc = 1.0 / d_bc; + let csc_ca = 1.0 / d_ca; + let csc_cb = 1.0 / d_cb; + let seca = 1.0 / caa; + let secb = 1.0 / cbb; + let secc = 1.0 / ccc; + let u = seca * csc_ca + secb * csc_cb; + csc_ba * (seca * csc_ba + secc * csc_bc) - csc_ca * u + }; + push_bary( + &mut out, + "垂心X110线共轭", + "X_{247}", + "X(247) = X(4)\\text{-line conjugate of }X(110);\\ \\csc/\\sec\\text{ form}", + "X(247):垂心对 X(110) 的线共轭", + "X247", + sa * f(g[0], g[1], g[2]), + sb * f(g[1], g[2], g[0]), + sc * f(g[2], g[0], g[1]), + ); + } + // X(248): skip equilateral (A+ω→π/2) + if !equil && area > 1e-12 { + let sum_sq = a * a + b * b + c * c; + let tan_w = (4.0 * area) / sum_sq; + let cos_w = 1.0 / (1.0 + tan_w * tan_w).sqrt(); + let sin_w = tan_w * cos_w; + let f = |aa: f64, saa: f64, caa: f64| { + let caw = caa * cos_w - saa * sin_w; + if caw.abs() < 1e-12 { + return f64::NAN; + } + saa * (2.0 * aa).sin() / caw + }; + push_bary( + &mut out, + "垂心X132线共轭", + "X_{248}", + "X(248) = X(4)\\text{-line conjugate of }X(132);\\ \\sin A\\sin 2A\\sec(A+\\omega)", + "X(248):垂心对 X(132) 的线共轭", + "X248", + f(g[0], sa, ca), + f(g[1], sb, cb), + f(g[2], sc, cc), + ); + } + // X(249): isogonal of X(115); finite on equilateral (=G) + { + let wa = (g[1] - g[2]).cos().powi(2); + let wb = (g[2] - g[0]).cos().powi(2); + let wc = (g[0] - g[1]).cos().powi(2); + push_bary( + &mut out, + "X115等角", + "X_{249}", + "X(249) = \\mathrm{isog}(X_{115});\\ \\cos^2(B-C)", + "X(249):X(115) 的等角共轭", + "X249", + wa, + wb, + wc, + ); + } + // X(250): skip right (tan) and isosceles (csc) + if !right && !isos { + let f = |aa: f64, bb: f64, cc: f64| { + let d = (bb - cc).sin(); + if d.abs() < 1e-12 { + return f64::NAN; + } + aa.tan() / (d * d) + }; + push_bary( + &mut out, + "X125等角", + "X_{250}", + "X(250) = \\mathrm{isog}(X_{125});\\ \\tan A\\csc^2(B-C)", + "X(250):X(125) 的等角共轭", + "X250", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -15871,6 +16184,110 @@ mod tests { } } + #[test] + fn x241_to_x250_line_conjugates_isogonals() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("内心X55线共轭", "X_{241}", 9.9719387755102, 11.826431289311914), + ("垂心X71线共轭", "X_{242}", 6.437913907284766, 6.59497246949392), + ("垂心X73线共轭", "X_{243}", 6.642321785476351, 9.348636100085107), + ("内心X100线共轭", "X_{244}", 6.25, 0.968245836551854), + ("内心X110线共轭", "X_{245}", 5.908751393534002, 0.633335682459522), + ("外心X110线共轭", "X_{246}", 2.141120233091034, 5.041372798371628), + ("垂心X110线共轭", "X_{247}", 4.703399507007825, -1.249103798621572), + ("垂心X132线共轭", "X_{248}", 6.775670970419633, -0.719280998734576), + ("X115等角", "X_{249}", 4.079602071065873, 1.854246025083043), + ("X125等角", "X_{250}", 4.526900018908428, 4.296278811013081), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + assert!(fs.iter().any(|f| f.group == "内心X55线共轭" && f.label.contains("IO"))); + + // Isosceles 5-5-6: X245/246/247/250 skip; others finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for skip in ["X_{245}", "X_{246}", "X_{247}", "X_{250}"] { + assert!( + fs2.iter().all(|f| f.label != skip), + "{} should skip isos", + skip + ); + } + for (grp, lab, ..) in want { + if matches!(lab, "X_{245}" | "X_{246}" | "X_{247}" | "X_{250}") { + continue; + } + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: most line-conjugates skip; X249 → G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (gx3, gy3) = ptxy(g3); + for skip in [ + "X_{241}", "X_{242}", "X_{243}", "X_{244}", "X_{245}", "X_{246}", "X_{247}", "X_{248}", + "X_{250}", + ] { + assert!(fs3.iter().all(|f| f.label != skip), "{} should skip equil", skip); + } + let f249 = fs3 + .iter() + .find(|f| f.group == "X115等角" && f.label == "X_{249}") + .expect("equil X249"); + let (x, y) = ptxy(f249); + assert!((x - gx3).abs() < 1e-5 && (y - gy3).abs() < 1e-5, "equilateral X249 != G {:?}", (x, y)); + + // Right 3-4-5: X242/243/247/250 skip; X245/246 still finite (scalene). + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for skip in ["X_{242}", "X_{243}", "X_{247}", "X_{250}"] { + assert!(fs4.iter().all(|f| f.label != skip), "{} should skip right", skip); + } + for (grp, lab, ..) in want { + if matches!(lab, "X_{242}" | "X_{243}" | "X_{247}" | "X_{250}") { + continue; + } + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 6ee580a4f2e4e887785c82ce089a184ce6b2979d Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 18:44:46 +0800 Subject: [PATCH 077/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X241=E2=80=93X250=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 809242 -> 814038 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index a3e628c82efdb158a1c5ee8d81383a6c7212e6db..01a9a571f57e25f9c8979d7d58974ba46543ed7e 100644 GIT binary patch delta 125881 zcmce<2YeJo|39ADBo`nFB!*BDAae@|Nq`Utpd=yTFjNy-=t2r1K zV?^QZVgVmS5EVP%gNj%YAG?UXU;(l4h~@wO%UU$hwrf}G@UOJ018+VX7VQpm9e5YNQIALHj``K|7cN<@g+-QE 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Date: Mon, 2 Nov 2026 18:47:54 +0800 Subject: [PATCH 078/123] =?UTF-8?q?feat:=20ETC=20X251=E2=80=93X260=20isogo?= =?UTF-8?q?nals=20and=20cross=20conjugates?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(251)–X(260) in geometry.rs: isogonals of X141/X143/X158/X171– X174/X177, X(4)-cross of X(2), X(3)-cross of X(4), and the congruent- incircles isoscelizer X(258). Right-triangle guards for X252–X254. --- crates/mathcore/src/geometry.rs | 334 ++++++++++++++++++++++++++++++++ 1 file changed, 334 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index d9b9957..467405c 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -10592,6 +10592,237 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // X(251)–X(260): next isogonal / cross-conjugate band (ETC). + // X(251)=isogonal of X(141); bary a²/(b²+c²) = a³ csc(A+ω); →G on equil. + // X(252)=isogonal of X(143); bary 1/f, f=(v+w)²[…], u=sin2A; skip right; →G on equil. + // X(253)=X(4)-cross conjugate of X(2)=isog(X154); bary 1/(tanB+tanC−tanA); skip right. + // X(254)=X(3)-cross conjugate of X(4)=isog(X155); bary tanA/(cos²B+cos²C−cos²A); skip right. + // X(255)=isogonal of X(158); bary sin A cos² A. + // X(256)=isogonal of X(171); bary a/(a²+bc). + // X(257)=isogonal of X(172); bary 1/(a²+bc). + // X(258)=congruent-incircles isoscelizer=isog(X173); bary (sin A)/(cos B/2+cos C/2−cos A/2). + // X(259)=isogonal of X(174); bary sin A cos(A/2). + // X(260)=isogonal of X(177); bary (sin A)cos(A/2)/(cos B/2+cos C/2−cos A/2). + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let right = ca.abs() < 1e-9 || cb.abs() < 1e-9 || cc.abs() < 1e-9; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(251): always finite (=G on equilateral) + { + let wa = a * a / (b * b + c * c); + let wb = b * b / (c * c + a * a); + let wc = c * c / (a * a + b * b); + push_bary( + &mut out, + "X141等角", + "X_{251}", + "X(251) = \\mathrm{isog}(X_{141});\\ a^2/(b^2+c^2)", + "X(251):X(141) 的等角共轭", + "X251", + wa, + wb, + wc, + ); + } + // X(252): isogonal of X(143); skip right (f→0); →G on equilateral + if !right { + let u = (2.0 * g[0]).sin(); + let v = (2.0 * g[1]).sin(); + let w = (2.0 * g[2]).sin(); + let f = |uu: f64, vv: f64, ww: f64| { + let bracket = uu.powi(4) + + vv.powi(4) + + ww.powi(4) + - uu * uu * (2.0 * vv * vv + 2.0 * ww * ww - vv * ww) + - vv * ww * (vv * vv + ww * ww); + (vv + ww).powi(2) * bracket + }; + let fa = f(u, v, w); + let fb = f(v, w, u); + let fc = f(w, u, v); + if fa.abs() > 1e-14 && fb.abs() > 1e-14 && fc.abs() > 1e-14 { + push_bary( + &mut out, + "X143等角", + "X_{252}", + "X(252) = \\mathrm{isog}(X_{143});\\ 1/f,\\ f=(v+w)^2[\\cdots]", + "X(252):X(143) 的等角共轭", + "X252", + 1.0 / fa, + 1.0 / fb, + 1.0 / fc, + ); + } + } + // X(253): skip right (tan ∞) + if !right { + let f = |aa: f64, bb: f64, cc: f64| { + let den = bb.tan() + cc.tan() - aa.tan(); + if den.abs() < 1e-12 { + return f64::NAN; + } + 1.0 / den + }; + push_bary( + &mut out, + "垂心X2交叉共轭", + "X_{253}", + "X(253) = X(4)\\text{-cross conjugate of }X(2);\\ 1/(\\tan B+\\tan C-\\tan A)", + "X(253):垂心对重心的交叉共轭(X(154) 等角)", + "X253", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(254): skip right (tan ∞) + if !right { + let f = |aa: f64, bb: f64, cc: f64| { + let den = bb.cos().powi(2) + cc.cos().powi(2) - aa.cos().powi(2); + if den.abs() < 1e-12 { + return f64::NAN; + } + aa.tan() / den + }; + push_bary( + &mut out, + "外心X4交叉共轭", + "X_{254}", + "X(254) = X(3)\\text{-cross conjugate of }X(4);\\ \\tan A/(\\cos^2 B+\\cos^2 C-\\cos^2 A)", + "X(254):外心对垂心的交叉共轭(X(155) 等角)", + "X254", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(255) + { + push_bary( + &mut out, + "X158等角", + "X_{255}", + "X(255) = \\mathrm{isog}(X_{158});\\ \\sin A\\cos^2 A", + "X(255):X(158) 的等角共轭", + "X255", + sa * ca * ca, + sb * cb * cb, + sc * cc * cc, + ); + } + // X(256) + { + push_bary( + &mut out, + "X171等角", + "X_{256}", + "X(256) = \\mathrm{isog}(X_{171});\\ a/(a^2+bc)", + "X(256):X(171) 的等角共轭", + "X256", + a / (a * a + b * c), + b / (b * b + c * a), + c / (c * c + a * b), + ); + } + // X(257) + { + push_bary( + &mut out, + "X172等角", + "X_{257}", + "X(257) = \\mathrm{isog}(X_{172});\\ 1/(a^2+bc)", + "X(257):X(172) 的等角共轭", + "X257", + 1.0 / (a * a + b * c), + 1.0 / (b * b + c * a), + 1.0 / (c * c + a * b), + ); + } + // X(258) + { + let f = |aa: f64, bb: f64, cc: f64| { + let den = (bb * 0.5).cos() + (cc * 0.5).cos() - (aa * 0.5).cos(); + if den.abs() < 1e-12 { + return f64::NAN; + } + aa.sin() / den + }; + push_bary( + &mut out, + "等内切等腰截点", + "X_{258}", + "X(258) = \\mathrm{isog}(X_{173});\\ (\\sin A)/(\\cos\\tfrac{B}{2}+\\cos\\tfrac{C}{2}-\\cos\\tfrac{A}{2})", + "X(258):等内切圆等腰截点(Yff)", + "X258", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(259) + { + push_bary( + &mut out, + "X174等角", + "X_{259}", + "X(259) = \\mathrm{isog}(X_{174});\\ \\sin A\\cos\\tfrac{A}{2}", + "X(259):X(174) 的等角共轭", + "X259", + sa * (g[0] * 0.5).cos(), + sb * (g[1] * 0.5).cos(), + sc * (g[2] * 0.5).cos(), + ); + } + // X(260) + { + let f = |aa: f64, bb: f64, cc: f64| { + let den = (bb * 0.5).cos() + (cc * 0.5).cos() - (aa * 0.5).cos(); + if den.abs() < 1e-12 { + return f64::NAN; + } + aa.sin() * (aa * 0.5).cos() / den + }; + push_bary( + &mut out, + "X177等角", + "X_{260}", + "X(260) = \\mathrm{isog}(X_{177});\\ (\\sin A)\\cos\\tfrac{A}{2}/(\\cos\\tfrac{B}{2}+\\cdots)", + "X(260):X(177) 的等角共轭", + "X260", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -16288,6 +16519,109 @@ mod tests { } } + + #[test] + fn x251_to_x260_isogonals_cross_conjugates() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("X141等角", "X_{251}", 4.830872523494094, 2.45107713945113), + ("X143等角", "X_{252}", 3.5796847571466697, 0.9295524601828009), + ("垂心X2交叉共轭", "X_{253}", 5.275133924920259, 14.257077450117105), + ("外心X4交叉共轭", "X_{254}", 21.240054327106364, 7.8069025655417335), + ("X158等角", "X_{255}", 3.4285714285714284, 0.4785153169059357), + ("X171等角", "X_{256}", 4.418648310387986, 1.802383363660565), + ("X172等角", "X_{257}", 4.177179017887975, 1.5665199837105783), + ("等内切等腰截点", "X_{258}", 4.324611036295447, 1.6616741313298702), + ("X174等角", "X_{259}", 4.422767815154589, 1.7899737714567256), + ("X177等角", "X_{260}", 4.237027402124663, 1.5244390480382009), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: all finite; X251/X252 → G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (gx3, gy3) = ptxy(g3); + for (grp, lab, ..) in want { + assert!( + fs3.iter().any(|f| f.group == grp && f.label == lab), + "equil missing {} {}", + grp, + lab + ); + } + for (grp, lab) in [("X141等角", "X_{251}"), ("X143等角", "X_{252}")] { + let f = fs3 + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("equil {}", lab)); + let (x, y) = ptxy(f); + assert!( + (x - gx3).abs() < 1e-5 && (y - gy3).abs() < 1e-5, + "equilateral {} != G {:?}", + lab, + (x, y) + ); + } + + // Right 3-4-5: X252/X253/X254 skip; others finite. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for skip in ["X_{252}", "X_{253}", "X_{254}"] { + assert!(fs4.iter().all(|f| f.label != skip), "{} should skip right", skip); + } + for (grp, lab, ..) in want { + if matches!(lab, "X_{252}" | "X_{253}" | "X_{254}") { + continue; + } + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 979f7e15e95794cb12857b63905170e2605a1737 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 18:48:11 +0800 Subject: [PATCH 079/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X251=E2=80=93X260=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 814038 -> 817253 bytes 1 file changed, 0 insertions(+), 0 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Right guards for X264/X270; equilateral/60° guard for X265. --- crates/mathcore/src/geometry.rs | 327 ++++++++++++++++++++++++++++++++ 1 file changed, 327 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 467405c..23a0632 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -10823,6 +10823,241 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // X(261)–X(270): continue isogonal band (ETC). + // X(261)=isog(X181)=isotomic(X12); bary (sin A)[(csc A)sec(B/2−C/2)]². + // X(262)=isog(X182)=isotomic(X183); bary sin A sec(A−ω). + // X(263)=isog(X183); bary a³ sec(A−ω). + // X(264)=isotomic(O)=isog(X184); bary csc 2A; skip right. + // X(265)=isog(X186); bary sin A sin 2A csc 3A; skip equil / 60° (sin 3A=0). + // X(266)=isog(X188); bary sin A sin(A/2). + // X(267)=isog(X191); bary a/[b³+c³−a³+(b+c−a)(bc+ca+ab)]. + // X(268)=isog(X196); bary (sin A)(cos A cot(A/2))/(−1−cos A+cos B+cos C). + // X(269)=isog(X200); bary sin A tan²(A/2). + // X(270)=isog(X201); bary (tan A)/[1+cos(B−C)]; skip right. + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let right = ca.abs() < 1e-9 || cb.abs() < 1e-9 || cc.abs() < 1e-9; + let equil = (a - b).abs() < 1e-12 && (b - c).abs() < 1e-12; + let has_60 = (3.0 * g[0]).sin().abs() < 1e-9 + || (3.0 * g[1]).sin().abs() < 1e-9 + || (3.0 * g[2]).sin().abs() < 1e-9; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(261): always finite for non-degen + { + let f = |aa: f64, bb: f64, cc: f64| { + let half_diff = (bb - cc) * 0.5; + let csc_a = 1.0 / aa.sin(); + let sec_d = 1.0 / half_diff.cos(); + aa.sin() * (csc_a * sec_d).powi(2) + }; + push_bary( + &mut out, + "X181等角", + "X_{261}", + "X(261) = \\mathrm{isog}(X_{181})=\\mathrm{isotomic}(X_{12});\\ (\\sin A)[(\\csc A)\\sec(\\tfrac{B-C}{2})]^2", + "X(261):X(181) 的等角共轭(X(12) 等截)", + "X261", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(262)/X(263): Brocard form sec(A−ω) + if area > 1e-12 { + let sum_sq = a * a + b * b + c * c; + let tan_w = (4.0 * area) / sum_sq; + let cos_w = 1.0 / (1.0 + tan_w * tan_w).sqrt(); + let sin_w = tan_w * cos_w; + // cos(A−ω) = cos A cos ω + sin A sin ω + let caw = |caa: f64, saa: f64| caa * cos_w + saa * sin_w; + let cawa = caw(ca, sa); + let cawb = caw(cb, sb); + let cawc = caw(cc, sc); + if cawa.abs() > 1e-12 && cawb.abs() > 1e-12 && cawc.abs() > 1e-12 { + push_bary( + &mut out, + "X182等角", + "X_{262}", + "X(262) = \\mathrm{isog}(X_{182});\\ \\sin A\\sec(A-\\omega)", + "X(262):X(182) 的等角共轭(X(183) 等截)", + "X262", + sa / cawa, + sb / cawb, + sc / cawc, + ); + push_bary( + &mut out, + "X183等角", + "X_{263}", + "X(263) = \\mathrm{isog}(X_{183});\\ a^3\\sec(A-\\omega)", + "X(263):X(183) 的等角共轭", + "X263", + a * a * a / cawa, + b * b * b / cawb, + c * c * c / cawc, + ); + } + } + // X(264): skip right (csc 2A → ∞) + if !right { + push_bary( + &mut out, + "外心等截", + "X_{264}", + "X(264) = \\mathrm{isotomic}(X_{3})=\\mathrm{isog}(X_{184});\\ \\csc 2A", + "X(264):外心的等截共轭(X(184) 等角)", + "X264", + 1.0 / (2.0 * g[0]).sin(), + 1.0 / (2.0 * g[1]).sin(), + 1.0 / (2.0 * g[2]).sin(), + ); + } + // X(265): skip equilateral / any 60° (sin 3A=0) + if !equil && !has_60 { + let f = |aa: f64| { + let s3 = (3.0 * aa).sin(); + if s3.abs() < 1e-12 { + return f64::NAN; + } + aa.sin() * (2.0 * aa).sin() / s3 + }; + push_bary( + &mut out, + "X186等角", + "X_{265}", + "X(265) = \\mathrm{isog}(X_{186});\\ \\sin A\\sin 2A\\csc 3A", + "X(265):X(186) 的等角共轭", + "X265", + f(g[0]), + f(g[1]), + f(g[2]), + ); + } + // X(266) + { + push_bary( + &mut out, + "X188等角", + "X_{266}", + "X(266) = \\mathrm{isog}(X_{188});\\ \\sin A\\sin\\tfrac{A}{2}", + "X(266):X(188) 的等角共轭", + "X266", + sa * (g[0] * 0.5).sin(), + sb * (g[1] * 0.5).sin(), + sc * (g[2] * 0.5).sin(), + ); + } + // X(267) + { + let f = |aa: f64, bb: f64, cc: f64| { + let den = bb.powi(3) + cc.powi(3) - aa.powi(3) + + (bb + cc - aa) * (bb * cc + cc * aa + aa * bb); + if den.abs() < 1e-14 { + return f64::NAN; + } + aa / den + }; + push_bary( + &mut out, + "X191等角", + "X_{267}", + "X(267) = \\mathrm{isog}(X_{191});\\ a/[b^3+c^3-a^3+(b+c-a)(\\cdots)]", + "X(267):X(191) 的等角共轭(X(229) 反射对)", + "X267", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(268) + { + let f = |aa: f64, bb: f64, cc: f64| { + let den = -1.0 - aa.cos() + bb.cos() + cc.cos(); + if den.abs() < 1e-12 { + return f64::NAN; + } + let half = aa * 0.5; + if half.tan().abs() < 1e-14 { + return f64::NAN; + } + aa.sin() * aa.cos() / half.tan() / den + }; + push_bary( + &mut out, + "X196等角", + "X_{268}", + "X(268) = \\mathrm{isog}(X_{196});\\ (\\sin A)(\\cos A\\cot\\tfrac{A}{2})/(-1-\\cos A+\\cdots)", + "X(268):X(196) 的等角共轭", + "X268", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(269) + { + push_bary( + &mut out, + "X200等角", + "X_{269}", + "X(269) = \\mathrm{isog}(X_{200});\\ \\sin A\\tan^2\\tfrac{A}{2}", + "X(269):X(200) 的等角共轭", + "X269", + sa * (g[0] * 0.5).tan().powi(2), + sb * (g[1] * 0.5).tan().powi(2), + sc * (g[2] * 0.5).tan().powi(2), + ); + } + // X(270): skip right (tan ∞) + if !right { + let f = |aa: f64, bb: f64, cc: f64| { + let den = 1.0 + (bb - cc).cos(); + if den.abs() < 1e-12 { + return f64::NAN; + } + aa.tan() / den + }; + push_bary( + &mut out, + "X201等角", + "X_{270}", + "X(270) = \\mathrm{isog}(X_{201});\\ (\\tan A)/[1+\\cos(B-C)]", + "X(270):X(201) 的等角共轭", + "X270", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -16622,6 +16857,98 @@ mod tests { } } + + #[test] + fn x261_to_x270_isogonals_isotomics() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("X181等角", "X_{261}", 4.065485269326483, 1.4282345064333561), + ("X182等角", "X_{262}", 4.629337867851194, 2.2854251555728413), + ("X183等角", "X_{263}", 4.929953418014204, 2.780990071519315), + ("外心等截", "X_{264}", 4.506444353518821, 2.5131666059084026), + ("X186等角", "X_{265}", 7.0733695652173925, -0.439920390955081), + ("X188等角", "X_{266}", 4.755100445484774, 2.3362093968005775), + ("X191等角", "X_{267}", 4.871009694963348, 2.8532228931447636), + ("X196等角", "X_{268}", 4.670704643374325, 4.018335908160631), + ("X200等角", "X_{269}", 4.996649586125344, 3.0295370321437214), + ("X201等角", "X_{270}", 4.844900838240842, 2.970127974199845), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + + // Isosceles 5-5-6: all finite (no 60°). + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: X265 skips (sin 3A=0); others finite. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.label != "X_{265}"), "X265 should skip equilateral"); + for (grp, lab, ..) in want { + if lab == "X_{265}" { + continue; + } + assert!( + fs3.iter().any(|f| f.group == grp && f.label == lab), + "equil missing {} {}", + grp, + lab + ); + } + + // Right 3-4-5: X264/X270 skip (csc2A / tan); others finite. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for skip in ["X_{264}", "X_{270}"] { + assert!(fs4.iter().all(|f| f.label != skip), "{} should skip right", skip); + } + for (grp, lab, ..) in want { + if matches!(lab, "X_{264}" | "X_{270}") { + continue; + } + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 305f4f03de070e05632f7fd35c4d88241803a775 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 18:50:56 +0800 Subject: [PATCH 081/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X261=E2=80=93X270=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 817253 -> 820512 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index c564c4283d0e065e61027049d8e8fb01b8bfe90e..b83ce819a6d94f930d2d61f21aec97dfffe0fc31 100644 GIT binary patch delta 110479 zcmb?^2Vhji_IGA(b_1lafe=Ch$?QVf0)fy;LXt(ANa%th5JHh&1jGgg5ET>!yuyHj zCL1gWPvD^j6)8$nQ9)4=3$Z*!1O${KD15&&_uefD@brEEhcEZusb@}~GiCpCDzoH~ z78?qA=-jZ`VfqOE%BEQD7#}tJm)#-Z#UY;Azv3D8W~j?Pan!`gQ}5v+w!%>}iYA0? z*Q$>gJ9Wf_QH7Il5Bb^_VSY@TJYmMDkTbTL#`m=-&$rJ9JI4a~5TZF<$;k0|EO&>Ke4K-_6t%^4Whz_7CkJ+4tCX+kOi@ z6Z&iD$+B!fzX?6gKC@r3&#}L(ZLq(g z&9`s1AGI&E9|=9d-mtH?mw9Y2+rPFiu)ksZfUgYw*0ejhj=#^;n2EooucYXn@b{TlFB+Smr$sbom-YS;705a5Y@!!MdXRIVsE)olvKMly zMLmj~C!@Z$uX}V?h~tEQSIzgeEsyTfoug{&w>aXGHvh3R#1kQE3A?a)DniF~WTJ<# zrST`3sO>rUsJ_UNfo8TkR;mtC^f}Qn^)FM|#cZ78psExy&Y@B&@N!V!7#&|{sXZiI zL{c*^+8p%Z331kzJC15`n=V9;X8hD6dQt5reDfdrqS^`eRe;P>Q}@Ki>+jWeu*-7a zZXU0ntvyzCnI-_0*#Taz(&eTXV(wzpn21f_n;y|S#1hC8Vo_gSS;JHGiG#w@BR!6B zPJl#XtkfEf#6KjxN!?%B8NGho{e1ZXfElB2h>O$qEZC*L9~ZBEg6Gk=8_<4}dJh`y z|91fOi}gnFqi8JtIe~@<-%+Bb58oLI-=QMLv*3|k@~?%g0S2Cwl_nNjpwf#PcqLF5 zCbVX&^tTi8m{)pU=MD6v`Y`~lRsGu(>N2!E$0~hCePrvbK_J)q;iRoP8! zT|{RT*xtY>P+MQ0TV1c8SSRYTP1r=|_SzxPS9H-m^?RBXx{0o+ur1N5P%9}B{beQ@ z{UyuG8Vl23PnxZroWD!Y5#8(yXt*_{XCjLSwoa9^UD5sdbHKCZ-n}xrcJ<-whZEs5Bk^Bhi2rUT4}Qw zeSL<-c0)xWxG1d|%23;N^jXasszL@EHPO?XlNO7Y^RHsw;;{O9p07&$Y2d>>sl*fsDxJL z==621x*~_TC9L%kSy%ZEa|1(KprBw>=oHzut!6+c6lZ$ey7PFA+Q>2?x+x1}DD-Z9|XSDC8y^rUP_CwHJQdSeEqM;8J zm6e=Z6zJ?|oLxPIRz)N3hg{&Q&nb05mtb=}c zCz2_Gt@-ES3D+P!(NquZ+!dYo=u8;dxKHToIx8juM!rH0(IHt@gt5>k#@fP71IqJ7 zvd-?VtxxHa$jXjNYMV8Cw3fCt8s#f~8AgXVs$oUWdZ+m|jCsXiqPKf8#!v?(R)v%Uooz zt`EbZgkk;T-aXh)dQzXe*?0Q#J|j`_uRf%Mh&+XTVdRX#Khf6!JXL4?TB1Vhe)pon zhJM}HTK$iHl;`Q68Lt3QR!-a?x|F)63y


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<3174600270@qq.com> Date: Mon, 2 Nov 2026 18:57:41 +0800 Subject: [PATCH 084/123] =?UTF-8?q?feat:=20ETC=20X281=E2=80=93X290=20isogo?= =?UTF-8?q?nals,=20cross=20conjugates,=20cevapoint?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(281)–X(290) in geometry.rs: isogonals of X222/X223/X225–X228/ X232/X233/X236/X237; X(37)/X(6)/X(3)/X(55)/X(58)/X(4) cross conjugates; cevapoint(X6,X54) as X(288). Right guards for X281/X286; equilateral guards for X287/X290 (A+ω→π/2). --- crates/mathcore/src/geometry.rs | 356 ++++++++++++++++++++++++++++++++ 1 file changed, 356 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 327823e..564dc10 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -11299,6 +11299,267 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // X(281)–X(290): continue isogonal / cross-conjugate / cevapoint band (ETC). + // X(281)=isog(X222)=X(37)-cross of X(9); bary 1+sec A; skip right. + // X(282)=isog(X223)=X(6)-cross of X(9); bary (sin A)cot(A/2)/(-1-cos A+cos B+cos C). + // X(283)=isog(X225)=X(3)-cross of X(21); bary sin 2A/(cos B+cos C). + // X(284)=isog(X226)=X(55)-cross of X(21)=isotomic(X349); bary a²/(cos B+cos C). + // X(285)=isog(X227)=X(58)-cross of X(21); bary (sin A)/[(cos B+cos C)(-1-cos A+…)]. + // X(286)=isog(X228)=X(4)-cross of X(27)=isotomic(X72); bary sec A/(sin B+sin C); skip right. + // X(287)=isog(X232)=X(2)-Hirst of X(98); bary cos A sec(A+ω); skip equil (A+ω→π/2). + // X(288)=isog(X233)=cevapoint(X6,X54); bary (sin A)sec(B−C)/[b cos(C−A)+c cos(B−A)]. + // X(289)=isog(X236); bary (sin A)sin(A/2)/(cos B/2+cos C/2−cos A/2) [=a(1−sin A/2)tan(A/2)]. + // X(290)=isog(X237)=isotomic(X511); bary csc A sec(A+ω); skip equil. + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let equil = (a - b).abs() < 1e-12 && (b - c).abs() < 1e-12; + let right = ca.abs() < 1e-9 || cb.abs() < 1e-9 || cc.abs() < 1e-9; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(281): skip right (sec A → ∞) + if !right { + push_bary( + &mut out, + "X222等角", + "X_{281}", + "X(281) = \\mathrm{isog}(X_{222});\\ 1+\\sec A", + "X(281):X(222) 的等角共轭(X(37) 对 X(9) 交叉共轭)", + "X281", + 1.0 + 1.0 / ca, + 1.0 + 1.0 / cb, + 1.0 + 1.0 / cc, + ); + } + // X(282) + { + let f = |aa: f64, bb: f64, cc_: f64| { + let den = -1.0 - aa.cos() + bb.cos() + cc_.cos(); + let half = aa * 0.5; + if den.abs() < 1e-12 || half.tan().abs() < 1e-14 { + return f64::NAN; + } + aa.sin() / half.tan() / den + }; + push_bary( + &mut out, + "X223等角", + "X_{282}", + "X(282) = \\mathrm{isog}(X_{223});\\ (\\sin A)\\cot\\tfrac{A}{2}/(-1-\\cos A+\\cdots)", + "X(282):X(223) 的等角共轭(X(6) 对 X(9) 交叉共轭)", + "X282", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(283) + { + let f = |aa: f64, bb: f64, cc_: f64| { + let den = bb.cos() + cc_.cos(); + if den.abs() < 1e-14 { + return f64::NAN; + } + (2.0 * aa).sin() / den + }; + push_bary( + &mut out, + "X225等角", + "X_{283}", + "X(283) = \\mathrm{isog}(X_{225});\\ \\sin 2A/(\\cos B+\\cos C)", + "X(283):X(225) 的等角共轭(外心对 X(21) 交叉共轭)", + "X283", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(284) + { + let f = |side: f64, bb: f64, cc_: f64| { + let den = bb.cos() + cc_.cos(); + if den.abs() < 1e-14 { + return f64::NAN; + } + side * side / den + }; + push_bary( + &mut out, + "X226等角", + "X_{284}", + "X(284) = \\mathrm{isog}(X_{226})=\\mathrm{isotomic}(X_{349});\\ a^2/(\\cos B+\\cos C)", + "X(284):X(226) 的等角共轭(X(55) 对 X(21) 交叉共轭)", + "X284", + f(a, g[1], g[2]), + f(b, g[2], g[0]), + f(c, g[0], g[1]), + ); + } + // X(285) + { + let f = |aa: f64, bb: f64, cc_: f64| { + let d1 = bb.cos() + cc_.cos(); + let d2 = -1.0 - aa.cos() + bb.cos() + cc_.cos(); + if d1.abs() < 1e-14 || d2.abs() < 1e-12 { + return f64::NAN; + } + aa.sin() / (d1 * d2) + }; + push_bary( + &mut out, + "X227等角", + "X_{285}", + "X(285) = \\mathrm{isog}(X_{227});\\ (\\sin A)/[(\\cos B+\\cos C)(-1-\\cos A+\\cdots)]", + "X(285):X(227) 的等角共轭(X(58) 对 X(21) 交叉共轭)", + "X285", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(286): skip right (sec A → ∞) + if !right { + let f = |aa: f64, bb: f64, cc_: f64| { + let caa = aa.cos(); + let den = bb.sin() + cc_.sin(); + if caa.abs() < 1e-14 || den.abs() < 1e-14 { + return f64::NAN; + } + (1.0 / caa) / den + }; + push_bary( + &mut out, + "X228等角", + "X_{286}", + "X(286) = \\mathrm{isog}(X_{228})=\\mathrm{isotomic}(X_{72});\\ \\sec A/(\\sin B+\\sin C)", + "X(286):X(228) 的等角共轭(垂心对 X(27) 交叉共轭)", + "X286", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(287): skip equilateral (A+ω → π/2) + if !equil && area > 1e-12 { + let sum_sq = a * a + b * b + c * c; + let tan_w = (4.0 * area) / sum_sq; + let cos_w = 1.0 / (1.0 + tan_w * tan_w).sqrt(); + let sin_w = tan_w * cos_w; + let f = |caa: f64, saa: f64| { + let caw = caa * cos_w - saa * sin_w; + if caw.abs() < 1e-12 { + return f64::NAN; + } + caa / caw + }; + push_bary( + &mut out, + "X232等角", + "X_{287}", + "X(287) = \\mathrm{isog}(X_{232});\\ \\cos A\\sec(A+\\omega)", + "X(287):X(232) 的等角共轭(重心对 X(98) 的 Hirst 逆)", + "X287", + f(ca, sa), + f(cb, sb), + f(cc, sc), + ); + } + // X(288): cevapoint of K=X(6) and X(54) + { + let f = |aa: f64, bb: f64, cc_: f64, side_b: f64, side_c: f64| { + let cbc = (bb - cc_).cos(); + let den = side_b * (cc_ - aa).cos() + side_c * (bb - aa).cos(); + if cbc.abs() < 1e-14 || den.abs() < 1e-14 { + return f64::NAN; + } + aa.sin() / cbc / den + }; + push_bary( + &mut out, + "对称中线X54截点", + "X_{288}", + "X(288) = \\mathrm{cevapoint}(X_6,X_{54})=\\mathrm{isog}(X_{233});\\ (\\sin A)\\sec(B-C)/[b\\cos(C-A)+c\\cos(B-A)]", + "X(288):对称中线点与 X(54) 的截点(X(233) 等角)", + "X288", + f(g[0], g[1], g[2], b, c), + f(g[1], g[2], g[0], c, a), + f(g[2], g[0], g[1], a, b), + ); + } + // X(289) + { + let f = |aa: f64, bb: f64, cc_: f64| { + let den = (bb * 0.5).cos() + (cc_ * 0.5).cos() - (aa * 0.5).cos(); + if den.abs() < 1e-14 { + return f64::NAN; + } + aa.sin() * (aa * 0.5).sin() / den + }; + push_bary( + &mut out, + "X236等角", + "X_{289}", + "X(289) = \\mathrm{isog}(X_{236});\\ (\\sin A)\\sin\\tfrac{A}{2}/(\\cos\\tfrac{B}{2}+\\cos\\tfrac{C}{2}-\\cos\\tfrac{A}{2})", + "X(289):X(236) 的等角共轭", + "X289", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(290): skip equilateral (A+ω → π/2) + if !equil && area > 1e-12 { + let sum_sq = a * a + b * b + c * c; + let tan_w = (4.0 * area) / sum_sq; + let cos_w = 1.0 / (1.0 + tan_w * tan_w).sqrt(); + let sin_w = tan_w * cos_w; + let f = |saa: f64, caa: f64| { + let caw = caa * cos_w - saa * sin_w; + if saa.abs() < 1e-14 || caw.abs() < 1e-12 { + return f64::NAN; + } + (1.0 / saa) / caw + }; + push_bary( + &mut out, + "X237等角", + "X_{290}", + "X(290) = \\mathrm{isog}(X_{237});\\ \\csc A\\sec(A+\\omega)", + "X(290):X(237) 的等角共轭(X(511) 等截)", + "X290", + f(sa, ca), + f(sb, cb), + f(sc, cc), + ); + } + } + + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -17277,6 +17538,101 @@ mod tests { } } + + #[test] + fn x281_to_x290_isogonals_cross_cevapoint() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("X222等角", "X_{281}", 4.558555354371444, 2.45880845844486), + ("X223等角", "X_{282}", 4.795830440641973, 4.575314483089601), + ("X225等角", "X_{283}", 3.6399604352126613, 0.7661688123061161), + ("X226等角", "X_{284}", 4.4468617426302615, 1.7694474115164964), + ("X227等角", "X_{285}", 4.809474322334805, 4.620277612713879), + ("X228等角", "X_{286}", 4.741837557771125, 2.901212445241758), + ("X232等角", "X_{287}", 6.254824522998894, -0.49666816698873906), + ("对称中线X54截点", "X_{288}", 4.645629690252596, 2.0249208989494853), + ("X236等角", "X_{289}", 4.620344800335799, 2.048224463774928), + ("X237等角", "X_{290}", 6.568580111030933, -1.0367981087109945), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: X287/X290 skip (A+ω→π/2); others finite. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + for skip in ["X_{287}", "X_{290}"] { + assert!(fs3.iter().all(|f| f.label != skip), "{} should skip equil", skip); + } + for (grp, lab, ..) in want { + if matches!(lab, "X_{287}" | "X_{290}") { + continue; + } + assert!( + fs3.iter().any(|f| f.group == grp && f.label == lab), + "equil missing {} {}", + grp, + lab + ); + } + + // Right 3-4-5: X281/X286 skip (sec); others finite. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for skip in ["X_{281}", "X_{286}"] { + assert!(fs4.iter().all(|f| f.label != skip), "{} should skip right", skip); + } + for (grp, lab, ..) in want { + if matches!(lab, "X_{281}" | "X_{286}") { + continue; + } + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From f36218e474591173ed170e97c4dac480841e3b55 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 18:57:41 +0800 Subject: [PATCH 085/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X281=E2=80=93X290=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 824707 -> 829225 bytes 1 file changed, 0 insertions(+), 0 deletions(-) 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zX12mwOX@Ub>GSuYwXLLY-`C$@t1yBnQia-$*Q42Lv+kFSpd)x`s+mG#(i~vKlkvKZ ztwlej;#VB;M>43OZ(2%HT>2pJqjlDP20!*rh(`bt-21t-VS?ThT-R@+{)TOXwNX=e zmnd>3kYS^B*gpvk#aW&;wQyz(PK29239b9c>}wUXbst;n%buH%6-v)$YrO0Vn2U50 zcbTj=V_Q6XP|2y=ePVrfOoHM3a?rWSdN&yFn@-W=z;YK%(R0~0Yb7}lVb;`mEaT5; z@Koe&r=wH#dI)C&)ZG%*eFuiu5Kkt3p!?urwhJHVF*+D)T(1#vBNNh6cFB|%*=}na z1EI2~fsZ9kgZQ<_+Rh_>E^iu?zP;9t5`WF5!M?ykH>R=4bUjkrXC2|PhAe`SWAk*q zu4TV92d9TZ4k%6Qlc1+sv+W<#sVoH59kAX)n2$3|1z|8VfYS%98z^TvtdwVGLUR7n zx=}(^r10I&NWx`Pum!+EIf;F3{kU)lQX5&K86BIYe}oey77>V1-fVq5`&QN>W0jyB zSfoFqwNVwqfR4_BMbG7pen&YXU)rP`r4Dlt8*mIn$56h3V!GWJr-VMoJqduE+3&0q zOv+PkuAanBSmR8g{nNP^|L-Y(uHKcMw7zPN(ZG2SPES$JJbeQD!P={!qzx6Fwob>T z0AJbRgIlauM!b%lb}fKt_# Date: Mon, 2 Nov 2026 19:00:28 +0800 Subject: [PATCH 086/123] =?UTF-8?q?feat:=20ETC=20X291=E2=80=93X300=20isogo?= =?UTF-8?q?nals,=20Hirst,=20isotomics?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(291)–X(300) in geometry.rs: isogonals of X238–X243/X248; X(1)-Hirst of X(291) as X(292); X(2)-Hirst of X(4) as X(297); isotomics of X(13)/X(14)/X(15) as X(298)–X(300). Equilateral guards for X291–X297/X299; right guard for X297; 120° guard for X300. --- crates/mathcore/src/geometry.rs | 331 ++++++++++++++++++++++++++++++++ 1 file changed, 331 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 564dc10..7bf70fd 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -11560,6 +11560,251 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } + // X(291)–X(300): continue isogonal / Hirst / isotomic band (ETC). + // X(291)=isog(X238)=isotomic(X350); bary a/(a²−bc); skip equil. + // X(292)=isog(X239); bary a²/(a²−bc); X(1)-Hirst of X(291); skip equil. + // X(293)=isog(X240); bary sin 2A sec(A+ω); skip equil (A+ω→π/2). + // X(294)=isog(X241); bary a(b+c−a)/(b²+c²−ab−ac); skip equil. + // X(295)=isog(X242); bary sin 2A/(a²−bc); skip equil. + // X(296)=isog(X243); bary sin 2A/(cos²A−cos B cos C); skip equil. + // X(297)=isog(X248)=X(2)-Hirst of X(4)=isotomic(X287); bary sec A cos(A+ω); skip right/equil. + // X(298)=isotomic(X13); bary csc A sin(A+π/3). + // X(299)=isotomic(X14); bary csc A sin(A−π/3); skip equil (sin→0). + // X(300)=isotomic(X15); bary csc A csc(A+π/3); skip 120° (csc(A+π/3)→∞). + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let equil = (a - b).abs() < 1e-12 && (b - c).abs() < 1e-12; + let right = ca.abs() < 1e-9 || cb.abs() < 1e-9 || cc.abs() < 1e-9; + let has_120 = (g[0] - std::f64::consts::FRAC_PI_3 * 2.0).abs() < 1e-9 + || (g[1] - std::f64::consts::FRAC_PI_3 * 2.0).abs() < 1e-9 + || (g[2] - std::f64::consts::FRAC_PI_3 * 2.0).abs() < 1e-9; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(291)/X(292)/X(295): skip equilateral (a²−bc → 0) + if !equil { + let da = a * a - b * c; + let db = b * b - c * a; + let dc = c * c - a * b; + if da.abs() > 1e-12 && db.abs() > 1e-12 && dc.abs() > 1e-12 { + push_bary( + &mut out, + "X238等角", + "X_{291}", + "X(291) = \\mathrm{isog}(X_{238});\\ a/(a^2-bc)", + "X(291):X(238) 的等角共轭(X(350) 等截)", + "X291", + a / da, + b / db, + c / dc, + ); + push_bary( + &mut out, + "X239等角", + "X_{292}", + "X(292) = \\mathrm{isog}(X_{239});\\ a^2/(a^2-bc)", + "X(292):X(239) 的等角共轭(内心对 X(291) 的 Hirst 逆)", + "X292", + a * a / da, + b * b / db, + c * c / dc, + ); + push_bary( + &mut out, + "X242等角", + "X_{295}", + "X(295) = \\mathrm{isog}(X_{242});\\ \\sin 2A/(a^2-bc)", + "X(295):X(242) 的等角共轭", + "X295", + (2.0 * g[0]).sin() / da, + (2.0 * g[1]).sin() / db, + (2.0 * g[2]).sin() / dc, + ); + } + } + // X(293): skip equilateral (A+ω → π/2) + if !equil && area > 1e-12 { + let sum_sq = a * a + b * b + c * c; + let tan_w = (4.0 * area) / sum_sq; + let cos_w = 1.0 / (1.0 + tan_w * tan_w).sqrt(); + let sin_w = tan_w * cos_w; + let f = |aa: f64, saa: f64, caa: f64| { + let caw = caa * cos_w - saa * sin_w; + if caw.abs() < 1e-12 { + return f64::NAN; + } + (2.0 * aa).sin() / caw + }; + push_bary( + &mut out, + "X240等角", + "X_{293}", + "X(293) = \\mathrm{isog}(X_{240});\\ \\sin 2A\\sec(A+\\omega)", + "X(293):X(240) 的等角共轭", + "X293", + f(g[0], sa, ca), + f(g[1], sb, cb), + f(g[2], sc, cc), + ); + } + // X(294): skip equilateral (b²+c²−ab−ac → 0) + if !equil { + let f = |aa: f64, bb: f64, cc_: f64| { + let den = bb * bb + cc_ * cc_ - aa * bb - aa * cc_; + if den.abs() < 1e-12 { + return f64::NAN; + } + aa * (bb + cc_ - aa) / den + }; + push_bary( + &mut out, + "X241等角", + "X_{294}", + "X(294) = \\mathrm{isog}(X_{241});\\ a(b+c-a)/(b^2+c^2-ab-ac)", + "X(294):X(241) 的等角共轭", + "X294", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(296): skip equilateral (cos²A−cos B cos C → 0) + if !equil { + let f = |saa2: f64, caa: f64, cbb: f64, ccc: f64| { + let den = caa * caa - cbb * ccc; + if den.abs() < 1e-12 { + return f64::NAN; + } + saa2 / den + }; + push_bary( + &mut out, + "X243等角", + "X_{296}", + "X(296) = \\mathrm{isog}(X_{243});\\ \\sin 2A/(\\cos^2 A-\\cos B\\cos C)", + "X(296):X(243) 的等角共轭", + "X296", + f((2.0 * g[0]).sin(), ca, cb, cc), + f((2.0 * g[1]).sin(), cb, cc, ca), + f((2.0 * g[2]).sin(), cc, ca, cb), + ); + } + // X(297): skip right (sec) and equilateral (cos(A+ω)→0) + if !right && !equil && area > 1e-12 { + let sum_sq = a * a + b * b + c * c; + let tan_w = (4.0 * area) / sum_sq; + let cos_w = 1.0 / (1.0 + tan_w * tan_w).sqrt(); + let sin_w = tan_w * cos_w; + let f = |saa: f64, caa: f64| { + if caa.abs() < 1e-12 { + return f64::NAN; + } + let caw = caa * cos_w - saa * sin_w; + (1.0 / caa) * caw + }; + push_bary( + &mut out, + "X248等角", + "X_{297}", + "X(297) = \\mathrm{isog}(X_{248})=\\mathrm{isotomic}(X_{287});\\ \\sec A\\cos(A+\\omega)", + "X(297):X(248) 的等角共轭(重心对垂心的 Hirst 逆)", + "X297", + f(sa, ca), + f(sb, cb), + f(sc, cc), + ); + } + // X(298): isotomic of 1st isogonic center + { + let pi3 = std::f64::consts::FRAC_PI_3; + let f = |aa: f64, saa: f64| { + if saa.abs() < 1e-14 { + return f64::NAN; + } + (1.0 / saa) * (aa + pi3).sin() + }; + push_bary( + &mut out, + "第一等角线等截", + "X_{298}", + "X(298) = \\mathrm{isotomic}(X_{13});\\ \\csc A\\sin(A+\\pi/3)", + "X(298):第一等角线中心的等截共轭", + "X298", + f(g[0], sa), + f(g[1], sb), + f(g[2], sc), + ); + } + // X(299): isotomic of 2nd isogonic; skip equilateral + if !equil { + let pi3 = std::f64::consts::FRAC_PI_3; + let f = |aa: f64, saa: f64| { + if saa.abs() < 1e-14 { + return f64::NAN; + } + (1.0 / saa) * (aa - pi3).sin() + }; + push_bary( + &mut out, + "第二等角线等截", + "X_{299}", + "X(299) = \\mathrm{isotomic}(X_{14});\\ \\csc A\\sin(A-\\pi/3)", + "X(299):第二等角线中心的等截共轭", + "X299", + f(g[0], sa), + f(g[1], sb), + f(g[2], sc), + ); + } + // X(300): isotomic of 1st isodynamic; skip 120° angle + if !has_120 { + let pi3 = std::f64::consts::FRAC_PI_3; + let f = |aa: f64, saa: f64| { + let s = (aa + pi3).sin(); + if saa.abs() < 1e-14 || s.abs() < 1e-12 { + return f64::NAN; + } + (1.0 / saa) / s + }; + push_bary( + &mut out, + "第一等动力等截", + "X_{300}", + "X(300) = \\mathrm{isotomic}(X_{15});\\ \\csc A\\csc(A+\\pi/3)", + "X(300):第一等动力点的等截共轭", + "X300", + f(g[0], sa), + f(g[1], sb), + f(g[2], sc), + ); + } + } + + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -17633,6 +17878,92 @@ mod tests { } + #[test] + fn x291_to_x300_isogonals_hirst_isotomics() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("X238等角", "X_{291}", 8.175675675675675, 0.2616880639329336), + ("X239等角", "X_{292}", 8.10232220609579, 0.2951112128822778), + ("X240等角", "X_{293}", 6.5180052846609176, -0.5979255705588283), + ("X241等角", "X_{294}", 7.5120924855491324, -0.432520452304782), + ("X242等角", "X_{295}", 8.37748344370861, 0.12824448166249725), + ("X243等角", "X_{296}", 6.061579621844016, -0.8560286714306778), + ("X248等角", "X_{297}", 7.708213417753903, 10.091807886017781), + ("第一等角线等截", "X_{298}", 3.831703156647867, 1.1917226177001814), + ("第二等角线等截", "X_{299}", -11.390595346800717, -16.234465552890185), + ("第一等动力等截", "X_{300}", 4.186903587004856, 1.7645719906151849), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: skip X291–X297/X299 (denom/ω/sin); keep X298/X300. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + for skip in [ + "X_{291}", "X_{292}", "X_{293}", "X_{294}", "X_{295}", "X_{296}", "X_{297}", "X_{299}", + ] { + assert!(fs3.iter().all(|f| f.label != skip), "{} should skip equil", skip); + } + for keep in ["X_{298}", "X_{300}"] { + assert!(fs3.iter().any(|f| f.label == keep), "equil missing {}", keep); + } + + // Right 3-4-5: X297 skips (sec); others finite. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().all(|f| f.label != "X_{297}"), "X297 should skip right"); + for (grp, lab, ..) in want { + if lab == "X_{297}" { + continue; + } + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 9c995bfef88be045a36d550fe1b34c70babe124d Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: 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MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(301)–X(310) as isotomics of X(16)/X(17)/X(18)/X(19)/X(25)/ X(27)/X(29)/X(39)/X(40)/X(42) with 60°/150° guards where needed. --- crates/mathcore/src/geometry.rs | 334 ++++++++++++++++++++++++++++++++ 1 file changed, 334 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 7bf70fd..1c3690f 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -11804,6 +11804,255 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(301)–X(310): continue isotomic band (ETC). + // X(301)=isotomic(X16); bary csc A csc(A−π/3); skip 60° (incl. equil). + // X(302)=isotomic(X17); bary csc A sin(A+π/6); skip 150°. + // X(303)=isotomic(X18); bary csc A sin(A−π/6); skip 30° (weight 0 ok, keep). + // X(304)=isotomic(X19); bary cos A csc² A. + // X(305)=isotomic(X25); bary b³c³ cos A. + // X(306)=isotomic(X27); bary bc(b+c) cos A. + // X(307)=isotomic(X29); bary a·b²c²(b+c)cos A/(b+c−a). + // X(308)=isotomic(X39); bary b²c²/(b²+c²) [= csc A csc(A+ω)]. + // X(309)=isotomic(X40); bary (csc A)/(-1-cos A+cos B+cos C). + // X(310)=isotomic(X42); bary b²c²/(b+c). + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let equil = (a - b).abs() < 1e-12 && (b - c).abs() < 1e-12; + let has_60 = (g[0] - std::f64::consts::FRAC_PI_3).abs() < 1e-9 + || (g[1] - std::f64::consts::FRAC_PI_3).abs() < 1e-9 + || (g[2] - std::f64::consts::FRAC_PI_3).abs() < 1e-9; + let has_150 = (g[0] - std::f64::consts::PI * 5.0 / 6.0).abs() < 1e-9 + || (g[1] - std::f64::consts::PI * 5.0 / 6.0).abs() < 1e-9 + || (g[2] - std::f64::consts::PI * 5.0 / 6.0).abs() < 1e-9; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(301): isotomic of 2nd isodynamic; skip 60° (csc(A−π/3)→∞) + if !has_60 && !equil { + let pi3 = std::f64::consts::FRAC_PI_3; + let f = |aa: f64, saa: f64| { + let s = (aa - pi3).sin(); + if saa.abs() < 1e-14 || s.abs() < 1e-12 { + return f64::NAN; + } + (1.0 / saa) / s + }; + push_bary( + &mut out, + "第二等动力等截", + "X_{301}", + "X(301) = \\mathrm{isotomic}(X_{16});\\ \\csc A\\csc(A-\\pi/3)", + "X(301):第二等动力点的等截共轭", + "X301", + f(g[0], sa), + f(g[1], sb), + f(g[2], sc), + ); + } + // X(302): isotomic of 1st Napoleon; skip 150° (sin(A+π/6)→0 all-zero risk rare) + if !has_150 { + let pi6 = std::f64::consts::FRAC_PI_6; + let f = |aa: f64, saa: f64| { + if saa.abs() < 1e-14 { + return f64::NAN; + } + (1.0 / saa) * (aa + pi6).sin() + }; + push_bary( + &mut out, + "第一拿破仑等截", + "X_{302}", + "X(302) = \\mathrm{isotomic}(X_{17});\\ \\csc A\\sin(A+\\pi/6)", + "X(302):第一拿破仑点的等截共轭", + "X302", + f(g[0], sa), + f(g[1], sb), + f(g[2], sc), + ); + } + // X(303): isotomic of 2nd Napoleon + { + let pi6 = std::f64::consts::FRAC_PI_6; + let f = |aa: f64, saa: f64| { + if saa.abs() < 1e-14 { + return f64::NAN; + } + (1.0 / saa) * (aa - pi6).sin() + }; + push_bary( + &mut out, + "第二拿破仑等截", + "X_{303}", + "X(303) = \\mathrm{isotomic}(X_{18});\\ \\csc A\\sin(A-\\pi/6)", + "X(303):第二拿破仑点的等截共轭", + "X303", + f(g[0], sa), + f(g[1], sb), + f(g[2], sc), + ); + } + // X(304): isotomic of X(19) Clawson; bary cos A / sin² A + { + let f = |caa: f64, saa: f64| { + let s2 = saa * saa; + if s2 < 1e-28 { + return f64::NAN; + } + caa / s2 + }; + push_bary( + &mut out, + "克劳森等截", + "X_{304}", + "X(304) = \\mathrm{isotomic}(X_{19});\\ \\cos A\\csc^2 A", + "X(304):克劳森点的等截共轭", + "X304", + f(ca, sa), + f(cb, sb), + f(cc, sc), + ); + } + // X(305): isotomic of X(25); bary b³c³ cos A + { + push_bary( + &mut out, + "X25等截", + "X_{305}", + "X(305) = \\mathrm{isotomic}(X_{25});\\ b^3 c^3\\cos A", + "X(305):X(25) 的等截共轭", + "X305", + b.powi(3) * c.powi(3) * ca, + c.powi(3) * a.powi(3) * cb, + a.powi(3) * b.powi(3) * cc, + ); + } + // X(306): isotomic of X(27); bary bc(b+c) cos A + { + push_bary( + &mut out, + "X27等截", + "X_{306}", + "X(306) = \\mathrm{isotomic}(X_{27});\\ bc(b+c)\\cos A", + "X(306):X(27) 的等截共轭", + "X306", + b * c * (b + c) * ca, + c * a * (c + a) * cb, + a * b * (a + b) * cc, + ); + } + // X(307): isotomic of X(29); bary a b²c² (b+c) cos A / (b+c−a) + { + let f = |aa: f64, bb: f64, cc_: f64, caa: f64| { + let den = bb + cc_ - aa; + if den.abs() < 1e-14 { + return f64::NAN; + } + aa * bb * bb * cc_ * cc_ * (bb + cc_) * caa / den + }; + push_bary( + &mut out, + "X29等截", + "X_{307}", + "X(307) = \\mathrm{isotomic}(X_{29});\\ a b^2 c^2(b+c)\\cos A/(b+c-a)", + "X(307):X(29) 的等截共轭", + "X307", + f(a, b, c, ca), + f(b, c, a, cb), + f(c, a, b, cc), + ); + } + // X(308): isotomic of Brocard midpoint X(39); bary b²c²/(b²+c²) + { + let f = |bb: f64, cc_: f64| { + let den = bb * bb + cc_ * cc_; + if den < 1e-28 { + return f64::NAN; + } + (bb * bb * cc_ * cc_) / den + }; + push_bary( + &mut out, + "布罗卡尔中点等截", + "X_{308}", + "X(308) = \\mathrm{isotomic}(X_{39});\\ b^2 c^2/(b^2+c^2)", + "X(308):布罗卡尔中点的等截共轭", + "X308", + f(b, c), + f(c, a), + f(a, b), + ); + } + // X(309): isotomic of X(40); bary csc A / (−1−cos A+cos B+cos C) + { + let f = |saa: f64, caa: f64, cbb: f64, ccc: f64| { + if saa.abs() < 1e-14 { + return f64::NAN; + } + let den = -1.0 - caa + cbb + ccc; + if den.abs() < 1e-12 { + return f64::NAN; + } + (1.0 / saa) / den + }; + push_bary( + &mut out, + "X40等截", + "X_{309}", + "X(309) = \\mathrm{isotomic}(X_{40});\\ \\csc A/(-1-\\cos A+\\cos B+\\cos C)", + "X(309):X(40) 的等截共轭", + "X309", + f(sa, ca, cb, cc), + f(sb, cb, cc, ca), + f(sc, cc, ca, cb), + ); + } + // X(310): isotomic of X(42); bary b²c²/(b+c) + { + let f = |bb: f64, cc_: f64| { + let den = bb + cc_; + if den.abs() < 1e-14 { + return f64::NAN; + } + (bb * bb * cc_ * cc_) / den + }; + push_bary( + &mut out, + "X42等截", + "X_{310}", + "X(310) = \\mathrm{isotomic}(X_{42});\\ b^2 c^2/(b+c)", + "X(310):X(42) 的等截共轭", + "X310", + f(b, c), + f(c, a), + f(a, b), + ); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. @@ -17963,6 +18212,91 @@ mod tests { } } + #[test] + fn x301_to_x310_isotomics() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("第二等动力等截", "X_{301}", 6.980035984420878, -0.569704917658939), + ("第一拿破仑等截", "X_{302}", 4.048146288386569, 1.439502461266907), + ("第二拿破仑等截", "X_{303}", 4.736052005774706, 2.227003407468617), + ("克劳森等截", "X_{304}", 3.118113713687516, 0.586687038229961), + ("X25等截", "X_{305}", 2.823863062471592, 0.475494718798144), + ("X27等截", "X_{306}", 3.280024509803921, 0.647870375928079), + ("X29等截", "X_{307}", 3.786017197005147, 0.974079325155319), + ("布罗卡尔中点等截", "X_{308}", 3.972226143175291, 1.474498640597638), + ("X40等截", "X_{309}", 4.785798695210563, 4.595574343104375), + ("X42等截", "X_{310}", 3.867019616360488, 1.354255379025548), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + + // Isosceles 5-5-6: all finite (no 60°). + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: skip X301 (60°); keep the rest. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.label != "X_{301}"), "X301 should skip equil"); + for (grp, lab, ..) in want { + if lab == "X_{301}" { + continue; + } + assert!( + fs3.iter().any(|f| f.group == grp && f.label == lab), + "equil missing {} {}", + grp, + lab + ); + } + + // Right 3-4-5: all finite (no sec/60°/150° issues). + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { From 390ea7727125178002aff4cded3416b1ea017030 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:03:35 +0800 Subject: [PATCH 089/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X301=E2=80=93X310=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 832691 -> 836103 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 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Date: Mon, 2 Nov 2026 19:07:28 +0800 Subject: [PATCH 090/123] =?UTF-8?q?feat:=20ETC=20X311=E2=80=93X320=20isoto?= =?UTF-8?q?mics=20(Kosnita/Droussent=20band)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(311)–X(320) as isotomics of X(54)/X(57)/X(58)/X(65)/X(66)/ X(67)/X(68)/X(77)/X(79)/X(80) with right/equilateral guards where needed. --- crates/mathcore/src/geometry.rs | 319 ++++++++++++++++++++++++++++++++ 1 file changed, 319 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 1c3690f..1d7580b 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -12053,6 +12053,233 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(311)–X(320): continue isotomic band (ETC). + // X(311)=isotomic(X54); bary csc A cos(B−C). + // X(312)=isotomic(X57); bary bc(b+c−a). + // X(313)=isotomic(X58); bary (b+c)b²c². + // X(314)=isotomic(X65); bary bc(b+c−a)/(b+c). + // X(315)=isotomic(X66); bary b⁴+c⁴−a⁴. + // X(316)=Droussent pivot=isotomic(X67); bary b⁴+c⁴−a⁴−b²c²; skip equil (all 0). + // X(317)=isotomic(X68); bary tan A cos 2A csc² A; skip right (tan∞). + // X(318)=isotomic(X77); bary (1+sec A)/a; skip right (sec∞). + // X(319)=isotomic(X79); bary (1+2 cos A)/a. + // X(320)=isotomic(X80); bary (1−2 cos A)/a; skip equilateral (all zero). + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let equil = (a - b).abs() < 1e-12 && (b - c).abs() < 1e-12; + let right = ca.abs() < 1e-9 || cb.abs() < 1e-9 || cc.abs() < 1e-9; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(311): isotomic of Kosnita X(54); bary csc A cos(B−C) + { + let f = |saa: f64, bb: f64, cc_: f64| { + if saa.abs() < 1e-14 { + return f64::NAN; + } + (1.0 / saa) * (bb - cc_).cos() + }; + push_bary( + &mut out, + "科斯尼塔等截", + "X_{311}", + "X(311) = \\mathrm{isotomic}(X_{54});\\ \\csc A\\cos(B-C)", + "X(311):科斯尼塔点的等截共轭", + "X311", + f(sa, g[1], g[2]), + f(sb, g[2], g[0]), + f(sc, g[0], g[1]), + ); + } + // X(312): isotomic of X(57); bary bc(b+c−a) + { + push_bary( + &mut out, + "X57等截", + "X_{312}", + "X(312) = \\mathrm{isotomic}(X_{57});\\ bc(b+c-a)", + "X(312):X(57) 的等截共轭", + "X312", + b * c * (b + c - a), + c * a * (c + a - b), + a * b * (a + b - c), + ); + } + // X(313): isotomic of X(58); bary (b+c)b²c² + { + push_bary( + &mut out, + "X58等截", + "X_{313}", + "X(313) = \\mathrm{isotomic}(X_{58});\\ (b+c)b^2 c^2", + "X(313):X(58) 的等截共轭", + "X313", + (b + c) * b * b * c * c, + (c + a) * c * c * a * a, + (a + b) * a * a * b * b, + ); + } + // X(314): isotomic of X(65); bary bc(b+c−a)/(b+c) + { + let f = |aa: f64, bb: f64, cc_: f64| { + let den = bb + cc_; + if den.abs() < 1e-14 { + return f64::NAN; + } + bb * cc_ * (bb + cc_ - aa) / den + }; + push_bary( + &mut out, + "X65等截", + "X_{314}", + "X(314) = \\mathrm{isotomic}(X_{65});\\ bc(b+c-a)/(b+c)", + "X(314):X(65) 的等截共轭", + "X314", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(315): isotomic of X(66); bary b⁴+c⁴−a⁴ + { + push_bary( + &mut out, + "X66等截", + "X_{315}", + "X(315) = \\mathrm{isotomic}(X_{66});\\ b^4+c^4-a^4", + "X(315):X(66) 的等截共轭", + "X315", + b.powi(4) + c.powi(4) - a.powi(4), + c.powi(4) + a.powi(4) - b.powi(4), + a.powi(4) + b.powi(4) - c.powi(4), + ); + } + // X(316): Droussent pivot = isotomic of X(67); bary b⁴+c⁴−a⁴−b²c²; skip equil + if !equil { + push_bary( + &mut out, + "德鲁桑枢轴", + "X_{316}", + "X(316) = \\mathrm{Droussent}=\\mathrm{isotomic}(X_{67});\\ b^4+c^4-a^4-b^2c^2", + "X(316):德鲁桑枢轴(X(67) 等截)", + "X316", + b.powi(4) + c.powi(4) - a.powi(4) - b * b * c * c, + c.powi(4) + a.powi(4) - b.powi(4) - c * c * a * a, + a.powi(4) + b.powi(4) - c.powi(4) - a * a * b * b, + ); + } + // X(317): isotomic of Prasolov X(68); bary tan A cos 2A csc² A; skip right + if !right { + let f = |aa: f64, saa: f64| { + let s2 = saa * saa; + if s2 < 1e-28 { + return f64::NAN; + } + let c2a = (2.0 * aa).cos(); + aa.tan() * c2a / s2 + }; + push_bary( + &mut out, + "普拉索洛夫等截", + "X_{317}", + "X(317) = \\mathrm{isotomic}(X_{68});\\ \\tan A\\cos 2A\\csc^2 A", + "X(317):普拉索洛夫点的等截共轭", + "X317", + f(g[0], sa), + f(g[1], sb), + f(g[2], sc), + ); + } + // X(318): isotomic of X(77); bary (1+sec A)/a; skip right + if !right { + let f = |aa: f64, side: f64| { + if side.abs() < 1e-14 { + return f64::NAN; + } + let caa = aa.cos(); + if caa.abs() < 1e-12 { + return f64::NAN; + } + (1.0 + 1.0 / caa) / side + }; + push_bary( + &mut out, + "X77等截", + "X_{318}", + "X(318) = \\mathrm{isotomic}(X_{77});\\ (1+\\sec A)/a", + "X(318):X(77) 的等截共轭", + "X318", + f(g[0], a), + f(g[1], b), + f(g[2], c), + ); + } + // X(319): isotomic of X(79); bary (1+2 cos A)/a + { + let f = |caa: f64, side: f64| { + if side.abs() < 1e-14 { + return f64::NAN; + } + (1.0 + 2.0 * caa) / side + }; + push_bary( + &mut out, + "X79等截", + "X_{319}", + "X(319) = \\mathrm{isotomic}(X_{79});\\ (1+2\\cos A)/a", + "X(319):X(79) 的等截共轭", + "X319", + f(ca, a), + f(cb, b), + f(cc, c), + ); + } + // X(320): isotomic of X(80); bary (1−2 cos A)/a; skip equilateral + if !equil { + let f = |caa: f64, side: f64| { + if side.abs() < 1e-14 { + return f64::NAN; + } + (1.0 - 2.0 * caa) / side + }; + push_bary( + &mut out, + "X80等截", + "X_{320}", + "X(320) = \\mathrm{isotomic}(X_{80});\\ (1-2\\cos A)/a", + "X(320):X(80) 的等截共轭", + "X320", + f(ca, a), + f(cb, b), + f(cc, c), + ); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. @@ -18298,6 +18525,98 @@ mod tests { } + #[test] + fn x311_to_x320_isotomics() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("科斯尼塔等截", "X_{311}", 3.911819183019623, 1.532926653323435), + ("X57等截", "X_{312}", 3.522500000000000, 1.016658128379447), + ("X58等截", "X_{313}", 3.603790057518488, 1.140294449661418), + ("X65等截", "X_{314}", 3.657306007509387, 1.113361529827304), + ("X66等截", "X_{315}", 2.824048825869370, -0.260263437202232), + ("德鲁桑枢轴", "X_{316}", -8.341999151103565, -18.667500268970660), + ("普拉索洛夫等截", "X_{317}", 5.357551988453238, 3.916218055971332), + ("X77等截", "X_{318}", 4.358616504854369, 2.197354022271805), + ("X79等截", "X_{319}", 3.712500000000000, 1.085584103184833), + ("X80等截", "X_{320}", -25.687500000000011, -35.583034493280657), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: skip X316/X320 (all weights 0); keep the rest. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.label != "X_{316}"), "X316 should skip equil"); + assert!(fs3.iter().all(|f| f.label != "X_{320}"), "X320 should skip equil"); + for (grp, lab, ..) in want { + if lab == "X_{316}" || lab == "X_{320}" { + continue; + } + assert!( + fs3.iter().any(|f| f.group == grp && f.label == lab), + "equil missing {} {}", + grp, + lab + ); + } + + // Right 3-4-5: skip X317/X318 (tan/sec ∞); keep others. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().all(|f| f.label != "X_{317}"), "X317 should skip right"); + assert!(fs4.iter().all(|f| f.label != "X_{318}"), "X318 should skip right"); + for (grp, lab, ..) in want { + if lab == "X_{317}" || lab == "X_{318}" { + continue; + } + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From bf3bb730ef4665a3585a6775e1f6305022b21567 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:07:28 +0800 Subject: [PATCH 091/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X311=E2=80=93X320=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 836103 -> 838930 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 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Content-Transfer-Encoding: 8bit Land X(321)–X(330) as isotomics of X(81)/X(84)/X(94)/X(97)/X(158)/ X(182)/X(186)/X(189)/X(192) plus X(2)-Hirst of X(69), with right/equilateral guards where needed. --- crates/mathcore/src/geometry.rs | 337 ++++++++++++++++++++++++++++++++ 1 file changed, 337 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 1d7580b..5680598 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -12280,6 +12280,249 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(321)–X(330): continue isotomic / Hirst band (ETC). + // X(321)=isotomic(X81); bary bc(b+c). + // X(322)=isotomic(X84); bary (−1−cos A+cos B+cos C)csc A. + // X(323)=isotomic(X94); bary sin 3A csc A; skip equilateral (sin 3A=0). + // X(324)=isotomic(X97); bary sec A cos(B−C); skip right (sec∞). + // X(325)=X(2)-Hirst of X(69); bary b⁴+c⁴−a²b²−a²c²; skip equil (all 0). + // X(326)=isotomic(X158); bary csc A−sin A. + // X(327)=isotomic(X182); bary csc A sec(A−ω). + // X(328)=isotomic(X186); bary cos A csc 3A; skip equilateral (sin 3A=0). + // X(329)=isotomic(X189); bary −1−cos A+cos B+cos C. + // X(330)=isotomic(X192); bary 1/(ab+ac−bc). + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let equil = (a - b).abs() < 1e-12 && (b - c).abs() < 1e-12; + let right = ca.abs() < 1e-9 || cb.abs() < 1e-9 || cc.abs() < 1e-9; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(321): isotomic of X(81); bary bc(b+c) + { + push_bary( + &mut out, + "X81等截", + "X_{321}", + "X(321) = \\mathrm{isotomic}(X_{81});\\ bc(b+c)", + "X(321):X(81) 的等截共轭", + "X321", + b * c * (b + c), + c * a * (c + a), + a * b * (a + b), + ); + } + // X(322): isotomic of X(84); bary (−1−cos A+cos B+cos C)csc A + { + let f = |caa: f64, cbb: f64, ccc: f64, saa: f64| { + if saa.abs() < 1e-14 { + return f64::NAN; + } + (-1.0 - caa + cbb + ccc) / saa + }; + push_bary( + &mut out, + "X84等截", + "X_{322}", + "X(322) = \\mathrm{isotomic}(X_{84});\\ (-1-\\cos A+\\cos B+\\cos C)\\csc A", + "X(322):X(84) 的等截共轭", + "X322", + f(ca, cb, cc, sa), + f(cb, cc, ca, sb), + f(cc, ca, cb, sc), + ); + } + // X(323): isotomic of X(94); bary sin 3A csc A; skip equilateral + if !equil { + let f = |aa: f64, saa: f64| { + if saa.abs() < 1e-14 { + return f64::NAN; + } + (3.0 * aa).sin() / saa + }; + push_bary( + &mut out, + "X94等截", + "X_{323}", + "X(323) = \\mathrm{isotomic}(X_{94});\\ \\sin 3A\\csc A", + "X(323):X(94) 的等截共轭", + "X323", + f(g[0], sa), + f(g[1], sb), + f(g[2], sc), + ); + } + // X(324): isotomic of X(97); bary sec A cos(B−C); skip right + if !right { + let f = |aa: f64, bb: f64, cc_: f64| { + let caa = aa.cos(); + if caa.abs() < 1e-12 { + return f64::NAN; + } + (1.0 / caa) * (bb - cc_).cos() + }; + push_bary( + &mut out, + "X97等截", + "X_{324}", + "X(324) = \\mathrm{isotomic}(X_{97});\\ \\sec A\\cos(B-C)", + "X(324):X(97) 的等截共轭", + "X324", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(325): X(2)-Hirst inverse of X(69); bary b⁴+c⁴−a²b²−a²c²; skip equil + if !equil { + let f = |aa: f64, bb: f64, cc_: f64| { + bb.powi(4) + cc_.powi(4) - aa * aa * bb * bb - aa * aa * cc_ * cc_ + }; + push_bary( + &mut out, + "X69-Hirst", + "X_{325}", + "X(325) = X(2)\\text{-Hirst of }X(69);\\ b^4+c^4-a^2b^2-a^2c^2", + "X(325):重心对 X(69) 的 Hirst 逆", + "X325", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(326): isotomic of X(158); bary csc A−sin A + { + let f = |saa: f64| { + if saa.abs() < 1e-14 { + return f64::NAN; + } + 1.0 / saa - saa + }; + push_bary( + &mut out, + "X158等截", + "X_{326}", + "X(326) = \\mathrm{isotomic}(X_{158});\\ \\csc A-\\sin A", + "X(326):X(158) 的等截共轭", + "X326", + f(sa), + f(sb), + f(sc), + ); + } + // X(327): isotomic of X(182); bary csc A sec(A−ω) + if area > 1e-12 { + let sum_sq = a * a + b * b + c * c; + let tan_w = (4.0 * area) / sum_sq; + let cos_w = 1.0 / (1.0 + tan_w * tan_w).sqrt(); + let sin_w = tan_w * cos_w; + let f = |caa: f64, saa: f64| { + if saa.abs() < 1e-14 { + return f64::NAN; + } + let caw = caa * cos_w + saa * sin_w; // cos(A−ω) + if caw.abs() < 1e-12 { + return f64::NAN; + } + (1.0 / saa) * (1.0 / caw) + }; + push_bary( + &mut out, + "X182等截", + "X_{327}", + "X(327) = \\mathrm{isotomic}(X_{182});\\ \\csc A\\sec(A-\\omega)", + "X(327):X(182) 的等截共轭", + "X327", + f(ca, sa), + f(cb, sb), + f(cc, sc), + ); + } + // X(328): isotomic of X(186); bary cos A csc 3A; skip equilateral + if !equil { + let f = |aa: f64, caa: f64| { + let s3 = (3.0 * aa).sin(); + if s3.abs() < 1e-12 { + return f64::NAN; + } + caa / s3 + }; + push_bary( + &mut out, + "X186等截", + "X_{328}", + "X(328) = \\mathrm{isotomic}(X_{186});\\ \\cos A\\csc 3A", + "X(328):X(186) 的等截共轭", + "X328", + f(g[0], ca), + f(g[1], cb), + f(g[2], cc), + ); + } + // X(329): isotomic of X(189); bary −1−cos A+cos B+cos C + { + let f = |caa: f64, cbb: f64, ccc: f64| -1.0 - caa + cbb + ccc; + push_bary( + &mut out, + "X189等截", + "X_{329}", + "X(329) = \\mathrm{isotomic}(X_{189});\\ -1-\\cos A+\\cos B+\\cos C", + "X(329):X(189) 的等截共轭", + "X329", + f(ca, cb, cc), + f(cb, cc, ca), + f(cc, ca, cb), + ); + } + // X(330): isotomic of X(192); bary 1/(ab+ac−bc) + { + let f = |aa: f64, bb: f64, cc_: f64| { + let den = aa * bb + aa * cc_ - bb * cc_; + if den.abs() < 1e-14 { + return f64::NAN; + } + 1.0 / den + }; + push_bary( + &mut out, + "X192等截", + "X_{330}", + "X(330) = \\mathrm{isotomic}(X_{192});\\ 1/(ab+ac-bc)", + "X(330):X(192) 的等截共轭", + "X330", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + } + + + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. @@ -18617,6 +18860,100 @@ mod tests { } + + #[test] + fn x321_to_x330_isotomics_hirst() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("X81等截", "X_{321}", 3.889030612244898, 1.348628129482940), + ("X84等截", "X_{322}", 2.908504654771140, 0.082815441023927), + ("X94等截", "X_{323}", -9.565217391304380, -14.144808742670605), + ("X97等截", "X_{324}", 4.608069490996023, 2.866308824482292), + ("X69-Hirst", "X_{325}", -3.779446095076401, -7.521371467594975), + ("X158等截", "X_{326}", 2.837852693294247, 0.312932512949334), + ("X182等截", "X_{327}", 4.197417914700023, 1.781695822447367), + ("X186等截", "X_{328}", 6.673399984546004, -0.313443046787493), + ("X189等截", "X_{329}", 3.200255102040816, 0.103740625344842), + ("X192等截", "X_{330}", 3.625542848870874, 1.250954558660292), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: skip X323/X325/X328 (sin3A / all-zero); keep the rest. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.label != "X_{323}"), "X323 should skip equil"); + assert!(fs3.iter().all(|f| f.label != "X_{325}"), "X325 should skip equil"); + assert!(fs3.iter().all(|f| f.label != "X_{328}"), "X328 should skip equil"); + for (grp, lab, ..) in want { + if lab == "X_{323}" || lab == "X_{325}" || lab == "X_{328}" { + continue; + } + assert!( + fs3.iter().any(|f| f.group == grp && f.label == lab), + "equil missing {} {}", + grp, + lab + ); + } + + // Right 3-4-5: skip X324 (sec ∞); keep others (X328 finite: only right-angle weight 0). + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().all(|f| f.label != "X_{324}"), "X324 should skip right"); + for (grp, lab, ..) in want { + if lab == "X_{324}" { + continue; + } + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + + + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 6ed06e9c647cd02ac5278871e5330b9198847280 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:10:52 +0800 Subject: [PATCH 093/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X321=E2=80=93X330=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 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zi(Xm!8XcOuD*DX{k#@CL3qp+6V=Gv-484r%LZ<21#)moijkSkCxT)b5T~XIsKQdo1 zY##{t;4MJZ>#Xm2J|%?OY|}MtL4UbLuP1G=4l-r@gsosXH(L97pvore@~t(3<@EBV zp>Y#;Kn=-ht;vazEE#UL#q_aH~ zz7uS1wVirHKe!#md^|Yjv$({BeOAie37QKs96)z=0&Z}pu%3_9);-|6e6(^jMKK(kz{1A0xwxj=Q`!wAfP zr#;dcYkBV9P}QKyXRTEYD4zit{TA2lTn=Iglg?X5dpLYM9XOcbrK?ImTHndttJN`hKUqh3>Zr&*DGpHFT}Sk8(naeeYI#B*Lg6qs&^JeQU&|$H zRQ+-kvklzKWy(6LCrVeWHH=2m=wr}2T(y2?&eh|`picS)*u*fItQ`SyzV2}>&}(^{ z5G7x?Rso^cRtbv#hgLZjHnT@o z34b43CD`>X From 70df8041d6c76d437b6cff2f2bee0d14fe533621 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:13:57 +0800 Subject: [PATCH 094/123] =?UTF-8?q?feat:=20ETC=20X331=E2=80=93X340=20isoto?= =?UTF-8?q?mics=20+=20cevapoints?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(331)–X(340) as isotomics of X(219)/X(225)/X(226)/X(238)/X(239)/ X(240)/X(242)/X(249)/X(250)/X(265), with X(333)/X(338) also as cevapoints of (X8,X9) and (X115,X125); right/equilateral guards where needed. --- crates/mathcore/src/geometry.rs | 367 ++++++++++++++++++++++++++++++++ 1 file changed, 367 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 5680598..3f0d639 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -12522,6 +12522,276 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } + // X(331)–X(340): continue isotomic / cevapoint band (ETC). + // X(331)=isotomic(X219); bary sec²(A/2) sec A; skip right (sec∞). + // X(332)=isotomic(X225); bary cot A/(cos B+cos C); skip right (cot∞). + // X(333)=isotomic(X226)=cevapoint(X8,X9); bary (b+c−a)/(b+c). + // X(334)=isotomic(X238); bary bc/(a²−bc); skip equil. + // X(335)=isotomic(X239); bary 1/(a²−bc); skip equil; X(2)-Hirst of X(291). + // X(336)=isotomic(X240); bary cot A sec(A+ω); skip right/equil. + // X(337)=isotomic(X242); bary cot A/(a²−bc); skip right/equil. + // X(338)=isotomic(X249)=cevapoint(X115,X125); bary sin²(B−C); skip equil. + // X(339)=isotomic(X250); bary cot A sin²(B−C); skip right/equil. + // X(340)=isotomic(X265); bary sec A sin 3A csc² A; skip right/equil. + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let equil = (a - b).abs() < 1e-12 && (b - c).abs() < 1e-12; + let right = ca.abs() < 1e-9 || cb.abs() < 1e-9 || cc.abs() < 1e-9; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(331): isotomic of X(219); bary sec²(A/2) sec A; skip right + if !right { + let f = |aa: f64| { + let caa = aa.cos(); + if caa.abs() < 1e-12 { + return f64::NAN; + } + let cah = (aa * 0.5).cos(); + if cah.abs() < 1e-12 { + return f64::NAN; + } + (1.0 / (cah * cah)) * (1.0 / caa) + }; + push_bary( + &mut out, + "X219等截", + "X_{331}", + "X(331) = \\mathrm{isotomic}(X_{219});\\ \\sec^2\\tfrac{A}{2}\\sec A", + "X(331):X(219) 的等截共轭", + "X331", + f(g[0]), + f(g[1]), + f(g[2]), + ); + } + // X(332): isotomic of X(225); bary cot A/(cos B+cos C); skip right + if !right { + let f = |aa: f64, cbb: f64, ccc: f64| { + let saa = aa.sin(); + let caa = aa.cos(); + if saa.abs() < 1e-14 { + return f64::NAN; + } + let den = cbb + ccc; + if den.abs() < 1e-14 { + return f64::NAN; + } + (caa / saa) / den + }; + push_bary( + &mut out, + "X225等截", + "X_{332}", + "X(332) = \\mathrm{isotomic}(X_{225});\\ \\cot A/(\\cos B+\\cos C)", + "X(332):X(225) 的等截共轭", + "X332", + f(g[0], cb, cc), + f(g[1], cc, ca), + f(g[2], ca, cb), + ); + } + // X(333): isotomic of X(226)=cevapoint(X8,X9); bary (b+c−a)/(b+c) + { + let f = |aa: f64, bb: f64, cc_: f64| { + let den = bb + cc_; + if den.abs() < 1e-14 { + return f64::NAN; + } + (bb + cc_ - aa) / den + }; + push_bary( + &mut out, + "X8X9截点", + "X_{333}", + "X(333) = \\mathrm{isotomic}(X_{226})=\\mathrm{cevapoint}(X_8,X_9);\\ (b+c-a)/(b+c)", + "X(333):X(226) 的等截共轭(奈格尔与米滕阿列夫的截点)", + "X333", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(334): isotomic of X(238); bary bc/(a²−bc); skip equil + if !equil { + let f = |aa: f64, bb: f64, cc_: f64| { + let den = aa * aa - bb * cc_; + if den.abs() < 1e-14 { + return f64::NAN; + } + bb * cc_ / den + }; + push_bary( + &mut out, + "X238等截", + "X_{334}", + "X(334) = \\mathrm{isotomic}(X_{238});\\ bc/(a^2-bc)", + "X(334):X(238) 的等截共轭", + "X334", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(335): isotomic of X(239); bary 1/(a²−bc); skip equil + if !equil { + let f = |aa: f64, bb: f64, cc_: f64| { + let den = aa * aa - bb * cc_; + if den.abs() < 1e-14 { + return f64::NAN; + } + 1.0 / den + }; + push_bary( + &mut out, + "X239等截", + "X_{335}", + "X(335) = \\mathrm{isotomic}(X_{239});\\ 1/(a^2-bc)", + "X(335):X(239) 的等截共轭(重心对 X(291) 的 Hirst 逆)", + "X335", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(336): isotomic of X(240); bary cot A sec(A+ω); skip right/equil + if !right && !equil && area > 1e-12 { + let sum_sq = a * a + b * b + c * c; + let tan_w = (4.0 * area) / sum_sq; + let cos_w = 1.0 / (1.0 + tan_w * tan_w).sqrt(); + let sin_w = tan_w * cos_w; + let f = |_aa: f64, caa: f64, saa: f64| { + if saa.abs() < 1e-14 { + return f64::NAN; + } + let caw = caa * cos_w - saa * sin_w; // cos(A+ω) + if caw.abs() < 1e-12 { + return f64::NAN; + } + (caa / saa) * (1.0 / caw) + }; + push_bary( + &mut out, + "X240等截", + "X_{336}", + "X(336) = \\mathrm{isotomic}(X_{240});\\ \\cot A\\sec(A+\\omega)", + "X(336):X(240) 的等截共轭", + "X336", + f(g[0], ca, sa), + f(g[1], cb, sb), + f(g[2], cc, sc), + ); + } + // X(337): isotomic of X(242); bary cot A/(a²−bc); skip right/equil + if !right && !equil { + let f = |aa: f64, saa: f64, caa: f64, bb: f64, cc_: f64| { + if saa.abs() < 1e-14 { + return f64::NAN; + } + let den = aa * aa - bb * cc_; + if den.abs() < 1e-14 { + return f64::NAN; + } + (caa / saa) / den + }; + push_bary( + &mut out, + "X242等截", + "X_{337}", + "X(337) = \\mathrm{isotomic}(X_{242});\\ \\cot A/(a^2-bc)", + "X(337):X(242) 的等截共轭", + "X337", + f(a, sa, ca, b, c), + f(b, sb, cb, c, a), + f(c, sc, cc, a, b), + ); + } + // X(338): isotomic of X(249)=cevapoint(X115,X125); bary sin²(B−C); skip equil + if !equil { + let f = |bb: f64, cc_: f64| (bb - cc_).sin().powi(2); + push_bary( + &mut out, + "X115X125截点", + "X_{338}", + "X(338) = \\mathrm{isotomic}(X_{249})=\\mathrm{cevapoint}(X_{115},X_{125});\\ \\sin^2(B-C)", + "X(338):X(249) 的等截共轭(X(115) 与 X(125) 的截点)", + "X338", + f(g[1], g[2]), + f(g[2], g[0]), + f(g[0], g[1]), + ); + } + // X(339): isotomic of X(250); bary cot A sin²(B−C); skip right/equil + if !right && !equil { + let f = |_aa: f64, saa: f64, caa: f64, bb: f64, cc_: f64| { + if saa.abs() < 1e-14 { + return f64::NAN; + } + (caa / saa) * (bb - cc_).sin().powi(2) + }; + push_bary( + &mut out, + "X250等截", + "X_{339}", + "X(339) = \\mathrm{isotomic}(X_{250});\\ \\cot A\\sin^2(B-C)", + "X(339):X(250) 的等截共轭", + "X339", + f(g[0], sa, ca, g[1], g[2]), + f(g[1], sb, cb, g[2], g[0]), + f(g[2], sc, cc, g[0], g[1]), + ); + } + // X(340): isotomic of X(265); bary sec A sin 3A csc² A; skip right/equil + if !right && !equil { + let f = |aa: f64, caa: f64, saa: f64| { + if caa.abs() < 1e-12 || saa.abs() < 1e-14 { + return f64::NAN; + } + let s3 = (3.0 * aa).sin(); + (1.0 / caa) * s3 / (saa * saa) + }; + push_bary( + &mut out, + "X265等截", + "X_{340}", + "X(340) = \\mathrm{isotomic}(X_{265});\\ \\sec A\\sin 3A\\csc^2 A", + "X(340):X(265) 的等截共轭", + "X340", + f(g[0], ca, sa), + f(g[1], cb, sb), + f(g[2], cc, sc), + ); + } + } + + + + + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. @@ -18954,6 +19224,103 @@ mod tests { + + #[test] + fn x331_to_x340_isotomics_cevapoint() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("X219等截", "X_{331}", 4.769073392555508, 3.0742351468193774), + ("X225等截", "X_{332}", 3.044366502748047, 0.5146519307677269), + ("X8X9截点", "X_{333}", 3.941062176165803, 1.316914674066641), + ("X238等截", "X_{334}", 8.34631898880741, 0.20599981373956375), + ("X239等截", "X_{335}", 8.256278538812786, 0.23211372794051305), + ("X240等截", "X_{336}", 5.9841189990450365, -0.4119053953863263), + ("X242等截", "X_{337}", 8.577022110932628, 0.10086847158635727), + ("X115X125截点", "X_{338}", 5.653052416823602, 0.5392819325051049), + ("X250等截", "X_{339}", 5.0231776939692505, 0.20838596892903413), + ("X265等截", "X_{340}", 12.275278204144273, 15.32009389925589), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + + // Isosceles 5-5-6: X338/X339 degenerate (B=C ⇒ sin(B−C)=0 chain); keep others. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + if lab == "X_{338}" || lab == "X_{339}" { + continue; + } + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: skip X334–X340 (a²−bc / A+ω / sin(B−C) / sin3A); keep X331–X333. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + for lab in ["X_{334}", "X_{335}", "X_{336}", "X_{337}", "X_{338}", "X_{339}", "X_{340}"] { + assert!(fs3.iter().all(|f| f.label != lab), "{} should skip equil", lab); + } + for (grp, lab, ..) in want { + if lab == "X_{331}" || lab == "X_{332}" || lab == "X_{333}" { + assert!( + fs3.iter().any(|f| f.group == grp && f.label == lab), + "equil missing {} {}", + grp, + lab + ); + } + } + + // Right 3-4-5: skip X331/X332/X336/X337/X339/X340 (sec/cot); keep X333–X335/X338. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for lab in ["X_{331}", "X_{332}", "X_{336}", "X_{337}", "X_{339}", "X_{340}"] { + assert!(fs4.iter().all(|f| f.label != lab), "{} should skip right", lab); + } + for (grp, lab, ..) in want { + if matches!(lab, "X_{333}" | "X_{334}" | "X_{335}" | "X_{338}") { + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + } + + + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 324bb3e7e118b82a1e4ff4b169f461cbdfb53f80 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:13:57 +0800 Subject: [PATCH 095/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X331=E2=80=93X340=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 841922 -> 845647 bytes 1 file changed, 0 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zxH$Xd76LQ%AUEhQO^ixTiElZLF`pR~oOY|grLPZ?&WQI{OJ}M0@9@Q(GgmfnHTrif z|MPCdBp1729%&G+^xwgTE}BCPRpF=GS~Xn0lzJPsv&-gBjp3?u2cvL>`rOe*va9CK znI(k{=Nfgq3oFERdU98*&VDn;xU6Z2j4)R-8nFGImRq@L&SJg%`<~VYo{!e|F&@9W zeJaoln}InH({Ms7rX#uM9W(3JJM6Bxm#gkz>U0Z4`kwhG>U38ds6+5-ct6y7OAl!9 zLtL%?kaj%O2Ev_D?-APl80$pW!ojwRN$E+Cwf??O%%&a#Vxr@pnw4%4U!R#-OmzR} zW|JOS`@$S9tOymUQy$n%Dr{A)Q0U)2)~eKdX=d>3yfQ0caP0nRX889nGefA*Ya}7( zjhP|p;;mWf(m6K%Z=?ZwXEq^tHNZc?5@L+VxO9j?Lo8)<$QsreitbR$2AG^PgLmGf zYm>ng6Q5`kXu=b%IrVs|HH8Nt<*C+=jj+_BK8p|q5%dfS!$?beomV>|pK0Tz{|8^o B6OjM_ From 5e93026945e12d761da0328950544573c835feb4 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:20:28 +0800 Subject: [PATCH 098/123] =?UTF-8?q?feat:=20ETC=20X351=E2=80=93X360=20Parry?= =?UTF-8?q?/Weill/Fuhrmann/Morley=20+=20Hofstadter=20duals?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(351)–X(358) (Parry-circle center, circum/Brocard inverses on the Parry circle, Weill, Fuhrmann, Morley + Taylor–Marr perspectors) and add X(359)/X(360) dual labels on existing Hofstadter Hf_1/Hf_0; equil/isos guards where bary weights vanish. --- crates/mathcore/src/geometry.rs | 304 ++++++++++++++++++++++++++++++++ 1 file changed, 304 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index a125a7c..101847e 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -2216,6 +2216,18 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] y: hz[1], label: "Hf0 霍夫".into(), })); + out.push(fact( + "霍夫斯塔特点", + "X_{360}", + pt(hz[0], hz[1]), + None, + "X(360) = (A:B:C)", + "X(360):霍夫斯塔特零点", + ).with(Shape::Point { + x: hz[0], + y: hz[1], + label: "X360".into(), + })); let wa = (a * a) / g[0]; let wb = (b * b) / g[1]; let wc = (c * c) / g[2]; @@ -2237,6 +2249,18 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] y: ho[1], label: "Hf1 霍夫".into(), })); + out.push(fact( + "霍夫斯塔特点", + "X_{359}", + pt(ho[0], ho[1]), + None, + "X(359) = (a^2/A:b^2/B:c^2/C)", + "X(359):霍夫斯塔特一点(等角共轭于 X(360))", + ).with(Shape::Point { + x: ho[0], + y: ho[1], + label: "X359".into(), + })); } } } @@ -13032,6 +13056,196 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(351)–X(360): Parry/Weill/Fuhrmann/Morley/Hofstadter band (ETC). + // X(351)=Parry-circle center=crosspoint(X110,X111); bary a²(b²−c²)(b²+c²−2a²); skip equil (and den=0 isos). + // X(352)=circumcircle-inverse of X(353); bary a²(−a⁴−b⁴−c⁴−5b²c²+4a²b²+4a²c²); skip equil. + // X(353)=Brocard-circle-inverse of X(111); bary a²(4a⁴−2b⁴−2c⁴−b²c²−4a²b²−4a²c²). + // X(354)=Weill=centroid(intouch)=crosspoint(X1,X7); bary a[(b−c)²−ab−ac]. + // X(355)=Fuhrmann=midpoint(X4,X8); bary a(a cos A−(b+c)cos(B−C)). + // X(356)=Morley center; bary sin A(cos A/3+2 cos B/3 cos C/3). + // X(357)=1st Morley–Taylor–Marr; bary sin A sec(A/3); isogonal of X(358). + // X(358)=2nd Morley–Taylor–Marr; bary sin A cos(A/3). + // X(359)/X(360)=Hofstadter one/zero: dual-labeled earlier as Hf_1/Hf_0 (a²/A and A:B:C). + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let equil = (a - b).abs() < 1e-12 && (b - c).abs() < 1e-12; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(351): Parry circle center; skip equil (weights vanish) + if !equil { + let f = |aa: f64, bb: f64, cc_: f64| { + aa * aa * (bb * bb - cc_ * cc_) * (bb * bb + cc_ * cc_ - 2.0 * aa * aa) + }; + push_bary( + &mut out, + "帕里圆心", + "X_{351}", + "X(351) = \\mathrm{crosspoint}(X_{110},X_{111});\\ a^2(b^2-c^2)(b^2+c^2-2a^2)", + "X(351):帕里圆圆心(X(110) 与 X(111) 的交点)", + "X351", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(352): inverse-in-circumcircle of X(353); skip equil + if !equil { + let f = |aa: f64, bb: f64, cc_: f64| { + let aa2 = aa * aa; + aa2 * (-aa.powi(4) + - bb.powi(4) + - cc_.powi(4) + - 5.0 * bb * bb * cc_ * cc_ + + 4.0 * aa2 * bb * bb + + 4.0 * aa2 * cc_ * cc_) + }; + push_bary( + &mut out, + "X353外接逆", + "X_{352}", + "X(352) = \\mathrm{circumcircle\\text{-}inverse}(X_{353});\\ a^2(-a^4-\\cdots)", + "X(352):X(353) 关于外接圆的反演(帕里圆上)", + "X352", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(353): inverse-in-Brocard-circle of X(111) + { + let f = |aa: f64, bb: f64, cc_: f64| { + let aa2 = aa * aa; + aa2 * (4.0 * aa.powi(4) + - 2.0 * bb.powi(4) + - 2.0 * cc_.powi(4) + - bb * bb * cc_ * cc_ + - 4.0 * aa2 * bb * bb + - 4.0 * aa2 * cc_ * cc_) + }; + push_bary( + &mut out, + "X111Brocard逆", + "X_{353}", + "X(353) = \\mathrm{Brocard\\text{-}circle\\text{-}inverse}(X_{111});\\ a^2(4a^4-\\cdots)", + "X(353):帕里点关于 Brocard 圆的反演(帕里圆上)", + "X353", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(354): Weill = centroid of intouch = crosspoint(I, Ge) + { + let f = |aa: f64, bb: f64, cc_: f64| aa * ((bb - cc_).powi(2) - aa * bb - aa * cc_); + push_bary( + &mut out, + "Weill点", + "X_{354}", + "X(354) = \\mathrm{crosspoint}(X_1,X_7);\\ a[(b-c)^2-ab-ac]", + "X(354):Weill 点(内切三角形重心;内心与热尔贡点交点)", + "X354", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(355): Fuhrmann = midpoint(H, Na) + { + let f = |aa: f64, bb: f64, cc_: f64, caa: f64, ang_b: f64, ang_c: f64| { + aa * (aa * caa - (bb + cc_) * (ang_b - ang_c).cos()) + }; + push_bary( + &mut out, + "Fuhrmann心", + "X_{355}", + "X(355) = \\mathrm{midpoint}(X_4,X_8);\\ a(a\\cos A-(b+c)\\cos(B-C))", + "X(355):Fuhrmann 圆心(垂心与奈格尔点的中点)", + "X355", + f(a, b, c, ca, g[1], g[2]), + f(b, c, a, cb, g[2], g[0]), + f(c, a, b, cc, g[0], g[1]), + ); + } + // X(356): Morley center (centroid of Morley equilateral) + { + let f = |saa: f64, aa: f64, bb: f64, cc_: f64| { + saa * ((aa / 3.0).cos() + 2.0 * (bb / 3.0).cos() * (cc_ / 3.0).cos()) + }; + push_bary( + &mut out, + "莫利中心", + "X_{356}", + "X(356) = \\mathrm{centroid}(\\mathrm{Morley});\\ \\sin A(\\cos\\tfrac{A}{3}+2\\cos\\tfrac{B}{3}\\cos\\tfrac{C}{3})", + "X(356):莫利三角形重心", + "X356", + f(sa, g[0], g[1], g[2]), + f(sb, g[1], g[2], g[0]), + f(sc, g[2], g[0], g[1]), + ); + } + // X(357): 1st Morley–Taylor–Marr; bary sin A sec(A/3) + { + let f = |saa: f64, aa: f64| { + let c3 = (aa / 3.0).cos(); + if c3.abs() < 1e-12 { + return f64::NAN; + } + saa / c3 + }; + push_bary( + &mut out, + "莫利透视1", + "X_{357}", + "X(357) = \\mathrm{perspector}(\\mathrm{Morley});\\ \\sin A\\sec\\tfrac{A}{3}", + "X(357):第一 Morley–Taylor–Marr 点(莫利三角形透视中心)", + "X357", + f(sa, g[0]), + f(sb, g[1]), + f(sc, g[2]), + ); + } + // X(358): 2nd Morley–Taylor–Marr; bary sin A cos(A/3); isogonal of X(357) + { + let f = |saa: f64, aa: f64| saa * (aa / 3.0).cos(); + push_bary( + &mut out, + "莫利透视2", + "X_{358}", + "X(358) = \\mathrm{isogonal}(X_{357});\\ \\sin A\\cos\\tfrac{A}{3}", + "X(358):第二 Morley–Taylor–Marr 点(X(357) 的等角共轭)", + "X358", + f(sa, g[0]), + f(sb, g[1]), + f(sc, g[2]), + ); + } + // X(359)/X(360) dual-labeled in the Hofstadter block above (Hf_1 / Hf_0). + } // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. @@ -19652,6 +19866,96 @@ mod tests { } } + #[test] + fn x351_to_x360_parry_weill_fuhrmann_morley_hofstadter() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("帕里圆心", "X_{351}", 11.85128205128205, 11.10255225912793), + ("X353外接逆", "X_{352}", 20.15527987178726, 19.87863244216875), + ("X111Brocard逆", "X_{353}", 4.447476932992233, 1.554796870948855), + ("Weill点", "X_{354}", 4.578125, 2.077694190934187), + ("Fuhrmann心", "X_{355}", 4.3125, 2.114003409804882), + ("莫利中心", "X_{356}", 4.509210790491602, 1.955745846402668), + ("莫利透视1", "X_{357}", 4.531119259517901, 1.998524871477102), + ("莫利透视2", "X_{358}", 4.467903088960554, 1.875087394301666), + ("霍夫斯塔特点", "X_{359}", 4.397629009565369, 1.746395448825259), + ("霍夫斯塔特点", "X_{360}", 4.592957569749832, 2.132793086433669), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + + // Isosceles 5-5-6: X351 den→0 (skip); keep X352–X360. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().all(|f| f.label != "X_{351}"), "X351 should skip isos 5-5-6"); + for (grp, lab, ..) in want { + if lab == "X_{351}" { + continue; + } + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: skip X351/X352 (weights vanish); keep X353–X360. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + for lab in ["X_{351}", "X_{352}"] { + assert!(fs3.iter().all(|f| f.label != lab), "{} should skip equil", lab); + } + for (grp, lab, ..) in want { + if matches!(lab, "X_{351}" | "X_{352}") { + continue; + } + assert!( + fs3.iter().any(|f| f.group == grp && f.label == lab), + "equil missing {} {}", + grp, + lab + ); + } + + // Right 3-4-5: all in this band finite. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } #[test] From e77ac0f5e88ef5b54d800a906d284d5061c17af7 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:20:28 +0800 Subject: [PATCH 099/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X351=E2=80=93X360=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 849146 -> 852808 bytes 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zj(LTuQeVYsutPd{u>)9Uh850NoF&*{y_<#O9_nF7z&K3otgSlhDMzWV>Ktx6rl;c^ zQ`4Q5o&^z6iaBp8nbS4rBjq?vc3`>lbfC9sqOY?dJE5@rnmQk=&I2&tN{i~E# z#QCl5n%)ou+;u!=I3H23>j`pmD@q`&177;*xTqU?BeS=3+0R*&-PBDNpQUZvBa%Sm ziP>O35B8v$sV-*#yXDoD`q);ztt0%f+juCUo~PLF=xktY#9jSE`K;dbOm`O1?&;$c z`k)2x0jBG0sQ#`?#i_4zVDv}f3GqqM$xt!x)4Tv@7|YRzTWtE@0OtVg&_@(?j$wa* z!c21+BGH%Z#hj(sLp?=eQ6=h7%=uQ(Bi%OW2!rVV1`#H?yS@LADv;t Date: Mon, 2 Nov 2026 19:31:26 +0800 Subject: [PATCH 104/123] =?UTF-8?q?feat:=20ETC=20X381=E2=80=93X390=20ortho?= =?UTF-8?q?centroidal=20+=20Conway/Taylor/Hirst=20band?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(381)–X(390): midpoint(G,H) orthocentroidal center X381, reflection of O in H (X382), Euler∩X14X98 (X383; skip isos), Conway Euler X32X76 (X384), X2-Hirst of K (X385; skip equil), Brocard-inverse of X58 (X386), X1X2∩X4X6 (X387), X1X4∩X7X8 (X388), Taylor-circle center (X389), and reflection of Ge in I (X390). --- crates/mathcore/src/geometry.rs | 355 ++++++++++++++++++++++++++++++++ 1 file changed, 355 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index ae37887..291f9ad 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -13623,6 +13623,239 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } + // X(381)–X(390): orthocentroidal / Euler mates / Conway / Hirst / Taylor (ETC). + // X(381)=midpoint(G,H)=center of orthocentroidal circle; bary a(cos A+4 cos B cos C); =complement(X376). + // X(382)=reflection(O in H)=2H−O; bary a(cos A−4 cos B cos C). + // X(383)=Euler ∩ X(14)X(98); Brocard form with csc(B−C); skip isos (den0); equil→G. + // X(384)=Euler ∩ X(32)X(76) (Conway); bary a⁴+b²c². + // X(385)=X(2)-Hirst of X(6); bary a⁴−b²c²; skip equil (all zero). + // X(386)=Brocard-inverse of X(58)=ext. similitude(circum, Apollonius); bary a²(b²+c²+bc+ca+ab). + // X(387)=X(1)X(2) ∩ X(4)X(6); bary −a⁴+2a²(a+b+c)²+(b²−c²)². + // X(388)=X(1)X(4) ∩ X(7)X(8); bary a(1+cos B cos C) = [a²+(b+c)²]/(b+c−a). + // X(389)=Taylor-circle center; bary a[cos A−cos 2A cos(B−C)]; =midpoint(O,X52)=midpoint(H,X185). + // X(390)=reflection(Ge in I)=2I−X(7); bary (b+c−a)[3a²+(b−c)²]. + { + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let equil = (a - b).abs() < 1e-9 && (b - c).abs() < 1e-9; + let isos = (a - b).abs() < 1e-9 || (b - c).abs() < 1e-9 || (c - a).abs() < 1e-9; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(381): midpoint of G and H (orthocentroidal-circle center) + { + let f = |aa: f64, ang_a: f64, ang_b: f64, ang_c: f64| { + aa * (ang_a.cos() + 4.0 * ang_b.cos() * ang_c.cos()) + }; + push_bary( + &mut out, + "垂心重心圆圆心", + "X_{381}", + "X(381) = \\mathrm{mid}(G,H);\\ a(\\cos A+4\\cos B\\cos C)", + "X(381):重心与垂心的中点(垂心–重心圆圆心;X(376) 的补点)", + "X381", + f(a, g[0], g[1], g[2]), + f(b, g[1], g[2], g[0]), + f(c, g[2], g[0], g[1]), + ); + } + // X(382): reflection of O in H + { + let f = |aa: f64, ang_a: f64, ang_b: f64, ang_c: f64| { + aa * (ang_a.cos() - 4.0 * ang_b.cos() * ang_c.cos()) + }; + push_bary( + &mut out, + "外心垂心反射", + "X_{382}", + "X(382) = 2H-O;\\ a(\\cos A-4\\cos B\\cos C)", + "X(382):外心关于垂心的反射", + "X382", + f(a, g[0], g[1], g[2]), + f(b, g[1], g[2], g[0]), + f(c, g[2], g[0], g[1]), + ); + } + // X(383): Euler ∩ X(14)X(98); Brocard form; skip isos; equil→G + if equil { + push_bary( + &mut out, + "X14X98欧拉截", + "X_{383}", + "X(383) = X_{14}X_{98}\\cap\\mathrm{Euler};\\ \\mathrm{equil}\\to G", + "X(383):X(14)X(98) 与欧拉线的交点(等边退化为重心)", + "X383", + 1.0, + 1.0, + 1.0, + ); + } else if !isos && area > 1e-12 { + let cot_w = (a * a + b * b + c * c) / (4.0 * area); + let tan_w = 1.0 / cot_w; + let omega = tan_w.atan(); + let pi3 = std::f64::consts::PI / 3.0; + let f = |ang_b: f64, ang_c: f64| { + let dbc = ang_b - ang_c; + if dbc.abs() < 1e-12 { + return f64::NAN; + } + (1.0 / dbc.sin()) + * ((2.0 * ang_b).sin() * (ang_c - omega).cos() * (ang_c + pi3).sin() + - (2.0 * ang_c).sin() * (ang_b - omega).cos() * (ang_b + pi3).sin()) + }; + let fa = f(g[1], g[2]); + let fb = f(g[2], g[0]); + let fc = f(g[0], g[1]); + push_bary( + &mut out, + "X14X98欧拉截", + "X_{383}", + "X(383) = X_{14}X_{98}\\cap\\mathrm{Euler};\\ (\\sin A)f(A,B,C)", + "X(383):X(14)X(98) 与欧拉线的交点(跳过等腰)", + "X383", + sa * fa, + sb * fb, + sc * fc, + ); + } + // X(384): Conway Euler point; bary a⁴+b²c² + { + let f = |aa: f64, bb: f64, cc_: f64| aa.powi(4) + bb * bb * cc_ * cc_; + push_bary( + &mut out, + "X32X76欧拉截", + "X_{384}", + "X(384) = X_{32}X_{76}\\cap\\mathrm{Euler};\\ a^4+b^2c^2", + "X(384):X(32)X(76) 与欧拉线的交点(Conway)", + "X384", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(385): X(2)-Hirst inverse of X(6); skip equilateral + if !equil { + let f = |aa: f64, bb: f64, cc_: f64| aa.powi(4) - bb * bb * cc_ * cc_; + push_bary( + &mut out, + "重心X6Hirst", + "X_{385}", + "X(385) = X_2\\text{-Hirst of }X_6;\\ a^4-b^2c^2", + "X(385):重心关于 X(6) 的 Hirst 逆(跳过等边)", + "X385", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(386): Brocard-inverse of X(58) + { + let f = |aa: f64, bb: f64, cc_: f64| { + aa * aa * (bb * bb + cc_ * cc_ + bb * cc_ + cc_ * aa + aa * bb) + }; + push_bary( + &mut out, + "X58布罗卡反演", + "X_{386}", + "X(386) = \\mathrm{Brocard}^{-1}(X_{58});\\ a^2(b^2+c^2+bc+ca+ab)", + "X(386):X(58) 在布罗卡圆上的反演(外接圆与阿波罗尼奥斯圆的外相似中心)", + "X386", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(387): X(1)X(2) ∩ X(4)X(6) + { + let f = |aa: f64, bb: f64, cc_: f64| { + -aa.powi(4) + 2.0 * aa * aa * (aa + bb + cc_).powi(2) + (bb * bb - cc_ * cc_).powi(2) + }; + push_bary( + &mut out, + "X1X2交X4X6", + "X_{387}", + "X(387) = X_1X_2\\cap X_4X_6;\\ -a^4+2a^2(a+b+c)^2+(b^2-c^2)^2", + "X(387):X(1)X(2) 与 X(4)X(6) 的交点", + "X387", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(388): X(1)X(4) ∩ X(7)X(8); bary a(1+cos B cos C) + { + let f = |aa: f64, ang_b: f64, ang_c: f64| aa * (1.0 + ang_b.cos() * ang_c.cos()); + push_bary( + &mut out, + "X1X4交X7X8", + "X_{388}", + "X(388) = X_1X_4\\cap X_7X_8;\\ a(1+\\cos B\\cos C)", + "X(388):X(1)X(4) 与 X(7)X(8) 的交点", + "X388", + f(a, g[1], g[2]), + f(b, g[2], g[0]), + f(c, g[0], g[1]), + ); + } + // X(389): Taylor-circle center + { + let f = |aa: f64, ang_a: f64, ang_b: f64, ang_c: f64| { + aa * (ang_a.cos() - (2.0 * ang_a).cos() * (ang_b - ang_c).cos()) + }; + push_bary( + &mut out, + "泰勒圆圆心", + "X_{389}", + "X(389) = \\mathrm{center}(\\mathrm{Taylor});\\ a[\\cos A-\\cos 2A\\cos(B-C)]", + "X(389):泰勒圆圆心(= mid(O,X52) = mid(H,X185))", + "X389", + f(a, g[0], g[1], g[2]), + f(b, g[1], g[2], g[0]), + f(c, g[2], g[0], g[1]), + ); + } + // X(390): reflection of Gergonne in incenter + { + let f = |aa: f64, bb: f64, cc_: f64| { + (bb + cc_ - aa) * (3.0 * aa * aa + (bb - cc_).powi(2)) + }; + push_bary( + &mut out, + "格尔巩内心反射", + "X_{390}", + "X(390) = 2I-X_7;\\ (b+c-a)[3a^2+(b-c)^2]", + "X(390):格尔巩点关于内心的反射", + "X390", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + } + + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -20512,6 +20745,128 @@ mod tests { } + + #[test] + fn x381_to_x390_orthocentroidal_conway_taylor_band() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("垂心重心圆圆心", "X_{381}", 4.541666666666667, 2.356064868942845), + ("外心垂心反射", "X_{382}", 5.625, 5.002603488851246), + ("X14X98欧拉截", "X_{383}", 14.200845560311862, 25.953040233837722), + ("X32X76欧拉截", "X_{384}", 4.390294725611789, 1.986269464660785), + ("重心X6Hirst", "X_{385}", 20.3713921901528, 20.126033577087185), + ("X58布罗卡反演", "X_{386}", 4.634146341463414, 2.078186185769833), + ("X1X2交X4X6", "X_{387}", 4.691916961130742, 2.139207453371190), + ("X1X4交X7X8", "X_{388}", 4.559335443037975, 2.141784303005525), + ("泰勒圆圆心", "X_{389}", 4.76171875, 2.288489378266831), + ("格尔巩内心反射", "X_{390}", 4.362325174825175, 1.633491664812132), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + // Cross-checks: X381=mid(G,H), X382=2H−O, X390=2I−Ge. + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let h = fs.iter().find(|f| f.group == "特殊点" && f.label == "H").expect("H"); + let o = fs.iter().find(|f| f.group == "特殊点" && f.label == "O").expect("O"); + let ii = fs.iter().find(|f| f.group == "特殊点" && f.label == "I").expect("I"); + let ge = fs + .iter() + .find(|f| f.group == "格尔巩点" && f.label == "Ge") + .expect("Ge"); + let (gx, gy) = ptxy(g); + let (hx, hy) = ptxy(h); + let (ox, oy) = ptxy(o); + let (ix, iy) = ptxy(ii); + let (gex, gey) = ptxy(ge); + let x381 = fs.iter().find(|f| f.label == "X_{381}").unwrap(); + let x382 = fs.iter().find(|f| f.label == "X_{382}").unwrap(); + let x390 = fs.iter().find(|f| f.label == "X_{390}").unwrap(); + let (x381x, x381y) = ptxy(x381); + let (x382x, x382y) = ptxy(x382); + let (x390x, x390y) = ptxy(x390); + assert!((x381x - (gx + hx) / 2.0).abs() < 1e-9 && (x381y - (gy + hy) / 2.0).abs() < 1e-9); + assert!((x382x - (2.0 * hx - ox)).abs() < 1e-9 && (x382y - (2.0 * hy - oy)).abs() < 1e-9); + assert!((x390x - (2.0 * ix - gex)).abs() < 1e-9 && (x390y - (2.0 * iy - gey)).abs() < 1e-9); + + // Isosceles 5-5-6: skip X383 (csc(B−C)); keep the rest except maybe X385 ok. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + assert!(fs2.iter().all(|f| f.label != "X_{383}"), "X383 skip isos"); + for (grp, lab, ..) in want { + if lab == "X_{383}" { + continue; + } + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: skip X385 (Hirst den0); X383→G; others finite at G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.label != "X_{385}"), "X385 skip equil"); + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (g3x, g3y) = ptxy(g3); + for (grp, lab, ..) in want { + if lab == "X_{385}" { + continue; + } + let f = fs3 + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("equil missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - g3x).abs() < 1e-9 && (y - g3y).abs() < 1e-9, + "equil {} {:?} want G {:?}", + lab, + (x, y), + (g3x, g3y) + ); + } + + // Right 3-4-5: all finite (no tan/sec singularity in this band). + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 4a33b435bf21edff5003d7c618c5991e94311ed1 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:31:49 +0800 Subject: [PATCH 105/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X381=E2=80=93X390=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 858652 -> 861782 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 23f9a91993ef00936cc0478739b56e1bb8ac4561..745e838f74658a2667a113e447f4cce518743b91 100644 GIT binary patch delta 126065 zcmce9349bq_J699On?vwCLsxgq^1KQ1PFwi0J%gt(ieMu} zL}6y)0VoK9Mo|b#^h|={?(g$w-OO}Vb=9kP*Q-}G 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zdXI=A8sx0%i=iq}9LB!z11KZRBec$wqGz}=(y8IZQ{LOUGJip+Sp>rs~f3caRS>` z3#om?M;a;1bJC?ev>2V@j*S&kvy|qz=72%Eh%@wjfGE*EsDw*m)lf*nKQu28o{Sd% z(!@ZM?&2&hNfOG3e_&*!ec@roB}z)+z4a6_Zs1{Bmq|>Tl759>X{x3KUFFkF)e_G&(lo0H zTok7y-ZfVor=Aw&G&2y=n*3BVm1a~BkX3(}YnS!lwToqwNLL#532*b%>(nKno-OX} zRgJ|Bny!VX1s8bL(6~x6U(Cy%ntPLsNpKc#k;tAp<2IRKx@9F*ak*E$;JHIwuwORg zyyhybM>PqgRqm3Jj>PIc68L+c1SljmC_>F_OQ30iWn@gu$(>^vx}&+42|j3I!aOV0 znXYrql~>HSoE5IGH*ESu1gZ--Aztk=7g}!xr8r!fQSpEhJGTH+<5D~*ll$?XSY(ZI g*qR4hs$}t|1r|#=)bg^H*sP1KF?QWf)GZDA50sL2*#H0l From c61b1f0d80423e608ea31fc05241381837cce6b4 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:36:09 +0800 Subject: [PATCH 106/123] =?UTF-8?q?feat:=20ETC=20X391=E2=80=93X400=20G?= =?UTF-8?q?=E2=80=93K=20/=20Napoleon=20/=20Parry=20/=20Yff=E2=80=93Malfatt?= =?UTF-8?q?i=20band?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(391)–X(400): X2X6∩X8X9 (X391), X1X6∩X10X11 (X392), tan²A X25-cross of H (X393; skip right), cos²A X69-Ceva of O (X394), mid(X14,X16)/mid(X13,X15) (X395/X396; X395 equil→G), crosspoint(H,X17/X18) (X397/X398), Parry reflection (X399), and Yff–Malfatti sin A csc⁴(A/4) (X400). --- crates/mathcore/src/geometry.rs | 347 ++++++++++++++++++++++++++++++++ 1 file changed, 347 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 291f9ad..937e197 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -13856,6 +13856,244 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } + // X(391)–X(400): G–K / Spieker–mitten / tan²–cos² / Napoleon mates / Parry / Yff–Malfatti (ETC). + // X(391)=X(2)X(6) ∩ X(8)X(9); bary (3a+b+c)(b+c−a); {X8,X9}-harmonic of X346. + // X(392)=X(1)X(6) ∩ X(10)X(11); bary a[(b+c)(b²+c²−a²)+4abc]; =reflection(X354 in X551). + // X(393)=X(25)-cross conjugate of X(4); bary tan² A; skip right (tan∞). + // X(394)=X(69)-Ceva of X(3); bary cos² A. + // X(395)=midpoint(X14,X16); bary (sin A)[cos(B−C)+2 cos(A+π/3)]; equil→G (weights 0). + // X(396)=midpoint(X13,X15); bary (sin A)[cos(B−C)+2 cos(A−π/3)]. + // X(397)=crosspoint(X4,X17); bary (sin A)[cos(B−C)−2 cos(A+π/3)]. + // X(398)=crosspoint(X4,X18); bary (sin A)[cos(B−C)−2 cos(A−π/3)]. + // X(399)=Parry reflection point; bary (sin A)[5 cos A−4 cos B cos C−8 sin B sin C cos 2A]. + // X(400)=Yff–Malfatti; bary sin A csc⁴(A/4). + { + let right = g.iter().any(|ang| (*ang - std::f64::consts::FRAC_PI_2).abs() < 1e-9); + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(391): X(2)X(6) ∩ X(8)X(9) + { + let f = |aa: f64, bb: f64, cc_: f64| (3.0 * aa + bb + cc_) * (bb + cc_ - aa); + push_bary( + &mut out, + "X2X6交X8X9", + "X_{391}", + "X(391) = X_2X_6\\cap X_8X_9;\\ (3a+b+c)(b+c-a)", + "X(391):X(2)X(6) 与 X(8)X(9) 的交点({X8,X9}-调和共轭于 X346)", + "X391", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(392): X(1)X(6) ∩ X(10)X(11) + { + let f = |aa: f64, bb: f64, cc_: f64| { + aa * ((bb + cc_) * (bb * bb + cc_ * cc_ - aa * aa) + 4.0 * aa * bb * cc_) + }; + push_bary( + &mut out, + "X1X6交X10X11", + "X_{392}", + "X(392) = X_1X_6\\cap X_{10}X_{11};\\ a[(b+c)(b^2+c^2-a^2)+4abc]", + "X(392):X(1)X(6) 与 X(10)X(11) 的交点(= X354 关于 X551 的反射)", + "X392", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(393): tan² A; skip right + if !right { + let f = |ang: f64| { + let t = ang.tan(); + t * t + }; + push_bary( + &mut out, + "X25叉共轭X4", + "X_{393}", + "X(393) = X_{25}\\text{-cross conj of }X_4;\\ \\tan^2 A", + "X(393):X(25) 关于 X(4) 的叉共轭(跳过直角)", + "X393", + f(g[0]), + f(g[1]), + f(g[2]), + ); + } + // X(394): cos² A + { + let f = |ang: f64| { + let c0 = ang.cos(); + c0 * c0 + }; + push_bary( + &mut out, + "X69塞瓦X3", + "X_{394}", + "X(394) = X_{69}\\text{-Ceva of }X_3;\\ \\cos^2 A", + "X(394):X(69) 关于外心的塞瓦共轭", + "X394", + f(g[0]), + f(g[1]), + f(g[2]), + ); + } + // X(395): midpoint(X14,X16); equilateral weights vanish → G + { + let equil = (a - b).abs() < 1e-9 && (b - c).abs() < 1e-9; + if equil { + push_bary( + &mut out, + "X14X16中点", + "X_{395}", + "X(395) = \\mathrm{mid}(X_{14},X_{16});\\ \\mathrm{equil}\\to G", + "X(395):第二费马点与第二等动力点的中点(等边退化为重心)", + "X395", + 1.0, + 1.0, + 1.0, + ); + } else { + let pi3 = std::f64::consts::PI / 3.0; + let f = |ang_a: f64, ang_b: f64, ang_c: f64| { + ang_a.sin() * ((ang_b - ang_c).cos() + 2.0 * (ang_a + pi3).cos()) + }; + push_bary( + &mut out, + "X14X16中点", + "X_{395}", + "X(395) = \\mathrm{mid}(X_{14},X_{16});\\ (\\sin A)[\\cos(B-C)+2\\cos(A+\\pi/3)]", + "X(395):第二费马点与第二等动力点的中点", + "X395", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + } + // X(396): midpoint(X13,X15) + { + let pi3 = std::f64::consts::PI / 3.0; + let f = |ang_a: f64, ang_b: f64, ang_c: f64| { + ang_a.sin() * ((ang_b - ang_c).cos() + 2.0 * (ang_a - pi3).cos()) + }; + push_bary( + &mut out, + "X13X15中点", + "X_{396}", + "X(396) = \\mathrm{mid}(X_{13},X_{15});\\ (\\sin A)[\\cos(B-C)+2\\cos(A-\\pi/3)]", + "X(396):第一费马点与第一等动力点的中点", + "X396", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(397): crosspoint(X4,X17) + { + let pi3 = std::f64::consts::PI / 3.0; + let f = |ang_a: f64, ang_b: f64, ang_c: f64| { + ang_a.sin() * ((ang_b - ang_c).cos() - 2.0 * (ang_a + pi3).cos()) + }; + push_bary( + &mut out, + "X4X17截点", + "X_{397}", + "X(397) = \\mathrm{crosspoint}(X_4,X_{17});\\ (\\sin A)[\\cos(B-C)-2\\cos(A+\\pi/3)]", + "X(397):垂心与第一拿破仑点的截点", + "X397", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(398): crosspoint(X4,X18) + { + let pi3 = std::f64::consts::PI / 3.0; + let f = |ang_a: f64, ang_b: f64, ang_c: f64| { + ang_a.sin() * ((ang_b - ang_c).cos() - 2.0 * (ang_a - pi3).cos()) + }; + push_bary( + &mut out, + "X4X18截点", + "X_{398}", + "X(398) = \\mathrm{crosspoint}(X_4,X_{18});\\ (\\sin A)[\\cos(B-C)-2\\cos(A-\\pi/3)]", + "X(398):垂心与第二拿破仑点的截点", + "X398", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(399): Parry reflection point + { + let f = |ang_a: f64, ang_b: f64, ang_c: f64| { + ang_a.sin() + * (5.0 * ang_a.cos() + - 4.0 * ang_b.cos() * ang_c.cos() + - 8.0 * ang_b.sin() * ang_c.sin() * (2.0 * ang_a).cos()) + }; + push_bary( + &mut out, + "帕里反射点", + "X_{399}", + "X(399) = \\mathrm{Parry\\ reflection};\\ (\\sin A)[5\\cos A-4\\cos B\\cos C-8\\sin B\\sin C\\cos 2A]", + "X(399):帕里反射点(过顶点且平行于欧拉线的反射线共点)", + "X399", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(400): Yff–Malfatti; bary sin A csc⁴(A/4) + { + let f = |ang: f64| { + let s4 = (ang / 4.0).sin(); + if s4.abs() < 1e-14 { + return f64::NAN; + } + ang.sin() / s4.powi(4) + }; + push_bary( + &mut out, + "伊夫马尔法蒂", + "X_{400}", + "X(400) = \\mathrm{Yff\\text{-}Malfatti};\\ \\sin A\\,\\csc^4(A/4)", + "X(400):伊夫–马尔法蒂点(Ajima–Malfatti 的外切变体)", + "X400", + f(g[0]), + f(g[1]), + f(g[2]), + ); + } + } + + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -20867,6 +21105,115 @@ mod tests { } + + #[test] + fn x391_to_x400_gk_napoleon_parry_yff_band() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("X2X6交X8X9", "X_{391}", 3.920649931224209, 1.2935471372090626), + ("X1X6交X10X11", "X_{392}", 4.192708333333333, 1.5532276961352662), + ("X25叉共轭X4", "X_{393}", 4.959201648313755, 4.08647533176635), + ("X69塞瓦X3", "X_{394}", 3.130227001194743, 0.38868650069465116), + ("X14X16中点", "X_{395}", 12.101547673400342, 10.658878097393696), + ("X13X15中点", "X_{396}", 4.490398421676066, 1.945784012098527), + ("X4X17截点", "X_{397}", 4.725427515862568, 2.383344248128183), + ("X4X18截点", "X_{398}", 4.645290377716149, 1.7995155349172816), + ("帕里反射点", "X_{399}", 4.864265927977838, 1.999789738872749), + ("伊夫马尔法蒂", "X_{400}", 2.90668340537787, 0.6040116450051041), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + // Cross-checks: X395=mid(F2,S2)=mid(X14,X16), X396=mid(F1,S1)=mid(X13,X15). + let find_lab = |lab: &str| { + fs.iter() + .find(|f| f.label == lab) + .unwrap_or_else(|| panic!("missing {}", lab)) + }; + let (f1x, f1y) = ptxy(find_lab("F_1")); + let (f2x, f2y) = ptxy(find_lab("F_2")); + let (s1x, s1y) = ptxy(find_lab("S_{1}")); + let (s2x, s2y) = ptxy(find_lab("S_{2}")); + let (x395x, x395y) = ptxy(find_lab("X_{395}")); + let (x396x, x396y) = ptxy(find_lab("X_{396}")); + assert!((x395x - (f2x + s2x) / 2.0).abs() < 1e-9 && (x395y - (f2y + s2y) / 2.0).abs() < 1e-9); + assert!((x396x - (f1x + s1x) / 2.0).abs() < 1e-9 && (x396y - (f1y + s1y) / 2.0).abs() < 1e-9); + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: all collapse to G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (g3x, g3y) = ptxy(g3); + for (grp, lab, ..) in want { + let f = fs3 + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("equil missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - g3x).abs() < 1e-9 && (y - g3y).abs() < 1e-9, + "equil {} {:?} want G {:?}", + lab, + (x, y), + (g3x, g3y) + ); + } + + // Right 3-4-5: skip X393 (tan∞); keep the rest. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().all(|f| f.label != "X_{393}"), "X393 skip right"); + for (grp, lab, ..) in want { + if lab == "X_{393}" { + continue; + } + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 882db172ce4f5cb78c576d4bb0057eaedcbe799e Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:36:09 +0800 Subject: [PATCH 107/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X391=E2=80=93X400=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 861782 -> 865204 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git 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=?UTF-8?q?feat:=20ETC=20X401=E2=80=93X410=20Baile?= =?UTF-8?q?y=20/=20Zeeman=E2=80=93Gossard=20/=20Euler-subst=20band?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(401)–X(410) barycentrics: Bailey Hirst, Zeeman–Gossard p·y, orthic-X36 mid(H,X186), Schiffler Euler harmonic, X1X6/X10X33 Euler intercepts, X4×X225 crosspoint, X73X228 Euler cut, and X21/X29 1st-substitutions. Skip equil for X401–X403; skip right for tan/sec centers X403/X406–X408/X410. Unit test on 6-7-8 / isos / equil / 3-4-5. --- crates/mathcore/src/geometry.rs | 361 ++++++++++++++++++++++++++++++++ 1 file changed, 361 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 937e197..9d5fd82 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -14093,6 +14093,256 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(401)–X(410): Bailey / Zeeman–Gossard / orthic-X36 / Euler intercepts / X21·X29 substitutions (ETC). + // X(401)=Bailey=X(2)-Hirst of X(3)=anticomplement(X297); bary sin2B sin2C−sin²(2A); skip equil (weights 0). + // X(402)=Zeeman–Gossard perspector; bary p·y with p=2a⁴−a²b²−a²c²−(b²−c²)², + // y=a⁸−a⁶(b²+c²)+a⁴(2b²−c²)(2c²−b²)+[(b²−c²)²][3a²(b²+c²)−b⁴−c⁴−3b²c²]; skip equil (p=0). + // X(403)=X(36)-of-orthic=mid(H,X186); bary tan A(1+cos2B+cos2C); skip right/equil. + // X(404)={X2,X3}-harmonic of X(21); bary abc(a+b+c)−a²(b²+c²−a²). + // X(405)=Euler ∩ X(1)X(6)=complement(X377); bary b+c+a(1+cos A). + // X(406)=Euler ∩ X(10)X(33); bary b+c+a(1+sec A); skip right. + // X(407)=crosspoint(X4,X225); bary (v+w)tan A with u:v:w=X(21) tril 1/(cosB+cosC); skip right. + // X(408)=Euler ∩ X(73)X(228); bary (v+w)sin2A with u:v:w=X(29) tril (sec A)/(cosB+cosC); skip right. + // X(409)=Euler X(21)-1st-substitution; bary a(u²+vw), u:v:w=X(21). + // X(410)=Euler X(29)-1st-substitution; bary a(u²+vw), u:v:w=X(29); skip right. + { + let right = g.iter().any(|ang| (*ang - std::f64::consts::FRAC_PI_2).abs() < 1e-9); + let equil = (a - b).abs() < 1e-9 && (b - c).abs() < 1e-9; + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(401): Bailey = X(2)-Hirst of O; skip equilateral + if !equil { + let f = |ang_a: f64, ang_b: f64, ang_c: f64| { + (2.0 * ang_b).sin() * (2.0 * ang_c).sin() - (2.0 * ang_a).sin().powi(2) + }; + push_bary( + &mut out, + "贝利点", + "X_{401}", + "X(401) = \\mathrm{Bailey}=X_2\\text{-Hirst of }X_3;\\ \\sin 2B\\sin 2C-\\sin^2 2A", + "X(401):贝利点(重心对圆心的 Hirst 逆;跳过等边)", + "X401", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(402): Zeeman–Gossard perspector; skip equilateral + if !equil { + let p = |aa: f64, bb: f64, cc_: f64| { + 2.0 * aa.powi(4) + - aa * aa * bb * bb + - aa * aa * cc_ * cc_ + - (bb * bb - cc_ * cc_).powi(2) + }; + let y = |aa: f64, bb: f64, cc_: f64| { + let a2 = aa * aa; + let b2 = bb * bb; + let c2 = cc_ * cc_; + let dbc = (b2 - c2).powi(2); + aa.powi(8) + - aa.powi(6) * (b2 + c2) + + aa.powi(4) * (2.0 * b2 - c2) * (2.0 * c2 - b2) + + dbc * (3.0 * a2 * (b2 + c2) - b2 * b2 - c2 * c2 - 3.0 * b2 * c2) + }; + let f = |aa: f64, bb: f64, cc_: f64| p(aa, bb, cc_) * y(aa, bb, cc_); + push_bary( + &mut out, + "齐曼戈萨德", + "X_{402}", + "X(402) = \\mathrm{Zeeman\\text{-}Gossard};\\ p(a,b,c)\\,y(a,b,c)", + "X(402):齐曼–戈萨德透视中心(欧拉线侧三角形的欧拉线透视点)", + "X402", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(403): X(36) of orthic = mid(H, X186); skip right / equilateral + if !right && !equil { + let f = |ang_a: f64, ang_b: f64, ang_c: f64| { + ang_a.tan() * (1.0 + (2.0 * ang_b).cos() + (2.0 * ang_c).cos()) + }; + push_bary( + &mut out, + "垂足X36", + "X_{403}", + "X(403) = X_{36}\\text{-of-orthic}=\\mathrm{mid}(X_4,X_{186});\\ \\tan A(1+\\cos 2B+\\cos 2C)", + "X(403):垂足三角形的 X(36)(= 垂心与 X186 的中点;跳过直角/等边)", + "X403", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(404): {X2,X3}-harmonic conjugate of Schiffler X(21) + { + let f = |aa: f64, bb: f64, cc_: f64| { + aa * bb * cc_ * (aa + bb + cc_) - aa * aa * (bb * bb + cc_ * cc_ - aa * aa) + }; + push_bary( + &mut out, + "X21欧拉调和", + "X_{404}", + "X(404) = \\{X_2,X_3\\}\\text{-harmonic of }X_{21};\\ abc(a+b+c)-a^2(b^2+c^2-a^2)", + "X(404):席弗勒点关于 {重心,外心} 的调和共轭", + "X404", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(405): Euler ∩ X(1)X(6) = complement of X(377) + { + let f = |aa: f64, bb: f64, cc_: f64, caa: f64| bb + cc_ + aa * (1.0 + caa); + push_bary( + &mut out, + "X1X6欧拉截", + "X_{405}", + "X(405) = \\mathrm{Euler}\\cap X_1X_6;\\ b+c+a(1+\\cos A)", + "X(405):内心–类似重心线与欧拉线的交点(= X377 的补点)", + "X405", + f(a, b, c, ca), + f(b, c, a, cb), + f(c, a, b, cc), + ); + } + // X(406): Euler ∩ X(10)X(33); skip right + if !right { + let f = |aa: f64, bb: f64, cc_: f64, ang: f64| { + let c0 = ang.cos(); + if c0.abs() < 1e-14 { + return f64::NAN; + } + bb + cc_ + aa * (1.0 + 1.0 / c0) + }; + push_bary( + &mut out, + "X10X33欧拉截", + "X_{406}", + "X(406) = \\mathrm{Euler}\\cap X_{10}X_{33};\\ b+c+a(1+\\sec A)", + "X(406):斯皮克–垂足透视线与欧拉线的交点(跳过直角)", + "X406", + f(a, b, c, g[0]), + f(b, c, a, g[1]), + f(c, a, b, g[2]), + ); + } + // X(21) trilinears u:v:w = 1/(cos B + cos C) + let x21_tril = { + let da = cb + cc; + let db = cc + ca; + let dc = ca + cb; + if da.abs() > 1e-14 && db.abs() > 1e-14 && dc.abs() > 1e-14 { + Some((1.0 / da, 1.0 / db, 1.0 / dc)) + } else { + None + } + }; + // X(407): crosspoint(X4, X225); (v+w) tan A; skip right + if !right { + if let Some((u21, v21, w21)) = x21_tril { + push_bary( + &mut out, + "X4X225截点", + "X_{407}", + "X(407) = \\mathrm{crosspoint}(X_4,X_{225});\\ (v+w)\\tan A\\ (u:v:w=X_{21})", + "X(407):垂心与 X(225) 的截点(跳过直角)", + "X407", + (v21 + w21) * g[0].tan(), + (w21 + u21) * g[1].tan(), + (u21 + v21) * g[2].tan(), + ); + } + } + // X(29) trilinears u:v:w = (sec A)/(cos B + cos C); skip right (sec∞) + let x29_tril = if !right { + let da = cb + cc; + let db = cc + ca; + let dc = ca + cb; + if ca.abs() > 1e-14 + && cb.abs() > 1e-14 + && cc.abs() > 1e-14 + && da.abs() > 1e-14 + && db.abs() > 1e-14 + && dc.abs() > 1e-14 + { + Some((1.0 / ca / da, 1.0 / cb / db, 1.0 / cc / dc)) + } else { + None + } + } else { + None + }; + // X(408): Euler ∩ X(73)X(228); (v+w) sin 2A + if let Some((u29, v29, w29)) = x29_tril { + push_bary( + &mut out, + "X73X228欧拉截", + "X_{408}", + "X(408) = \\mathrm{Euler}\\cap X_{73}X_{228};\\ (v+w)\\sin 2A\\ (u:v:w=X_{29})", + "X(408):X(73)X(228) 与欧拉线的交点(跳过直角)", + "X408", + (v29 + w29) * (2.0 * g[0]).sin(), + (w29 + u29) * (2.0 * g[1]).sin(), + (u29 + v29) * (2.0 * g[2]).sin(), + ); + } + // X(409): Euler X(21)-1st-substitution; a(u²+vw) + if let Some((u21, v21, w21)) = x21_tril { + push_bary( + &mut out, + "X21一次替换", + "X_{409}", + "X(409) = \\mathrm{Euler}\\ X_{21}\\text{-1st-subst};\\ a(u^2+vw)\\ (u:v:w=X_{21})", + "X(409):席弗勒点的欧拉一次替换点", + "X409", + a * (u21 * u21 + v21 * w21), + b * (v21 * v21 + w21 * u21), + c * (w21 * w21 + u21 * v21), + ); + } + // X(410): Euler X(29)-1st-substitution; a(u²+vw); skip right + if let Some((u29, v29, w29)) = x29_tril { + push_bary( + &mut out, + "X29一次替换", + "X_{410}", + "X(410) = \\mathrm{Euler}\\ X_{29}\\text{-1st-subst};\\ a(u^2+vw)\\ (u:v:w=X_{29})", + "X(410):X(29) 的欧拉一次替换点(跳过直角)", + "X410", + a * (u29 * u29 + v29 * w29), + b * (v29 * v29 + w29 * u29), + c * (w29 * w29 + u29 * v29), + ); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. @@ -21213,6 +21463,117 @@ mod tests { } } + #[test] + fn x401_to_x410_bailey_gossard_euler_subst_band() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("贝利点", "X_{401}", -2.6039268355078, -15.100325130138327), + ("齐曼戈萨德", "X_{402}", 4.669315529960855, 2.6679057734002094), + ("垂足X36", "X_{403}", 5.913496376811594, 5.707388230022506), + ("X21欧拉调和", "X_{404}", 4.393939393939394, 1.9951732389553358), + ("X1X6欧拉截", "X_{405}", 4.2342342342342345, 1.605020125455326), + ("X10X33欧拉截", "X_{406}", 4.520593179634966, 2.304583209910045), + ("X4X225截点", "X_{407}", 4.8876421859545, 3.2012687827934143), + ("X73X228欧拉截", "X_{408}", 3.907987244632432, 0.8080121953537639), + ("X21一次替换", "X_{409}", 4.303789805061146, 1.774941514153659), + ("X29一次替换", "X_{410}", 4.553501656026697, 2.384977259472869), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + // Cross-check: X403 = mid(H, X186). + let find_lab = |lab: &str| { + fs.iter() + .find(|f| f.label == lab) + .unwrap_or_else(|| panic!("missing {}", lab)) + }; + let (hx, hy) = ptxy(find_lab("H")); + let (x186x, x186y) = ptxy(find_lab("X_{186}")); + let (x403x, x403y) = ptxy(find_lab("X_{403}")); + assert!((x403x - (hx + x186x) / 2.0).abs() < 1e-9 && (x403y - (hy + x186y) / 2.0).abs() < 1e-9); + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: skip X401/X402/X403 (vanishing / X186 undefined); others → G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (g3x, g3y) = ptxy(g3); + for lab in ["X_{401}", "X_{402}", "X_{403}"] { + assert!(fs3.iter().all(|f| f.label != lab), "equil should skip {}", lab); + } + for (grp, lab, ..) in want { + if lab == "X_{401}" || lab == "X_{402}" || lab == "X_{403}" { + continue; + } + let f = fs3 + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("equil missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - g3x).abs() < 1e-9 && (y - g3y).abs() < 1e-9, + "equil {} {:?} want G {:?}", + lab, + (x, y), + (g3x, g3y) + ); + } + + // Right 3-4-5: skip X403/X406/X407/X408/X410 (tan/sec∞); keep the rest. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for lab in ["X_{403}", "X_{406}", "X_{407}", "X_{408}", "X_{410}"] { + assert!(fs4.iter().all(|f| f.label != lab), "{} should skip right", lab); + } + for (grp, lab, ..) in want { + if matches!(lab, "X_{403}" | "X_{406}" | "X_{407}" | "X_{408}" | "X_{410}") { + continue; + } + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { From c94f837d16f45ca258969766dc34e1f27db04fca Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:39:45 +0800 Subject: [PATCH 109/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X401=E2=80=93X410=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 865204 -> 868972 bytes 1 file changed, 0 insertions(+), 0 deletions(-) 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=?UTF-8?q?=20subst=20/=20Hirst=20/=20Ceva=20band?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(411)–X(420) barycentrics: X21/X29 2nd·3rd Euler substitutions, X4-Hirst of X29 (via X21), X3-Hirst of X21 (via X29), X3-Ceva of X185/X216, and X4-Hirst of X25/X427 (via X31/X38). Skip equil for vanishing/Hirst weights; skip right for X29/sec/csc/tan centers. Unit test on 6-7-8 / isos / equil / 3-4-5. --- crates/mathcore/src/geometry.rs | 296 +++++++++++++++++++++++++++++++- 1 file changed, 295 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 9d5fd82..99ae5f0 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -14093,7 +14093,7 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } - // X(401)–X(410): Bailey / Zeeman–Gossard / orthic-X36 / Euler intercepts / X21·X29 substitutions (ETC). + // X(401)–X(420): Bailey / Zeeman–Gossard / orthic-X36 / Euler intercepts / X21·X29 subst / Hirst / Ceva (ETC). // X(401)=Bailey=X(2)-Hirst of X(3)=anticomplement(X297); bary sin2B sin2C−sin²(2A); skip equil (weights 0). // X(402)=Zeeman–Gossard perspector; bary p·y with p=2a⁴−a²b²−a²c²−(b²−c²)², // y=a⁸−a⁶(b²+c²)+a⁴(2b²−c²)(2c²−b²)+[(b²−c²)²][3a²(b²+c²)−b⁴−c⁴−3b²c²]; skip equil (p=0). @@ -14105,6 +14105,16 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] // X(408)=Euler ∩ X(73)X(228); bary (v+w)sin2A with u:v:w=X(29) tril (sec A)/(cosB+cosC); skip right. // X(409)=Euler X(21)-1st-substitution; bary a(u²+vw), u:v:w=X(21). // X(410)=Euler X(29)-1st-substitution; bary a(u²+vw), u:v:w=X(29); skip right. + // X(411)=Euler X(21)-2nd-subst={X3,X4}-harmonic of X(21); bary a[(1/v)²+(1/w)²−(1/u)²]; skip equil (0). + // X(412)=Euler X(29)-2nd-subst={X3,X4}-harmonic of X(29); same form on X(29); skip right/equil. + // X(413)=Euler X(21)-3rd-subst; bary a u³(v²+w²−vw), u:v:w=X(21). + // X(414)=Euler X(29)-3rd-subst; same on X(29); skip right. + // X(415)=X(4)-Hirst of X(29); bary (u²−vw)tan A, u:v:w=X(21); skip right/equil. + // X(416)=X(3)-Hirst of X(21); bary (u²−vw)sin2A, u:v:w=X(29); skip right/equil. + // X(417)=X(3)-Ceva of X(185); bary sin2A(sec²B+sec²C); skip right (sec∞). + // X(418)=X(3)-Ceva of X(216); bary sin2A(csc2B+csc2C); skip right (csc π). + // X(419)=X(4)-Hirst of X(25); bary (u²−vw)tan A, u:v:w=X(31)=a²; skip right/equil. + // X(420)=X(4)-Hirst of X(427); bary (u²−vw)tan A, u:v:w=X(38)=b²+c²; skip right/equil. { let right = g.iter().any(|ang| (*ang - std::f64::consts::FRAC_PI_2).abs() < 1e-9); let equil = (a - b).abs() < 1e-9 && (b - c).abs() < 1e-9; @@ -14341,6 +14351,191 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] c * (w29 * w29 + u29 * v29), ); } + // X(411): Euler X(21)-2nd-substitution; skip equilateral (weights 0) + if !equil { + if let Some((u21, v21, w21)) = x21_tril { + let f = |u: f64, v: f64, w: f64| { + if u.abs() < 1e-14 || v.abs() < 1e-14 || w.abs() < 1e-14 { + return f64::NAN; + } + (1.0 / v).powi(2) + (1.0 / w).powi(2) - (1.0 / u).powi(2) + }; + push_bary( + &mut out, + "X21二次替换", + "X_{411}", + "X(411) = \\mathrm{Euler}\\ X_{21}\\text{-2nd-subst};\\ a[(1/v)^2+(1/w)^2-(1/u)^2]", + "X(411):席弗勒点的欧拉二次替换点(={X3,X4}-调和;跳过等边)", + "X411", + a * f(u21, v21, w21), + b * f(v21, w21, u21), + c * f(w21, u21, v21), + ); + } + } + // X(412): Euler X(29)-2nd-substitution; skip right / equilateral + if !equil { + if let Some((u29, v29, w29)) = x29_tril { + let f = |u: f64, v: f64, w: f64| { + if u.abs() < 1e-14 || v.abs() < 1e-14 || w.abs() < 1e-14 { + return f64::NAN; + } + (1.0 / v).powi(2) + (1.0 / w).powi(2) - (1.0 / u).powi(2) + }; + push_bary( + &mut out, + "X29二次替换", + "X_{412}", + "X(412) = \\mathrm{Euler}\\ X_{29}\\text{-2nd-subst};\\ a[(1/v)^2+(1/w)^2-(1/u)^2]", + "X(412):X(29) 的欧拉二次替换点(跳过直角/等边)", + "X412", + a * f(u29, v29, w29), + b * f(v29, w29, u29), + c * f(w29, u29, v29), + ); + } + } + // X(413): Euler X(21)-3rd-substitution + if let Some((u21, v21, w21)) = x21_tril { + let f = |u: f64, v: f64, w: f64| u.powi(3) * (v * v + w * w - v * w); + push_bary( + &mut out, + "X21三次替换", + "X_{413}", + "X(413) = \\mathrm{Euler}\\ X_{21}\\text{-3rd-subst};\\ a\\,u^3(v^2+w^2-vw)", + "X(413):席弗勒点的欧拉三次替换点", + "X413", + a * f(u21, v21, w21), + b * f(v21, w21, u21), + c * f(w21, u21, v21), + ); + } + // X(414): Euler X(29)-3rd-substitution; skip right + if let Some((u29, v29, w29)) = x29_tril { + let f = |u: f64, v: f64, w: f64| u.powi(3) * (v * v + w * w - v * w); + push_bary( + &mut out, + "X29三次替换", + "X_{414}", + "X(414) = \\mathrm{Euler}\\ X_{29}\\text{-3rd-subst};\\ a\\,u^3(v^2+w^2-vw)", + "X(414):X(29) 的欧拉三次替换点(跳过直角)", + "X414", + a * f(u29, v29, w29), + b * f(v29, w29, u29), + c * f(w29, u29, v29), + ); + } + // X(415): X(4)-Hirst inverse of X(29); (u²−vw) tan A on X(21); skip right/equil + if !right && !equil { + if let Some((u21, v21, w21)) = x21_tril { + let f = |u: f64, v: f64, w: f64, ang: f64| (u * u - v * w) * ang.tan(); + push_bary( + &mut out, + "X4HirstX29", + "X_{415}", + "X(415) = X_4\\text{-Hirst of }X_{29};\\ (u^2-vw)\\tan A\\ (u:v:w=X_{21})", + "X(415):垂心对 X(29) 的 Hirst 逆(用 X21 坐标;跳过直角/等边)", + "X415", + f(u21, v21, w21, g[0]), + f(v21, w21, u21, g[1]), + f(w21, u21, v21, g[2]), + ); + } + } + // X(416): X(3)-Hirst inverse of X(21); (u²−vw) sin 2A on X(29); skip right/equil + if !equil { + if let Some((u29, v29, w29)) = x29_tril { + let f = |u: f64, v: f64, w: f64, ang: f64| (u * u - v * w) * (2.0 * ang).sin(); + push_bary( + &mut out, + "X3HirstX21", + "X_{416}", + "X(416) = X_3\\text{-Hirst of }X_{21};\\ (u^2-vw)\\sin 2A\\ (u:v:w=X_{29})", + "X(416):外心对席弗勒点的 Hirst 逆(跳过直角/等边)", + "X416", + f(u29, v29, w29, g[0]), + f(v29, w29, u29, g[1]), + f(w29, u29, v29, g[2]), + ); + } + } + // X(417): X(3)-Ceva conjugate of X(185); sin2A(sec²B+sec²C); skip right + if !right { + let f = |ang_a: f64, ang_b: f64, ang_c: f64| { + let cb_ = ang_b.cos(); + let cc_ = ang_c.cos(); + if cb_.abs() < 1e-14 || cc_.abs() < 1e-14 { + return f64::NAN; + } + (2.0 * ang_a).sin() * (1.0 / (cb_ * cb_) + 1.0 / (cc_ * cc_)) + }; + push_bary( + &mut out, + "X3CevaX185", + "X_{417}", + "X(417) = X_3\\text{-Ceva of }X_{185};\\ \\sin 2A(\\sec^2 B+\\sec^2 C)", + "X(417):外心对 X(185) 的塞瓦共轭(跳过直角)", + "X417", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(418): X(3)-Ceva conjugate of X(216); sin2A(csc2B+csc2C); skip right + if !right { + let f = |ang_a: f64, ang_b: f64, ang_c: f64| { + let s2b = (2.0 * ang_b).sin(); + let s2c = (2.0 * ang_c).sin(); + if s2b.abs() < 1e-14 || s2c.abs() < 1e-14 { + return f64::NAN; + } + (2.0 * ang_a).sin() * (1.0 / s2b + 1.0 / s2c) + }; + push_bary( + &mut out, + "X3CevaX216", + "X_{418}", + "X(418) = X_3\\text{-Ceva of }X_{216};\\ \\sin 2A(\\csc 2B+\\csc 2C)", + "X(418):外心对 X(216) 的塞瓦共轭(跳过直角)", + "X418", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(419): X(4)-Hirst of X(25); (u²−vw)tan A on X(31)=a²; skip right/equil + if !right && !equil { + let (u31, v31, w31) = (a * a, b * b, c * c); + let f = |u: f64, v: f64, w: f64, ang: f64| (u * u - v * w) * ang.tan(); + push_bary( + &mut out, + "X4HirstX25", + "X_{419}", + "X(419) = X_4\\text{-Hirst of }X_{25};\\ (u^2-vw)\\tan A\\ (u:v:w=X_{31})", + "X(419):垂心对 X(25) 的 Hirst 逆(X31=a²;跳过直角/等边)", + "X419", + f(u31, v31, w31, g[0]), + f(v31, w31, u31, g[1]), + f(w31, u31, v31, g[2]), + ); + } + // X(420): X(4)-Hirst of X(427); (u²−vw)tan A on X(38)=b²+c²; skip right/equil + if !right && !equil { + let (u38, v38, w38) = (b * b + c * c, c * c + a * a, a * a + b * b); + let f = |u: f64, v: f64, w: f64, ang: f64| (u * u - v * w) * ang.tan(); + push_bary( + &mut out, + "X4HirstX427", + "X_{420}", + "X(420) = X_4\\text{-Hirst of }X_{427};\\ (u^2-vw)\\tan A\\ (u:v:w=X_{38})", + "X(420):垂心对 X(427) 的 Hirst 逆(X38=b²+c²;跳过直角/等边)", + "X420", + f(u38, v38, w38, g[0]), + f(v38, w38, u38, g[1]), + f(w38, u38, v38, g[2]), + ); + } + } @@ -21575,6 +21770,105 @@ mod tests { } + #[test] + fn x411_to_x420_euler_subst_hirst_ceva_band() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("X21二次替换", "X_{411}", 3.5806451612903225, 0.008328996443456811), + ("X29二次替换", "X_{412}", 5.116983967935872, 3.761541290337086), + ("X21三次替换", "X_{413}", 4.02886212929881, 1.1033045496121139), + ("X29三次替换", "X_{414}", 4.778473851942197, 2.934575048607608), + ("X4HirstX29", "X_{415}", 6.792375599216799, 7.8544538955582945), + ("X3HirstX21", "X_{416}", -0.8923491817207847, -10.91901156547412), + ("X3CevaX185", "X_{417}", 3.7250699765331223, 0.3611528591017998), + ("X3CevaX216", "X_{418}", 3.883182566283442, 0.747415389933758), + ("X4HirstX25", "X_{419}", 6.171935987509758, 6.338745532139536), + ("X4HirstX427", "X_{420}", 6.662746209799353, 7.537774647525915), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: skip vanishing/Hirst/X31·X38; keep X413/X414/X417/X418 → G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (g3x, g3y) = ptxy(g3); + for lab in [ + "X_{411}", "X_{412}", "X_{415}", "X_{416}", "X_{419}", "X_{420}", + ] { + assert!(fs3.iter().all(|f| f.label != lab), "equil should skip {}", lab); + } + // X414 needs X29 which is fine on equil (sec 60°=2); X413/X417/X418 also present. + for lab in ["X_{413}", "X_{414}", "X_{417}", "X_{418}"] { + let f = fs3 + .iter() + .find(|f| f.label == lab) + .unwrap_or_else(|| panic!("equil missing {}", lab)); + let (x, y) = ptxy(f); + assert!( + (x - g3x).abs() < 1e-9 && (y - g3y).abs() < 1e-9, + "equil {} {:?} want G {:?}", + lab, + (x, y), + (g3x, g3y) + ); + } + + // Right 3-4-5: keep X411/X413; skip the rest (X29/sec/csc/tan issues). + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for lab in [ + "X_{412}", "X_{414}", "X_{415}", "X_{416}", "X_{417}", "X_{418}", "X_{419}", "X_{420}", + ] { + assert!(fs4.iter().all(|f| f.label != lab), "{} should skip right", lab); + } + for lab in ["X_{411}", "X_{413}"] { + assert!( + fs4.iter().any(|f| f.label == lab), + "right missing {}", + lab + ); + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 984f154837b1d8a9c6d57b331823940be4a3583b Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:43:22 +0800 Subject: [PATCH 111/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X411=E2=80=93X420=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 868972 -> 872503 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 3b78cc7e8ab48ed215d236d418790f7a78203183..1ffb2b4cb042824051dec8393f0719a66dbecc48 100644 GIT binary patch delta 25139 zcmb_^34ByV^8a+dnKv`J1K~=5^h`Lyk#L1834{jXfK1;+QR@jMs3LX@n* 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X(421)–X(430) barycentrics: X4-Hirst of X24/X28/X27/X451/X21 (via X47/X58/X81/X191/X283), Euler X19-4th-subst, complement of X22, and Euler X38/X58/X81-5th-subst. Skip equil for vanishing Hirst weights; skip right for tan/sec centers. Unit test on 6-7-8 / isos / equil / 3-4-5. --- crates/mathcore/src/geometry.rs | 285 +++++++++++++++++++++++++++++++- 1 file changed, 284 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 99ae5f0..6bea994 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -14093,7 +14093,7 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } - // X(401)–X(420): Bailey / Zeeman–Gossard / orthic-X36 / Euler intercepts / X21·X29 subst / Hirst / Ceva (ETC). + // X(401)–X(430): Bailey / Zeeman–Gossard / orthic-X36 / Euler intercepts / X21·X29 subst / Hirst / Ceva / X4-Hirst band / Euler 4th·5th (ETC). // X(401)=Bailey=X(2)-Hirst of X(3)=anticomplement(X297); bary sin2B sin2C−sin²(2A); skip equil (weights 0). // X(402)=Zeeman–Gossard perspector; bary p·y with p=2a⁴−a²b²−a²c²−(b²−c²)², // y=a⁸−a⁶(b²+c²)+a⁴(2b²−c²)(2c²−b²)+[(b²−c²)²][3a²(b²+c²)−b⁴−c⁴−3b²c²]; skip equil (p=0). @@ -14115,6 +14115,16 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] // X(418)=X(3)-Ceva of X(216); bary sin2A(csc2B+csc2C); skip right (csc π). // X(419)=X(4)-Hirst of X(25); bary (u²−vw)tan A, u:v:w=X(31)=a²; skip right/equil. // X(420)=X(4)-Hirst of X(427); bary (u²−vw)tan A, u:v:w=X(38)=b²+c²; skip right/equil. + // X(421)=X(4)-Hirst of X(24); bary (u²−vw)tan A, u:v:w=X(47) tril cos2A; skip right/equil. + // X(422)=X(4)-Hirst of X(28); u:v:w=X(58) tril a/(b+c); skip right/equil. + // X(423)=X(4)-Hirst of X(27); u:v:w=X(81) tril 1/(b+c); skip right/equil. + // X(424)=X(4)-Hirst of X(451); u:v:w=X(191) tril; skip right/equil. + // X(425)=X(4)-Hirst of X(21); u:v:w=X(283) tril cosA/(cosB+cosC); skip right/equil. + // X(426)=Euler X(19)-4th-subst; bary (v²+w²)sin2A, u:v:w=tan A; skip right. + // X(427)=complement of X(22); bary sin A(sec A+cos(B−C)); skip right. + // X(428)=Euler X(38)-5th-subst; bary (v+w)tan A, u:v:w=b²+c²; skip right. + // X(429)=Euler X(58)-5th-subst; bary (v+w)tan A, u:v:w=a/(b+c); skip right. + // X(430)=Euler X(81)-5th-subst; bary (v+w)tan A, u:v:w=1/(b+c); skip right. { let right = g.iter().any(|ang| (*ang - std::f64::consts::FRAC_PI_2).abs() < 1e-9); let equil = (a - b).abs() < 1e-9 && (b - c).abs() < 1e-9; @@ -14535,6 +14545,187 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] f(w38, u38, v38, g[2]), ); } + // X(421)–X(430): X4-Hirst of X24/X28/X27/X451/X21; Euler X19-4th; complement X22; Euler X38/X58/X81-5th (ETC). + // X(421)=X(4)-Hirst of X(24); bary (u²−vw)tan A, u:v:w=X(47) tril cos2A; skip right/equil. + // X(422)=X(4)-Hirst of X(28); u:v:w=X(58) tril a/(b+c); skip right/equil. + // X(423)=X(4)-Hirst of X(27); u:v:w=X(81) tril 1/(b+c); skip right/equil. + // X(424)=X(4)-Hirst of X(451); u:v:w=X(191) tril (b+c−a)(Σbc)+b³+c³−a³; skip right/equil. + // X(425)=X(4)-Hirst of X(21); u:v:w=X(283) tril cosA/(cosB+cosC); skip right/equil. + // X(426)=Euler X(19)-4th-subst; bary (v²+w²)sin2A, u:v:w=X(19)=tan A; skip right. + // X(427)=complement of X(22); bary sin A(sec A+cos(B−C)); skip right (sec∞). + // X(428)=Euler X(38)-5th-subst; bary (v+w)tan A, u:v:w=X(38)=b²+c²; skip right. + // X(429)=Euler X(58)-5th-subst; bary (v+w)tan A, u:v:w=X(58) tril a/(b+c); skip right. + // X(430)=Euler X(81)-5th-subst; bary (v+w)tan A, u:v:w=X(81) tril 1/(b+c); skip right. + // X(421): X(4)-Hirst of X(24); (u²−vw)tan A on cos 2A; skip right/equil + if !right && !equil { + let (u47, v47, w47) = ((2.0 * g[0]).cos(), (2.0 * g[1]).cos(), (2.0 * g[2]).cos()); + let f = |u: f64, v: f64, w: f64, ang: f64| (u * u - v * w) * ang.tan(); + push_bary( + &mut out, + "X4HirstX24", + "X_{421}", + "X(421) = X_4\\text{-Hirst of }X_{24};\\ (u^2-vw)\\tan A\\ (u:v:w=\\cos 2A)", + "X(421):垂心对 X(24) 的 Hirst 逆(X47=cos2A;跳过直角/等边)", + "X421", + f(u47, v47, w47, g[0]), + f(v47, w47, u47, g[1]), + f(w47, u47, v47, g[2]), + ); + } + // X(422): X(4)-Hirst of X(28); on X(58) tril a/(b+c); skip right/equil + if !right && !equil { + let (u58, v58, w58) = (a / (b + c), b / (c + a), c / (a + b)); + let f = |u: f64, v: f64, w: f64, ang: f64| (u * u - v * w) * ang.tan(); + push_bary( + &mut out, + "X4HirstX28", + "X_{422}", + "X(422) = X_4\\text{-Hirst of }X_{28};\\ (u^2-vw)\\tan A\\ (u:v:w=X_{58})", + "X(422):垂心对 X(28) 的 Hirst 逆(X58=a/(b+c);跳过直角/等边)", + "X422", + f(u58, v58, w58, g[0]), + f(v58, w58, u58, g[1]), + f(w58, u58, v58, g[2]), + ); + } + // X(423): X(4)-Hirst of X(27); on X(81) tril 1/(b+c); skip right/equil + if !right && !equil { + let (u81, v81, w81) = (1.0 / (b + c), 1.0 / (c + a), 1.0 / (a + b)); + let f = |u: f64, v: f64, w: f64, ang: f64| (u * u - v * w) * ang.tan(); + push_bary( + &mut out, + "X4HirstX27", + "X_{423}", + "X(423) = X_4\\text{-Hirst of }X_{27};\\ (u^2-vw)\\tan A\\ (u:v:w=X_{81})", + "X(423):垂心对 X(27) 的 Hirst 逆(X81=1/(b+c);跳过直角/等边)", + "X423", + f(u81, v81, w81, g[0]), + f(v81, w81, u81, g[1]), + f(w81, u81, v81, g[2]), + ); + } + // X(424): X(4)-Hirst of X(451); on X(191) tril; skip right/equil + if !right && !equil { + let f191 = |aa: f64, bb: f64, cc_: f64| { + (bb + cc_ - aa) * (bb * cc_ + cc_ * aa + aa * bb) + bb.powi(3) + cc_.powi(3) - aa.powi(3) + }; + let (u191, v191, w191) = (f191(a, b, c), f191(b, c, a), f191(c, a, b)); + let f = |u: f64, v: f64, w: f64, ang: f64| (u * u - v * w) * ang.tan(); + push_bary( + &mut out, + "X4HirstX451", + "X_{424}", + "X(424) = X_4\\text{-Hirst of }X_{451};\\ (u^2-vw)\\tan A\\ (u:v:w=X_{191})", + "X(424):垂心对 X(451) 的 Hirst 逆(X191 三线坐标;跳过直角/等边)", + "X424", + f(u191, v191, w191, g[0]), + f(v191, w191, u191, g[1]), + f(w191, u191, v191, g[2]), + ); + } + // X(425): X(4)-Hirst of X(21); on X(283) tril cosA/(cosB+cosC); skip right/equil + if !right && !equil { + let da = cb + cc; + let db = cc + ca; + let dc = ca + cb; + if da.abs() > 1e-14 && db.abs() > 1e-14 && dc.abs() > 1e-14 { + let (u283, v283, w283) = (ca / da, cb / db, cc / dc); + let f = |u: f64, v: f64, w: f64, ang: f64| (u * u - v * w) * ang.tan(); + push_bary( + &mut out, + "X4HirstX21", + "X_{425}", + "X(425) = X_4\\text{-Hirst of }X_{21};\\ (u^2-vw)\\tan A\\ (u:v:w=X_{283})", + "X(425):垂心对席弗勒点的 Hirst 逆(X283;跳过直角/等边)", + "X425", + f(u283, v283, w283, g[0]), + f(v283, w283, u283, g[1]), + f(w283, u283, v283, g[2]), + ); + } + } + // X(426): Euler X(19)-4th-substitution; (v²+w²)sin2A on tan A; skip right + if !right { + let (u19, v19, w19) = (g[0].tan(), g[1].tan(), g[2].tan()); + let f = |v: f64, w: f64, ang: f64| (v * v + w * w) * (2.0 * ang).sin(); + push_bary( + &mut out, + "X19四次替换", + "X_{426}", + "X(426) = \\mathrm{Euler}\\ X_{19}\\text{-4th-subst};\\ (v^2+w^2)\\sin 2A\\ (u:v:w=\\tan A)", + "X(426):克劳森点的欧拉四次替换点(跳过直角)", + "X426", + f(v19, w19, g[0]), + f(w19, u19, g[1]), + f(u19, v19, g[2]), + ); + } + // X(427): complement of X(22); sin A(sec A + cos(B−C)); skip right + if !right { + let f = |ang_a: f64, ang_b: f64, ang_c: f64| { + let ca_ = ang_a.cos(); + if ca_.abs() < 1e-14 { + return f64::NAN; + } + ang_a.sin() * (1.0 / ca_ + (ang_b - ang_c).cos()) + }; + push_bary( + &mut out, + "X22补点", + "X_{427}", + "X(427) = \\mathrm{complement}(X_{22});\\ \\sin A(\\sec A+\\cos(B-C))", + "X(427):X(22) 的补点(跳过直角)", + "X427", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(428): Euler X(38)-5th-substitution; (v+w)tan A on b²+c²; skip right + if !right { + let (u38b, v38b, w38b) = (b * b + c * c, c * c + a * a, a * a + b * b); + push_bary( + &mut out, + "X38五次替换", + "X_{428}", + "X(428) = \\mathrm{Euler}\\ X_{38}\\text{-5th-subst};\\ (v+w)\\tan A\\ (u:v:w=b^2+c^2)", + "X(428):X(38) 的欧拉五次替换点(跳过直角)", + "X428", + (v38b + w38b) * g[0].tan(), + (w38b + u38b) * g[1].tan(), + (u38b + v38b) * g[2].tan(), + ); + } + // X(429): Euler X(58)-5th-substitution; (v+w)tan A on a/(b+c); skip right + if !right { + let (u58b, v58b, w58b) = (a / (b + c), b / (c + a), c / (a + b)); + push_bary( + &mut out, + "X58五次替换", + "X_{429}", + "X(429) = \\mathrm{Euler}\\ X_{58}\\text{-5th-subst};\\ (v+w)\\tan A\\ (u:v:w=X_{58})", + "X(429):X(58) 的欧拉五次替换点(跳过直角)", + "X429", + (v58b + w58b) * g[0].tan(), + (w58b + u58b) * g[1].tan(), + (u58b + v58b) * g[2].tan(), + ); + } + // X(430): Euler X(81)-5th-substitution; (v+w)tan A on 1/(b+c); skip right + if !right { + let (u81b, v81b, w81b) = (1.0 / (b + c), 1.0 / (c + a), 1.0 / (a + b)); + push_bary( + &mut out, + "X81五次替换", + "X_{430}", + "X(430) = \\mathrm{Euler}\\ X_{81}\\text{-5th-subst};\\ (v+w)\\tan A\\ (u:v:w=X_{81})", + "X(430):X(81) 的欧拉五次替换点(跳过直角)", + "X430", + (v81b + w81b) * g[0].tan(), + (w81b + u81b) * g[1].tan(), + (u81b + v81b) * g[2].tan(), + ); + } } @@ -21869,6 +22060,98 @@ mod tests { } } + #[test] + fn x421_to_x430_hirst_euler_subst_band() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("X4HirstX24", "X_{421}", 5.791494980780398, 5.409343854995461), + ("X4HirstX28", "X_{422}", 6.233150600408183, 6.488290304882697), + ("X4HirstX27", "X_{423}", 6.378590932237614, 6.8435950326478245), + ("X4HirstX451", "X_{424}", 7.259098618603891, 8.994638968427399), + ("X4HirstX21", "X_{425}", 7.91153738989469, 10.588519957978189), + ("X19四次替换", "X_{426}", 3.6863010770899614, 0.266442037907028), + ("X22补点", "X_{427}", 4.703817954220315, 2.752193771815401), + ("X38五次替换", "X_{428}", 4.861958821614583, 3.138525383764397), + ("X58五次替换", "X_{429}", 4.731596112886049, 2.820054666921994), + ("X81五次替换", "X_{430}", 4.78620413637937, 2.9534598144284), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: skip Hirst X421–X425; keep X426–X430 → G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (g3x, g3y) = ptxy(g3); + for lab in [ + "X_{421}", "X_{422}", "X_{423}", "X_{424}", "X_{425}", + ] { + assert!(fs3.iter().all(|f| f.label != lab), "equil should skip {}", lab); + } + for lab in ["X_{426}", "X_{427}", "X_{428}", "X_{429}", "X_{430}"] { + let f = fs3 + .iter() + .find(|f| f.label == lab) + .unwrap_or_else(|| panic!("equil missing {}", lab)); + let (x, y) = ptxy(f); + assert!( + (x - g3x).abs() < 1e-9 && (y - g3y).abs() < 1e-9, + "equil {} {:?} want G {:?}", + lab, + (x, y), + (g3x, g3y) + ); + } + + // Right 3-4-5: all skip (tan/sec issues). + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for lab in [ + "X_{421}", "X_{422}", "X_{423}", "X_{424}", "X_{425}", + "X_{426}", "X_{427}", "X_{428}", "X_{429}", "X_{430}", + ] { + assert!(fs4.iter().all(|f| f.label != lab), "{} should skip right", lab); + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 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zLLIxwlTtVLq#-5p_rSc^lsBGK^|C!1>BxCiw#Sp8zRLFGQ2y5{X0InsAAhswLVenJ zLVx6bPh1rDKK>EUi_tyj&+Ox~BRUXiHWdAVnI$%#!=Ia5iUTUjI8k7gD#6Ea--LC+ z=>fVG#_BgeV;>LiAm^~L{BGOJg@FNfWII%<$^x(fM->0 z+PqQkc*+xNPxy<}!vmjtM%Kak$0y8-n~Jl~kRvRVC z!nAFDFiYXX3AZh;ApjhSjpa1MsdI=%nEqV8{_+(MHmcmO@fR6Aov6-wjx^WcfB4vP zN1|W?+HXuY5T*n}2IL5QV}&?UEW&*BhTx!tTR~eT})t z*@7Ji@0}(%Z(X(8AcK4qF>BvqFt!rh%wU~LaDR31G=o(=UpCuztLW=R9+(doX4kVB zjHv_{F<3Ry+v`@d9^b?Jb>g5cki2yyhOIMZxSzFQ4f?G$=(qMz zcMb6ls#5~|8cVy99%|DNuU2PI4g8)S>f0gSlsbEXf5$?%k)Wmx^$zd&E2^y%X4opRmjPP^^l}f~_cw2foo?=-`aS4< zvd*k58$Ok+5_v(EzVAVAFQI*h3ZJEd;nZrd-erXMS3x7P^bQYs`%{h&TGYTo!LYRl z4RAwCJ;TX0VCx9UsE@bQGi;@2n9cY8aU-7__xw3^?GbOk4sC#xmPQPx)PSuf*+#wa zs5jBq9%NR{W7uzL)>+^9sCS3Z76YGT!82^N;3XMq{$t*W9oGPFoeRTOePg(%rJpq! z`t6T<4>^YX0=u&c@mIk0Erh?-sCS_wtEn<G_zXQ>Gzymi(0IbNrFeT=tD z$M4b3>Kqtmr%~arFVv{Nkgoqe#`}|p_T8xd^Dl2o$HUMx>jE=u6$ZmrNK|4`l)kTJ_Q)RffrQxm`^bA|+cV)ix=p?WH z=%k3biTdEh5s%ru70VE>moAG)6y#6Szj`y`b2~kjruMCjm_^HOP{US5jG{Yl(D$v1 z*zTxv$ZxZKZyEFuzN%gy(W}mU;PGGO!p`@rU)D!_Kt+DFX+y-_b(W(tV5wj3SH8C+ zv{r8cztDnbcn{#6(q?c From 3508b0d237d216a605c5931b33d4faf90f6f9d0a Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:51:04 +0800 Subject: [PATCH 114/123] =?UTF-8?q?feat:=20ETC=20X431=E2=80=93X440=20Euler?= =?UTF-8?q?=205th=E2=80=9310th=20subst=20/=20complement=20X27?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land closed barycentrics for X(431)–X(440) on the Euler-line band: X283-5th, X155/X159/X195/X399-6th, X48-7th, X214-8th, X204-9th, X193-10th, and complement of X(27). Guards: skip right for tan/sec forms; skip equilateral for X437 (X214 tril vanishes). --- crates/mathcore/src/geometry.rs | 307 +++++++++++++++++++++++++++++++- 1 file changed, 306 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 6bea994..23d450e 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -14093,7 +14093,7 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } - // X(401)–X(430): Bailey / Zeeman–Gossard / orthic-X36 / Euler intercepts / X21·X29 subst / Hirst / Ceva / X4-Hirst band / Euler 4th·5th (ETC). + // X(401)–X(440): Bailey / Zeeman–Gossard / orthic-X36 / Euler intercepts / X21·X29 subst / Hirst / Ceva / X4-Hirst / Euler 4th–10th subst / complement X27 (ETC). // X(401)=Bailey=X(2)-Hirst of X(3)=anticomplement(X297); bary sin2B sin2C−sin²(2A); skip equil (weights 0). // X(402)=Zeeman–Gossard perspector; bary p·y with p=2a⁴−a²b²−a²c²−(b²−c²)², // y=a⁸−a⁶(b²+c²)+a⁴(2b²−c²)(2c²−b²)+[(b²−c²)²][3a²(b²+c²)−b⁴−c⁴−3b²c²]; skip equil (p=0). @@ -14125,6 +14125,16 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] // X(428)=Euler X(38)-5th-subst; bary (v+w)tan A, u:v:w=b²+c²; skip right. // X(429)=Euler X(58)-5th-subst; bary (v+w)tan A, u:v:w=a/(b+c); skip right. // X(430)=Euler X(81)-5th-subst; bary (v+w)tan A, u:v:w=1/(b+c); skip right. + // X(431)=Euler X(283)-5th-subst; bary (v+w)tan A, u:v:w=cosA/(cosB+cosC); skip right. + // X(432)=Euler X(155)-6th-subst; bary (v²+w²)tan A, u:v:w=cosA(cos²B+cos²C−cos²A); skip right. + // X(433)=Euler X(159)-6th-subst; bary (v²+w²)tan A, u:v:w=X(159) tril; skip right. + // X(434)=Euler X(195)-6th-subst; bary (v²+w²)tan A, u:v:w=X(195) tril; skip right. + // X(435)=Euler X(399)-6th-subst; bary (v²+w²)tan A, u:v:w=X(399) tril; skip right. + // X(436)=Euler X(48)-7th-subst; bary (u²+vw)tan A, u:v:w=sin2A; skip right. + // X(437)=Euler X(214)-8th-subst; bary (u²+vw)tan A, u:v:w=(b+c−2a)(b²+c²−a²−bc); skip right/equil. + // X(438)=Euler X(204)-9th-subst; bary u²+vw, u:v:w=tanA(tanB+tanC−tanA); skip right. + // X(439)=Euler X(193)-10th-subst; bary (3a²−b²−c²)². + // X(440)=complement of X(27); bary v+w, u:v:w=tanA/(b+c); skip right. { let right = g.iter().any(|ang| (*ang - std::f64::consts::FRAC_PI_2).abs() < 1e-9); let equil = (a - b).abs() < 1e-9 && (b - c).abs() < 1e-9; @@ -14727,6 +14737,205 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] ); } + // X(431)–X(440): Euler X283-5th; X155/X159/X195/X399-6th; X48-7th; X214-8th; X204-9th; X193-10th; complement X27 (ETC). + // X(431): Euler X(283)-5th-substitution; (v+w)tan A on cosA/(cosB+cosC); skip right + if !right { + let da = cb + cc; + let db = cc + ca; + let dc = ca + cb; + if da.abs() > 1e-14 && db.abs() > 1e-14 && dc.abs() > 1e-14 { + let (u283b, v283b, w283b) = (ca / da, cb / db, cc / dc); + push_bary( + &mut out, + "X283五次替换", + "X_{431}", + "X(431) = \\mathrm{Euler}\\ X_{283}\\text{-5th-subst};\\ (v+w)\\tan A\\ (u:v:w=X_{283})", + "X(431):X(283) 的欧拉五次替换点(跳过直角)", + "X431", + (v283b + w283b) * g[0].tan(), + (w283b + u283b) * g[1].tan(), + (u283b + v283b) * g[2].tan(), + ); + } + } + // X(432): Euler X(155)-6th-substitution; (v²+w²)tan A on cosA(cos²B+cos²C−cos²A); skip right + if !right { + let u155 = ca * (cb * cb + cc * cc - ca * ca); + let v155 = cb * (cc * cc + ca * ca - cb * cb); + let w155 = cc * (ca * ca + cb * cb - cc * cc); + let f = |v: f64, w: f64, ang: f64| (v * v + w * w) * ang.tan(); + push_bary( + &mut out, + "X155六次替换", + "X_{432}", + "X(432) = \\mathrm{Euler}\\ X_{155}\\text{-6th-subst};\\ (v^2+w^2)\\tan A\\ (u:v:w=X_{155})", + "X(432):X(155) 的欧拉六次替换点(跳过直角)", + "X432", + f(v155, w155, g[0]), + f(w155, u155, g[1]), + f(u155, v155, g[2]), + ); + } + // X(433): Euler X(159)-6th-substitution; (v²+w²)tan A on X(159) tril; skip right + if !right { + let f159 = |aa: f64, bb: f64, cc_: f64, ang_a: f64, ang_b: f64, ang_c: f64| { + aa * ((a * a + b * b + c * c) * (2.0 * ang_a).sin() + + (cc_ * cc_ - bb * bb - aa * aa) * (2.0 * ang_b).sin() + + (bb * bb - cc_ * cc_ - aa * aa) * (2.0 * ang_c).sin()) + }; + let u159 = f159(a, b, c, g[0], g[1], g[2]); + let v159 = f159(b, c, a, g[1], g[2], g[0]); + let w159 = f159(c, a, b, g[2], g[0], g[1]); + let f = |v: f64, w: f64, ang: f64| (v * v + w * w) * ang.tan(); + push_bary( + &mut out, + "X159六次替换", + "X_{433}", + "X(433) = \\mathrm{Euler}\\ X_{159}\\text{-6th-subst};\\ (v^2+w^2)\\tan A\\ (u:v:w=X_{159})", + "X(433):X(159) 的欧拉六次替换点(跳过直角)", + "X433", + f(v159, w159, g[0]), + f(w159, u159, g[1]), + f(u159, v159, g[2]), + ); + } + // X(434): Euler X(195)-6th-substitution; (v²+w²)tan A on X(195) tril=bary/a; skip right + if !right && area > 1e-12 { + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + if sa.abs() > 1e-14 && sb.abs() > 1e-14 && sc.abs() > 1e-14 { + let cot_w = (a * a + b * b + c * c) / (4.0 * area); + let bary195 = |ang: f64, cang: f64, sang: f64| { + let cot = cang / sang; + 4.0 * (2.0 * ang).cos() + cot * cot - cot * cot_w + }; + // tril = bary/a (homogeneous; use bary as tril weights) + let u195 = bary195(g[0], ca, sa) / a; + let v195 = bary195(g[1], cb, sb) / b; + let w195 = bary195(g[2], cc, sc) / c; + let f = |v: f64, w: f64, ang: f64| (v * v + w * w) * ang.tan(); + push_bary( + &mut out, + "X195六次替换", + "X_{434}", + "X(434) = \\mathrm{Euler}\\ X_{195}\\text{-6th-subst};\\ (v^2+w^2)\\tan A\\ (u:v:w=X_{195})", + "X(434):X(195) 的欧拉六次替换点(跳过直角)", + "X434", + f(v195, w195, g[0]), + f(w195, u195, g[1]), + f(u195, v195, g[2]), + ); + } + } + // X(435): Euler X(399)-6th-substitution; (v²+w²)tan A on Parry tril; skip right + if !right { + let f399 = |ang_a: f64, ang_b: f64, ang_c: f64| { + 5.0 * ang_a.cos() + - 4.0 * ang_b.cos() * ang_c.cos() + - 8.0 * ang_b.sin() * ang_c.sin() * (2.0 * ang_a).cos() + }; + let u399 = f399(g[0], g[1], g[2]); + let v399 = f399(g[1], g[2], g[0]); + let w399 = f399(g[2], g[0], g[1]); + let f = |v: f64, w: f64, ang: f64| (v * v + w * w) * ang.tan(); + push_bary( + &mut out, + "X399六次替换", + "X_{435}", + "X(435) = \\mathrm{Euler}\\ X_{399}\\text{-6th-subst};\\ (v^2+w^2)\\tan A\\ (u:v:w=X_{399})", + "X(435):帕里反射点的欧拉六次替换点(跳过直角)", + "X435", + f(v399, w399, g[0]), + f(w399, u399, g[1]), + f(u399, v399, g[2]), + ); + } + // X(436): Euler X(48)-7th-substitution; (u²+vw)tan A on sin2A; skip right + if !right { + let (u48, v48, w48) = ((2.0 * g[0]).sin(), (2.0 * g[1]).sin(), (2.0 * g[2]).sin()); + let f = |u: f64, v: f64, w: f64, ang: f64| (u * u + v * w) * ang.tan(); + push_bary( + &mut out, + "X48七次替换", + "X_{436}", + "X(436) = \\mathrm{Euler}\\ X_{48}\\text{-7th-subst};\\ (u^2+vw)\\tan A\\ (u:v:w=\\sin 2A)", + "X(436):X(48) 的欧拉七次替换点(跳过直角)", + "X436", + f(u48, v48, w48, g[0]), + f(v48, w48, u48, g[1]), + f(w48, u48, v48, g[2]), + ); + } + // X(437): Euler X(214)-8th-substitution; (u²+vw)tan A on (b+c−2a)(b²+c²−a²−bc); skip right/equil + if !right && !equil { + let u214 = (b + c - 2.0 * a) * (b * b + c * c - a * a - b * c); + let v214 = (c + a - 2.0 * b) * (c * c + a * a - b * b - c * a); + let w214 = (a + b - 2.0 * c) * (a * a + b * b - c * c - a * b); + let f = |u: f64, v: f64, w: f64, ang: f64| (u * u + v * w) * ang.tan(); + push_bary( + &mut out, + "X214八次替换", + "X_{437}", + "X(437) = \\mathrm{Euler}\\ X_{214}\\text{-8th-subst};\\ (u^2+vw)\\tan A\\ (u:v:w=X_{214})", + "X(437):X(214) 的欧拉八次替换点(跳过直角/等边)", + "X437", + f(u214, v214, w214, g[0]), + f(v214, w214, u214, g[1]), + f(w214, u214, v214, g[2]), + ); + } + // X(438): Euler X(204)-9th-substitution; u²+vw on tanA(tanB+tanC−tanA); skip right + if !right { + let (ta, tb, tc) = (g[0].tan(), g[1].tan(), g[2].tan()); + let u204 = ta * (tb + tc - ta); + let v204 = tb * (tc + ta - tb); + let w204 = tc * (ta + tb - tc); + let f = |u: f64, v: f64, w: f64| u * u + v * w; + push_bary( + &mut out, + "X204九次替换", + "X_{438}", + "X(438) = \\mathrm{Euler}\\ X_{204}\\text{-9th-subst};\\ u^2+vw\\ (u:v:w=X_{204})", + "X(438):X(204) 的欧拉九次替换点(跳过直角)", + "X438", + f(u204, v204, w204), + f(v204, w204, u204), + f(w204, u204, v204), + ); + } + // X(439): Euler X(193)-10th-substitution; bary (3a²−b²−c²)² + { + let u193 = 3.0 * a * a - b * b - c * c; + let v193 = 3.0 * b * b - c * c - a * a; + let w193 = 3.0 * c * c - a * a - b * b; + push_bary( + &mut out, + "X193十次替换", + "X_{439}", + "X(439) = \\mathrm{Euler}\\ X_{193}\\text{-10th-subst};\\ (3a^2-b^2-c^2)^2", + "X(439):X(193) 的欧拉十次替换点", + "X439", + u193 * u193, + v193 * v193, + w193 * w193, + ); + } + // X(440): complement of X(27); bary v+w on tanA/(b+c); skip right + if !right { + let (u28, v28, w28) = (g[0].tan() / (b + c), g[1].tan() / (c + a), g[2].tan() / (a + b)); + push_bary( + &mut out, + "X27补点", + "X_{440}", + "X(440) = \\mathrm{complement}(X_{27});\\ v+w\\ (u:v:w=\\tan A/(b+c))", + "X(440):X(27) 的补点(跳过直角)", + "X440", + v28 + w28, + w28 + u28, + u28 + v28, + ); + } + + } @@ -22152,6 +22361,102 @@ mod tests { } } + + #[test] + fn x431_to_x440_euler_subst_complement_band() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("X283五次替换", "X_{431}", 5.007963472381891, 3.495208719403091), + ("X155六次替换", "X_{432}", 4.563562407094006, 2.409555259083562), + ("X159六次替换", "X_{433}", 4.961581016976578, 3.381898295234162), + ("X195六次替换", "X_{434}", 4.470032407560555, 2.18106533057406), + ("X399六次替换", "X_{435}", 4.586088164307535, 2.986281947148511), + ("X48七次替换", "X_{436}", 4.723728445515073, 2.80083428026426), + ("X214八次替换", "X_{437}", 4.8125, 3.017699523919946), + ("X204九次替换", "X_{438}", 5.542568596434214, 4.801226972208073), + ("X193十次替换", "X_{439}", 5.318300993934079, 4.253350475705726), + ("X27补点", "X_{440}", 3.974902956722828, 0.9714845181161382), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: skip X437 (X214 tril vanishes); keep X431–X436,X438–X440 → G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (g3x, g3y) = ptxy(g3); + assert!(fs3.iter().all(|f| f.label != "X_{437}"), "equil should skip X437"); + for lab in [ + "X_{431}", "X_{432}", "X_{433}", "X_{434}", "X_{435}", + "X_{436}", "X_{438}", "X_{439}", "X_{440}", + ] { + let f = fs3 + .iter() + .find(|f| f.label == lab) + .unwrap_or_else(|| panic!("equil missing {}", lab)); + let (x, y) = ptxy(f); + assert!( + (x - g3x).abs() < 1e-9 && (y - g3y).abs() < 1e-9, + "equil {} {:?} want G {:?}", + lab, + (x, y), + (g3x, g3y) + ); + } + + // Right 3-4-5: keep X439; skip tan/sec-dependent centers. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for lab in [ + "X_{431}", "X_{432}", "X_{433}", "X_{434}", "X_{435}", + "X_{436}", "X_{437}", "X_{438}", "X_{440}", + ] { + assert!(fs4.iter().all(|f| f.label != lab), "{} should skip right", lab); + } + assert!( + fs4.iter().any(|f| f.label == "X_{439}"), + "right missing X439" + ); + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 44ceb7b71c0d29ef2a8ebffdf26ce6a033088325 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:51:04 +0800 Subject: [PATCH 115/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X431=E2=80=93X440=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 875258 -> 877958 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 6164ce8a3d7ea77ae2ace39eb3b3595b51833b6a..d71715e11afcfeca244edcbd038981329f03ff3f 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z-7@@!d-v{maBq9(&0ileOJ+cpO#1AWAID_)gPzlmaXEiNor=O__LScIjbXfRy#++! zFwiQpWm@$u#)Vs^w9+EyDs52Ea%*C_5?2c zLGvwVT@ZsYn1KbzLLN4u2xo8w_wWvCjk8fm!V2VI19sp5DsT-C@Cx7XTjNpIVRP0C r!!QLY$iNzG!yX*L1=zOaed-X#t-EqEqPmz}-I-ccg(j&*gVWkS7YR Date: Mon, 2 Nov 2026 19:55:22 +0800 Subject: [PATCH 116/123] =?UTF-8?q?feat:=20ETC=20X441=E2=80=93X450=20compl?= =?UTF-8?q?ements=20/=20Euler=20/=20Hirst=20band?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land closed barycentrics for X(441)–X(450): complement of X(297)/X(21)/X(452), Euler∩X(19)X(232), Euler X(79)-11th-subst, crosspoint X(98)·X(511), X(2)-Hirst of X(27)/X(21)/X(452), and X(3)-Hirst of X(4). Guards: skip right for tan/sec forms; skip equilateral for ω/Hirst-vanishing centers. --- crates/mathcore/src/geometry.rs | 356 +++++++++++++++++++++++++++++++- 1 file changed, 355 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 23d450e..72bcf16 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -14093,7 +14093,7 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } - // X(401)–X(440): Bailey / Zeeman–Gossard / orthic-X36 / Euler intercepts / X21·X29 subst / Hirst / Ceva / X4-Hirst / Euler 4th–10th subst / complement X27 (ETC). + // X(401)–X(450): Bailey / Zeeman–Gossard / orthic-X36 / Euler intercepts / X21·X29 subst / Hirst / Ceva / X4-Hirst / Euler 4th–11th subst / complements X27/X297/X21/X452 / crosspoint X98·X511 / X2-Hirst X27/X21/X452 / X3-Hirst X4 (ETC). // X(401)=Bailey=X(2)-Hirst of X(3)=anticomplement(X297); bary sin2B sin2C−sin²(2A); skip equil (weights 0). // X(402)=Zeeman–Gossard perspector; bary p·y with p=2a⁴−a²b²−a²c²−(b²−c²)², // y=a⁸−a⁶(b²+c²)+a⁴(2b²−c²)(2c²−b²)+[(b²−c²)²][3a²(b²+c²)−b⁴−c⁴−3b²c²]; skip equil (p=0). @@ -14135,6 +14135,16 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] // X(438)=Euler X(204)-9th-subst; bary u²+vw, u:v:w=tanA(tanB+tanC−tanA); skip right. // X(439)=Euler X(193)-10th-subst; bary (3a²−b²−c²)². // X(440)=complement of X(27); bary v+w, u:v:w=tanA/(b+c); skip right. + // X(441)=complement of X(297); bary v+w, u:v:w=X(240) tril secA cos(A+ω); skip right/equil. + // X(442)=complement of X(21); bary v+w, u:v:w=X(284) tril sinA/(cosB+cosC); =mid(X79,X191). + // X(443)=complement of X(452); bary v+w, u:v:w=X(380) tril. + // X(444)=Euler ∩ X(19)X(232); bary (v+w)sinA tanA, u:v:w=X(256)=1/(a²+bc); skip right. + // X(445)=Euler X(79)-11th-subst; bary (v+w)secA, u:v:w=1/(1+2cosA); skip right. + // X(446)=crosspoint of X(98) and X(511); bary a u(v²+w²), u:v:w=sec(A+ω); skip equil. + // X(447)=X(2)-Hirst of X(27); bary u²−vw, u:v:w=tanA/(b+c); skip right/equil. + // X(448)=X(2)-Hirst of X(21); bary u²−vw, u:v:w=sinA/(cosB+cosC); skip equil. + // X(449)=X(2)-Hirst of X(452); bary u²−vw, u:v:w=X(380) tril; skip equil. + // X(450)=X(3)-Hirst of X(4); bary tanA(cos⁴A−(cosB cosC)²); skip right/equil. { let right = g.iter().any(|ang| (*ang - std::f64::consts::FRAC_PI_2).abs() < 1e-9); let equil = (a - b).abs() < 1e-9 && (b - c).abs() < 1e-9; @@ -14935,6 +14945,226 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] ); } + // X(441)–X(450): complements X297/X21/X452; Euler∩X19X232; Euler X79-11th; crosspoint X98·X511; X2-Hirst X27/X21/X452; X3-Hirst X4 (ETC). + // X(441): complement of X(297); v+w on secA cos(A+ω); skip right/equil + if !right && !equil && area > 1e-12 { + let sum_sq = a * a + b * b + c * c; + let tan_w = (4.0 * area) / sum_sq; + let cos_w = 1.0 / (1.0 + tan_w * tan_w).sqrt(); + let sin_w = tan_w * cos_w; + let tril240 = |ang: f64| { + let cang = ang.cos(); + let sang = ang.sin(); + if cang.abs() < 1e-14 { + 0.0 + } else { + (cang * cos_w - sang * sin_w) / cang + } + }; + let (u240, v240, w240) = (tril240(g[0]), tril240(g[1]), tril240(g[2])); + push_bary( + &mut out, + "X297补点", + "X_{441}", + "X(441) = \\mathrm{complement}(X_{297});\\ v+w\\ (u:v:w=\\sec A\\cos(A+\\omega))", + "X(441):X(297) 的补点(跳过直角/等边)", + "X441", + v240 + w240, + w240 + u240, + u240 + v240, + ); + } + // X(442): complement of X(21); v+w on sinA/(cosB+cosC); =mid(X79,X191) + { + let da = cb + cc; + let db = cc + ca; + let dc = ca + cb; + if da.abs() > 1e-14 && db.abs() > 1e-14 && dc.abs() > 1e-14 { + let (u284, v284, w284) = (g[0].sin() / da, g[1].sin() / db, g[2].sin() / dc); + push_bary( + &mut out, + "席弗勒补点", + "X_{442}", + "X(442) = \\mathrm{complement}(X_{21});\\ v+w\\ (u:v:w=\\sin A/(\\cos B+\\cos C))", + "X(442):席弗勒点的补点(= mid(X79,X191))", + "X442", + v284 + w284, + w284 + u284, + u284 + v284, + ); + } + } + // X(443): complement of X(452); v+w on X(380) tril + { + let f380 = |aa: f64, bb: f64, cc_: f64| { + let s = bb + cc_; + (s - aa) * (3.0 * aa.powi(3) + s * (3.0 * aa * aa + (bb - cc_).powi(2) + aa * s)) + }; + let (u380, v380, w380) = (f380(a, b, c), f380(b, c, a), f380(c, a, b)); + push_bary( + &mut out, + "X452补点", + "X_{443}", + "X(443) = \\mathrm{complement}(X_{452});\\ v+w\\ (u:v:w=X_{380})", + "X(443):X(452) 的补点(X380 三线坐标)", + "X443", + v380 + w380, + w380 + u380, + u380 + v380, + ); + } + // X(444): Euler ∩ X(19)X(232); (v+w)sinA tanA on 1/(a²+bc); skip right + if !right { + let (u256, v256, w256) = ( + 1.0 / (a * a + b * c), + 1.0 / (b * b + c * a), + 1.0 / (c * c + a * b), + ); + let f = |v: f64, w: f64, ang: f64| (v + w) * ang.sin() * ang.tan(); + push_bary( + &mut out, + "X19X232欧拉截", + "X_{444}", + "X(444) = \\mathrm{Euler}\\cap X_{19}X_{232};\\ (v+w)\\sin A\\tan A\\ (u:v:w=1/(a^2+bc))", + "X(444):X(19)X(232) 与欧拉线的交点(跳过直角)", + "X444", + f(v256, w256, g[0]), + f(w256, u256, g[1]), + f(u256, v256, g[2]), + ); + } + // X(445): Euler X(79)-11th-substitution; (v+w)secA on 1/(1+2cosA); skip right + if !right { + let d0 = 1.0 + 2.0 * ca; + let d1 = 1.0 + 2.0 * cb; + let d2 = 1.0 + 2.0 * cc; + if d0.abs() > 1e-14 + && d1.abs() > 1e-14 + && d2.abs() > 1e-14 + && ca.abs() > 1e-14 + && cb.abs() > 1e-14 + && cc.abs() > 1e-14 + { + let (u79, v79, w79) = (1.0 / d0, 1.0 / d1, 1.0 / d2); + let f = |v: f64, w: f64, cang: f64| (v + w) / cang; + push_bary( + &mut out, + "X79十一次替换", + "X_{445}", + "X(445) = \\mathrm{Euler}\\ X_{79}\\text{-11th-subst};\\ (v+w)\\sec A\\ (u:v:w=1/(1+2\\cos A))", + "X(445):X(79) 的欧拉十一次替换点(跳过直角)", + "X445", + f(v79, w79, ca), + f(w79, u79, cb), + f(u79, v79, cc), + ); + } + } + // X(446): crosspoint of X(98) and X(511); a u(v²+w²) on sec(A+ω); skip equil + if !equil && area > 1e-12 { + let sum_sq = a * a + b * b + c * c; + let tan_w = (4.0 * area) / sum_sq; + let cos_w = 1.0 / (1.0 + tan_w * tan_w).sqrt(); + let sin_w = tan_w * cos_w; + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let c0 = ca * cos_w - sa * sin_w; + let c1 = cb * cos_w - sb * sin_w; + let c2 = cc * cos_w - sc * sin_w; + if c0.abs() > 1e-14 && c1.abs() > 1e-14 && c2.abs() > 1e-14 { + let (u98, v98, w98) = (1.0 / c0, 1.0 / c1, 1.0 / c2); + let f = |u: f64, v: f64, w: f64, side: f64| side * u * (v * v + w * w); + push_bary( + &mut out, + "X98X511交叉", + "X_{446}", + "X(446) = \\mathrm{crosspoint}(X_{98},X_{511});\\ au(v^2+w^2)\\ (u:v:w=\\sec(A+\\omega))", + "X(446):塔里点与 X(511) 的交叉点(跳过等边)", + "X446", + f(u98, v98, w98, a), + f(v98, w98, u98, b), + f(w98, u98, v98, c), + ); + } + } + // X(447): X(2)-Hirst of X(27); u²−vw on tanA/(b+c); skip right/equil + if !right && !equil { + let (u28, v28, w28) = (g[0].tan() / (b + c), g[1].tan() / (c + a), g[2].tan() / (a + b)); + let f = |u: f64, v: f64, w: f64| u * u - v * w; + push_bary( + &mut out, + "重心HirstX27", + "X_{447}", + "X(447) = X_2\\text{-Hirst of }X_{27};\\ u^2-vw\\ (u:v:w=\\tan A/(b+c))", + "X(447):重心对 X(27) 的 Hirst 逆(跳过直角/等边)", + "X447", + f(u28, v28, w28), + f(v28, w28, u28), + f(w28, u28, v28), + ); + } + // X(448): X(2)-Hirst of X(21); u²−vw on sinA/(cosB+cosC); skip equil + if !equil { + let da = cb + cc; + let db = cc + ca; + let dc = ca + cb; + if da.abs() > 1e-14 && db.abs() > 1e-14 && dc.abs() > 1e-14 { + let (u284, v284, w284) = (g[0].sin() / da, g[1].sin() / db, g[2].sin() / dc); + let f = |u: f64, v: f64, w: f64| u * u - v * w; + push_bary( + &mut out, + "重心Hirst席弗勒", + "X_{448}", + "X(448) = X_2\\text{-Hirst of }X_{21};\\ u^2-vw\\ (u:v:w=\\sin A/(\\cos B+\\cos C))", + "X(448):重心对席弗勒点的 Hirst 逆(跳过等边)", + "X448", + f(u284, v284, w284), + f(v284, w284, u284), + f(w284, u284, v284), + ); + } + } + // X(449): X(2)-Hirst of X(452); u²−vw on X(380) tril; skip equil + if !equil { + let f380 = |aa: f64, bb: f64, cc_: f64| { + let s = bb + cc_; + (s - aa) * (3.0 * aa.powi(3) + s * (3.0 * aa * aa + (bb - cc_).powi(2) + aa * s)) + }; + let (u380, v380, w380) = (f380(a, b, c), f380(b, c, a), f380(c, a, b)); + let f = |u: f64, v: f64, w: f64| u * u - v * w; + push_bary( + &mut out, + "重心HirstX452", + "X_{449}", + "X(449) = X_2\\text{-Hirst of }X_{452};\\ u^2-vw\\ (u:v:w=X_{380})", + "X(449):重心对 X(452) 的 Hirst 逆(跳过等边)", + "X449", + f(u380, v380, w380), + f(v380, w380, u380), + f(w380, u380, v380), + ); + } + // X(450): X(3)-Hirst of X(4); tanA(cos⁴A−(cosB cosC)²); skip right/equil + if !right && !equil { + let h = |ang: f64, cb_: f64, cc_: f64| { + let ca_ = ang.cos(); + ang.tan() * (ca_.powi(4) - (cb_ * cc_).powi(2)) + }; + push_bary( + &mut out, + "外心Hirst垂心", + "X_{450}", + "X(450) = X_3\\text{-Hirst of }X_4;\\ \\tan A(\\cos^4 A-(\\cos B\\cos C)^2)", + "X(450):外心对垂心的 Hirst 逆(跳过直角/等边)", + "X450", + h(g[0], cb, cc), + h(g[1], cc, ca), + h(g[2], ca, cb), + ); + } + + + + } @@ -22457,6 +22687,130 @@ mod tests { ); } + #[test] + fn x441_to_x450_complement_hirst_euler_band() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("X297补点", "X_{441}", 2.552143291123049, -2.504258622060274), + ("席弗勒补点", "X_{442}", 4.303075396825397, 1.773196244320162), + ("X452补点", "X_{443}", 4.310084541062802, 1.790319294397209), + ("X19X232欧拉截", "X_{444}", 4.931844742034983, 3.309253802884796), + ("X79十一次替换", "X_{445}", 4.603639563828206, 2.507462098843424), + ("X98X511交叉", "X_{446}", -14.813888293398788, -44.928757018662928), + ("重心HirstX27", "X_{447}", 7.416698644154515, 9.379649326075041), + ("重心Hirst席弗勒", "X_{448}", -24.603159375799478, -68.843542231271428), + ("重心HirstX452", "X_{449}", -19.447089249168585, -56.247475723193276), + ("外心Hirst垂心", "X_{450}", 8.686260623229460, 12.481136841141982), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + // Cross-check: X(442)=mid(X79,X191); X(441)=mid(X297,X401). + let mid = |a: &str, b: &str| { + let fa = fs.iter().find(|f| f.label == a).unwrap_or_else(|| panic!("missing {}", a)); + let fb = fs.iter().find(|f| f.label == b).unwrap_or_else(|| panic!("missing {}", b)); + let (ax, ay) = ptxy(fa); + let (bx, by) = ptxy(fb); + ((ax + bx) / 2.0, (ay + by) / 2.0) + }; + let (m42x, m42y) = mid("X_{79}", "X_{191}"); + let f442 = fs.iter().find(|f| f.label == "X_{442}").expect("X442"); + let (x442, y442) = ptxy(f442); + assert!( + (x442 - m42x).abs() < 1e-9 && (y442 - m42y).abs() < 1e-9, + "X442 should be mid(X79,X191): {:?} vs {:?}", + (x442, y442), + (m42x, m42y) + ); + let (m41x, m41y) = mid("X_{297}", "X_{401}"); + let f441 = fs.iter().find(|f| f.label == "X_{441}").expect("X441"); + let (x441, y441) = ptxy(f441); + assert!( + (x441 - m41x).abs() < 1e-9 && (y441 - m41y).abs() < 1e-9, + "X441 should be mid(X297,X401): {:?} vs {:?}", + (x441, y441), + (m41x, m41y) + ); + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: skip ω/Hirst-vanishing; keep complements X442/X443 and Euler X444/X445 → G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (g3x, g3y) = ptxy(g3); + for lab in [ + "X_{441}", "X_{446}", "X_{447}", "X_{448}", "X_{449}", "X_{450}", + ] { + assert!(fs3.iter().all(|f| f.label != lab), "equil should skip {}", lab); + } + for lab in ["X_{442}", "X_{443}", "X_{444}", "X_{445}"] { + let f = fs3 + .iter() + .find(|f| f.label == lab) + .unwrap_or_else(|| panic!("equil missing {}", lab)); + let (x, y) = ptxy(f); + assert!( + (x - g3x).abs() < 1e-9 && (y - g3y).abs() < 1e-9, + "equil {} {:?} want G {:?}", + lab, + (x, y), + (g3x, g3y) + ); + } + + // Right 3-4-5: skip tan/sec-dependent; keep X442/X443/X446/X448/X449. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for lab in [ + "X_{441}", "X_{444}", "X_{445}", "X_{447}", "X_{450}", + ] { + assert!(fs4.iter().all(|f| f.label != lab), "{} should skip right", lab); + } + for lab in ["X_{442}", "X_{443}", "X_{446}", "X_{448}", "X_{449}"] { + assert!( + fs4.iter().any(|f| f.label == lab), + "right missing {}", + lab + ); + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From e49232b490ba3cfebf9250b984f22d0b31c68e69 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:55:47 +0800 Subject: [PATCH 117/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X441=E2=80=93X450=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 877958 -> 881079 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index d71715e11afcfeca244edcbd038981329f03ff3f..71262039c7a9ebc09359a856c9e5ec11d203bff9 100644 GIT binary patch delta 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z1W&I6e{2{}{TFM&vf~TR;hE{ck2H)U_~ANmrC}WPU#SJFM_zDlX2brD4x{A}Y+Nb9 z{R{(#*P$oaNIyK|`H~l%YRQWs-4oT={UQG}hXkWpp;w)MAS9mgQ(kpLamZ(8$IsYY z+JE`!;gI@r!{Ly}c{i_Y@^(lTuSiqpza4VW5(?tiZDo&wf0mc;3TP ziRTwQVP#RKcs$8??!xl|o&r4k@VtYk49`b+F5+RQqD+x^8skaA(+f}EQ&H_qqtTdz zCmYXFJe%?C#&Z Date: Sat, 7 Nov 2026 08:13:12 +0800 Subject: [PATCH 118/123] =?UTF-8?q?feat:=20ETC=20X451=E2=80=93X460=20Hirst?= =?UTF-8?q?=20/=20Alshain=20/=20Euler-11th=20/=20Antares=20band?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- crates/mathcore/src/geometry.rs | 343 +++++++++++++++++++++++++++++++- 1 file changed, 339 insertions(+), 4 deletions(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 72bcf16..1014fbd 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -14093,7 +14093,7 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } - // X(401)–X(450): Bailey / Zeeman–Gossard / orthic-X36 / Euler intercepts / X21·X29 subst / Hirst / Ceva / X4-Hirst / Euler 4th–11th subst / complements X27/X297/X21/X452 / crosspoint X98·X511 / X2-Hirst X27/X21/X452 / X3-Hirst X4 (ETC). + // X(401)–X(460): Bailey / Zeeman–Gossard / orthic-X36 / Euler intercepts / X21·X29 subst / Hirst / Ceva / X4-Hirst / Euler 4th–11th subst / complements X27/X297/X21/X452 / crosspoint X98·X511 / X2-Hirst X27/X21/X452 / X3-Hirst X4 / X4-Hirst-pair X451 / X452 / Alshain / Euler 11th X155·X159·X195·X399 / X458 / X459 / Antares X460 (ETC). // X(401)=Bailey=X(2)-Hirst of X(3)=anticomplement(X297); bary sin2B sin2C−sin²(2A); skip equil (weights 0). // X(402)=Zeeman–Gossard perspector; bary p·y with p=2a⁴−a²b²−a²c²−(b²−c²)², // y=a⁸−a⁶(b²+c²)+a⁴(2b²−c²)(2c²−b²)+[(b²−c²)²][3a²(b²+c²)−b⁴−c⁴−3b²c²]; skip equil (p=0). @@ -14145,6 +14145,16 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] // X(448)=X(2)-Hirst of X(21); bary u²−vw, u:v:w=sinA/(cosB+cosC); skip equil. // X(449)=X(2)-Hirst of X(452); bary u²−vw, u:v:w=X(380) tril; skip equil. // X(450)=X(3)-Hirst of X(4); bary tanA(cos⁴A−(cosB cosC)²); skip right/equil. + // X(451)=X(4)-Hirst inverse of X(424); bary u tan A, u:v:w=X(191) tril; skip right. + // X(452)=X(2)-Hirst inverse of X(449); bary = X(380) tril (anticomplement of X443). + // X(453)=Alshain; bary sinA (cosB+cosC−cosA)²/(cosB+cosC). + // X(454)=Euler X(155)-11th-subst; bary u² tan A, u:v:w=X(155) tril; skip right. + // X(455)=Euler X(159)-11th-subst; bary u² tan A, u:v:w=X(159) tril; skip right. + // X(456)=Euler X(195)-11th-subst; bary u² tan A, u:v:w=X(195) tril; skip right. + // X(457)=Euler X(399)-11th-subst; bary u² tan A, u:v:w=X(399) tril; skip right. + // X(458)=Euler ∩ X(76)X(275); bary tanA+cot ω = secA cos(A−ω); skip right. + // X(459)=X(253)-Ceva of X(4); bary 1/(tanB tanC−2). + // X(460)=Antares; bary tanA[a²(2a²−b²−c²)+(b²−c²)²]; =X4*X230 bary product; skip right/equil. { let right = g.iter().any(|ang| (*ang - std::f64::consts::FRAC_PI_2).abs() < 1e-9); let equil = (a - b).abs() < 1e-9 && (b - c).abs() < 1e-9; @@ -15162,9 +15172,215 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] ); } - - - + // X(451)–X(460): X4-Hirst-pair X451; X452; Alshain; Euler 11th X155/X159/X195/X399; X458; X459; Antares (ETC). + // X(451): X(4)-Hirst inverse of X(424); u tan A on X(191) tril; skip right + if !right { + let f191 = |aa: f64, bb: f64, cc_: f64| { + (bb + cc_ - aa) * (bb * cc_ + cc_ * aa + aa * bb) + bb.powi(3) + cc_.powi(3) + - aa.powi(3) + }; + let (u191, v191, w191) = (f191(a, b, c), f191(b, c, a), f191(c, a, b)); + push_bary( + &mut out, + "垂心HirstX424", + "X_{451}", + "X(451) = X_4\\text{-Hirst of }X_{424};\\ u\\tan A\\ (u:v:w=X_{191})", + "X(451):垂心对 X(424) 的 Hirst 逆(X191 三线坐标;跳过直角)", + "X451", + u191 * g[0].tan(), + v191 * g[1].tan(), + w191 * g[2].tan(), + ); + } + // X(452): X(2)-Hirst inverse of X(449); bary = X(380) tril; =anticomplement(X443) + { + let f380 = |aa: f64, bb: f64, cc_: f64| { + let s = bb + cc_; + (s - aa) * (3.0 * aa.powi(3) + s * (3.0 * aa * aa + (bb - cc_).powi(2) + aa * s)) + }; + push_bary( + &mut out, + "重心HirstX449", + "X_{452}", + "X(452) = X_2\\text{-Hirst of }X_{449} = \\mathrm{anticomplement}(X_{443});\\ u:v:w=X_{380}\\text{ tril}", + "X(452):重心对 X(449) 的 Hirst 逆(= X(443) 的反补;X380 三线坐标)", + "X452", + f380(a, b, c), + f380(b, c, a), + f380(c, a, b), + ); + } + // X(453): Alshain; sinA (cosB+cosC−cosA)²/(cosB+cosC) + { + let da = cb + cc; + let db = cc + ca; + let dc = ca + cb; + if da.abs() > 1e-14 && db.abs() > 1e-14 && dc.abs() > 1e-14 { + let f = |sang: f64, cang: f64, den: f64, cb_: f64, cc_: f64| { + sang * (cb_ + cc_ - cang).powi(2) / den + }; + push_bary( + &mut out, + "阿尔沙因点", + "X_{453}", + "X(453) = \\mathrm{Alshain};\\ \\sin A(\\cos B+\\cos C-\\cos A)^2/(\\cos B+\\cos C)", + "X(453):阿尔沙因点", + "X453", + f(g[0].sin(), ca, da, cb, cc), + f(g[1].sin(), cb, db, cc, ca), + f(g[2].sin(), cc, dc, ca, cb), + ); + } + } + // X(454): Euler X(155)-11th-substitution; u² tan A on X(155) tril; skip right + if !right { + let u155 = ca * (cb * cb + cc * cc - ca * ca); + let v155 = cb * (cc * cc + ca * ca - cb * cb); + let w155 = cc * (ca * ca + cb * cb - cc * cc); + push_bary( + &mut out, + "X155十一次替换", + "X_{454}", + "X(454) = \\mathrm{Euler}\\ X_{155}\\text{-11th-subst};\\ u^2\\tan A\\ (u:v:w=X_{155})", + "X(454):X(155) 的欧拉十一次替换点(跳过直角)", + "X454", + u155 * u155 * g[0].tan(), + v155 * v155 * g[1].tan(), + w155 * w155 * g[2].tan(), + ); + } + // X(455): Euler X(159)-11th-substitution; u² tan A on X(159) tril; skip right + if !right { + let f159 = |aa: f64, bb: f64, cc_: f64, ang_a: f64, ang_b: f64, ang_c: f64| { + aa * ((a * a + b * b + c * c) * (2.0 * ang_a).sin() + + (cc_ * cc_ - bb * bb - aa * aa) * (2.0 * ang_b).sin() + + (bb * bb - cc_ * cc_ - aa * aa) * (2.0 * ang_c).sin()) + }; + let u159 = f159(a, b, c, g[0], g[1], g[2]); + let v159 = f159(b, c, a, g[1], g[2], g[0]); + let w159 = f159(c, a, b, g[2], g[0], g[1]); + push_bary( + &mut out, + "X159十一次替换", + "X_{455}", + "X(455) = \\mathrm{Euler}\\ X_{159}\\text{-11th-subst};\\ u^2\\tan A\\ (u:v:w=X_{159})", + "X(455):X(159) 的欧拉十一次替换点(跳过直角)", + "X455", + u159 * u159 * g[0].tan(), + v159 * v159 * g[1].tan(), + w159 * w159 * g[2].tan(), + ); + } + // X(456): Euler X(195)-11th-substitution; u² tan A on X(195) tril; skip right + if !right && area > 1e-12 { + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + if sa.abs() > 1e-14 && sb.abs() > 1e-14 && sc.abs() > 1e-14 { + let cot_w = (a * a + b * b + c * c) / (4.0 * area); + let bary195 = |ang: f64, cang: f64, sang: f64| { + let cot = cang / sang; + 4.0 * (2.0 * ang).cos() + cot * cot - cot * cot_w + }; + let u195 = bary195(g[0], ca, sa) / a; + let v195 = bary195(g[1], cb, sb) / b; + let w195 = bary195(g[2], cc, sc) / c; + push_bary( + &mut out, + "X195十一次替换", + "X_{456}", + "X(456) = \\mathrm{Euler}\\ X_{195}\\text{-11th-subst};\\ u^2\\tan A\\ (u:v:w=X_{195})", + "X(456):X(195) 的欧拉十一次替换点(跳过直角)", + "X456", + u195 * u195 * g[0].tan(), + v195 * v195 * g[1].tan(), + w195 * w195 * g[2].tan(), + ); + } + } + // X(457): Euler X(399)-11th-substitution; u² tan A on Parry tril; skip right + if !right { + let f399 = |ang_a: f64, ang_b: f64, ang_c: f64| { + 5.0 * ang_a.cos() + - 4.0 * ang_b.cos() * ang_c.cos() + - 8.0 * ang_b.sin() * ang_c.sin() * (2.0 * ang_a).cos() + }; + let u399 = f399(g[0], g[1], g[2]); + let v399 = f399(g[1], g[2], g[0]); + let w399 = f399(g[2], g[0], g[1]); + push_bary( + &mut out, + "X399十一次替换", + "X_{457}", + "X(457) = \\mathrm{Euler}\\ X_{399}\\text{-11th-subst};\\ u^2\\tan A\\ (u:v:w=X_{399})", + "X(457):帕里反射点的欧拉十一次替换点(跳过直角)", + "X457", + u399 * u399 * g[0].tan(), + v399 * v399 * g[1].tan(), + w399 * w399 * g[2].tan(), + ); + } + // X(458): Euler ∩ X(76)X(275); tanA+cot ω; skip right + if !right && area > 1e-12 { + let cot_w = (a * a + b * b + c * c) / (4.0 * area); + push_bary( + &mut out, + "X76X275欧拉截", + "X_{458}", + "X(458) = \\mathrm{Euler}\\cap X_{76}X_{275};\\ \\tan A+\\cot\\omega", + "X(458):X(76)X(275) 与欧拉线的交点(跳过直角)", + "X458", + g[0].tan() + cot_w, + g[1].tan() + cot_w, + g[2].tan() + cot_w, + ); + } + // X(459): X(253)-Ceva of X(4); 1/(tanB tanC−2) + { + let tb = g[1].tan(); + let tc = g[2].tan(); + let ta = g[0].tan(); + let da = tb * tc - 2.0; + let db = tc * ta - 2.0; + let dc = ta * tb - 2.0; + if da.abs() > 1e-14 + && db.abs() > 1e-14 + && dc.abs() > 1e-14 + && ta.is_finite() + && tb.is_finite() + && tc.is_finite() + { + push_bary( + &mut out, + "X253垂心塞瓦", + "X_{459}", + "X(459) = X_{253}\\text{-Ceva of }X_4;\\ 1/(\\tan B\\tan C-2)", + "X(459):X(253) 对垂心的塞瓦共轭", + "X459", + 1.0 / da, + 1.0 / db, + 1.0 / dc, + ); + } + } + // X(460): Antares; tanA[a²(2a²−b²−c²)+(b²−c²)²]; skip right/equil + if !right && !equil { + let f = |aa: f64, bb: f64, cc_: f64| { + let a2 = aa * aa; + let b2 = bb * bb; + let c2 = cc_ * cc_; + a2 * (2.0 * a2 - b2 - c2) + (b2 - c2) * (b2 - c2) + }; + push_bary( + &mut out, + "安塔瑞斯点", + "X_{460}", + "X(460) = \\mathrm{Antares}=X_4\\cdot X_{230};\\ \\tan A[a^2(2a^2-b^2-c^2)+(b^2-c^2)^2]", + "X(460):安塔瑞斯点(X(4)·X(230) 重心积;跳过直角/等边)", + "X460", + g[0].tan() * f(a, b, c), + g[1].tan() * f(b, c, a), + g[2].tan() * f(c, a, b), + ); + } } @@ -22811,6 +23027,125 @@ mod tests { } } + #[test] + fn x451_to_x460_hirst_alshain_euler11_antares_band() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("垂心HirstX424", "X_{451}", 4.433130461922597, 2.090915400468877), + ("重心HirstX449", "X_{452}", 4.192330917874396, 1.502652053102817), + ("阿尔沙因点", "X_{453}", 5.295484278431903, 4.197610181469446), + ("X155十一次替换", "X_{454}", 5.155341031448409, 3.855246013351434), + ("X159十一次替换", "X_{455}", 4.403604538557236, 2.018784788338213), + ("X195十一次替换", "X_{456}", 5.234750870682093, 4.049240973043124), + ("X399十一次替换", "X_{457}", 5.232156804225402, 3.075932344762030), + ("X76X275欧拉截", "X_{458}", 4.564830921045434, 2.412654186310344), + ("X253垂心塞瓦", "X_{459}", 4.660705932529855, 6.571288767845640), + ("安塔瑞斯点", "X_{460}", 5.700709647677338, 5.187559033292232), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + // Cross-check: X(452)=anticomplement(X443)=3G−2·X443; X(451) mutual X4-Hirst with X424. + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (gx, gy) = ptxy(g); + let f443 = fs.iter().find(|f| f.label == "X_{443}").expect("X443"); + let (x443, y443) = ptxy(f443); + let f452 = fs.iter().find(|f| f.label == "X_{452}").expect("X452"); + let (x452, y452) = ptxy(f452); + let ax = 3.0 * gx - 2.0 * x443; + let ay = 3.0 * gy - 2.0 * y443; + assert!( + (x452 - ax).abs() < 1e-9 && (y452 - ay).abs() < 1e-9, + "X452 should be anticomplement(X443): {:?} vs {:?}", + (x452, y452), + (ax, ay) + ); + assert!( + fs.iter().any(|f| f.label == "X_{424}"), + "X424 should exist as mutual X4-Hirst of X451" + ); + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: skip Antares (weights vanish); Euler/Alshain/X451/X452/X459 → G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (g3x, g3y) = ptxy(g3); + assert!( + fs3.iter().all(|f| f.label != "X_{460}"), + "equil should skip X460" + ); + for lab in [ + "X_{451}", "X_{452}", "X_{453}", "X_{454}", "X_{455}", "X_{456}", "X_{457}", "X_{458}", + "X_{459}", + ] { + let f = fs3 + .iter() + .find(|f| f.label == lab) + .unwrap_or_else(|| panic!("equil missing {}", lab)); + let (x, y) = ptxy(f); + assert!( + (x - g3x).abs() < 1e-9 && (y - g3y).abs() < 1e-9, + "equil {} {:?} want G {:?}", + lab, + (x, y), + (g3x, g3y) + ); + } + + // Right 3-4-5: skip tan/sec-dependent; keep X452/X453/X459. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for lab in [ + "X_{451}", "X_{454}", "X_{455}", "X_{456}", "X_{457}", "X_{458}", "X_{460}", + ] { + assert!(fs4.iter().all(|f| f.label != lab), "{} should skip right", lab); + } + for lab in ["X_{452}", "X_{453}", "X_{459}"] { + assert!( + fs4.iter().any(|f| f.label == lab), + "right missing {}", + lab + ); + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 5cf8b17958e5be9180d1ad8693cff8ba2eca9f3c Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sat, 7 Nov 2026 08:13:12 +0800 Subject: [PATCH 119/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X451=E2=80=93X460=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 881079 -> 884036 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git 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z7!DsO!+pZqrPrWmIGjFRpZ?98ZsVIbBL=lKde8miyUL=26SsP%@`O7-~Jh@@l>(96Tn41WlCzqDAMw^cEl+|wvI8*$EN z%sU@(-{^?L=i)3M<2iOtUDqQ!=CnB-XGzC10MEmCp2L%a=S@6?csAnMiRToaay;MQ zv7Cvs)Wy>jPe(kx@H~yD0M9l&C-Gdua~01&@zB{gOG7*@@N~h`1J8YUMx2dnXZZ^X z)A1-g>+tNs^D&+;@Z7-j3!YjKSmJ4Y&N$X1vNJAfHyQR`k>3hx`swtWy(95N88>@J I-`(~90YaJ}8vp Date: Sat, 7 Nov 2026 07:40:56 +0000 Subject: [PATCH 120/123] feat: package MathScrap for Windows, Android, and iOS Bundle the existing sheet, CoMER ONNX, and mathcore WASM in a Tauri shell that does not call the Vite server. Android debug APKs are arm64 and debug-signed; Windows and iOS builds stay on the machines that can sign them. Co-authored-by: DNT_OF --- .github/workflows/package-ios.yml | 57 + .github/workflows/package.yml | 125 + .gitignore | 12 + README.md | 27 +- index.html | 3 +- package-lock.json | 253 +- package.json | 13 +- packaging/icon-source.png | Bin 0 -> 5873 bytes packaging/icon-source.svg | 3 + rust-toolchain.toml | 3 + scripts/android-release-signing.mjs | 62 + scripts/checksum-artifacts.mjs | 16 + scripts/compact-debug-apk.py | 21 + scripts/make-icon.mjs | 20 + scripts/pack-smoke.ts | 60 + scripts/package-android.sh | 136 + scripts/package-ios.sh | 112 + scripts/package-windows.sh | 49 + scripts/verify-packaged-dist.mjs | 61 + src-tauri/Cargo.lock | 4390 +++++++++++++++++ src-tauri/Cargo.toml | 29 + src-tauri/build.rs | 3 + src-tauri/capabilities/default.json | 18 + src-tauri/icons/128x128.png | Bin 0 -> 299 bytes src-tauri/icons/128x128@2x.png | Bin 0 -> 666 bytes src-tauri/icons/32x32.png | Bin 0 -> 106 bytes src-tauri/icons/64x64.png | Bin 0 -> 161 bytes src-tauri/icons/Square107x107Logo.png | Bin 0 -> 240 bytes src-tauri/icons/Square142x142Logo.png | Bin 0 -> 329 bytes src-tauri/icons/Square150x150Logo.png | Bin 0 -> 348 bytes src-tauri/icons/Square284x284Logo.png | Bin 0 -> 763 bytes src-tauri/icons/Square30x30Logo.png | Bin 0 -> 105 bytes src-tauri/icons/Square310x310Logo.png | Bin 0 -> 853 bytes src-tauri/icons/Square44x44Logo.png | Bin 0 -> 121 bytes src-tauri/icons/Square71x71Logo.png | Bin 0 -> 173 bytes src-tauri/icons/Square89x89Logo.png | Bin 0 -> 200 bytes src-tauri/icons/StoreLogo.png | Bin 0 -> 131 bytes .../android/mipmap-anydpi-v26/ic_launcher.xml | 5 + .../icons/android/mipmap-hdpi/ic_launcher.png | Bin 0 -> 230 bytes .../mipmap-hdpi/ic_launcher_foreground.png | Bin 0 -> 375 bytes .../android/mipmap-hdpi/ic_launcher_round.png | Bin 0 -> 340 bytes .../icons/android/mipmap-mdpi/ic_launcher.png | Bin 0 -> 175 bytes .../mipmap-mdpi/ic_launcher_foreground.png | Bin 0 -> 240 bytes .../android/mipmap-mdpi/ic_launcher_round.png | Bin 0 -> 244 bytes .../android/mipmap-xhdpi/ic_launcher.png | Bin 0 -> 277 bytes .../mipmap-xhdpi/ic_launcher_foreground.png | Bin 0 -> 516 bytes .../mipmap-xhdpi/ic_launcher_round.png | Bin 0 -> 421 bytes .../android/mipmap-xxhdpi/ic_launcher.png | Bin 0 -> 431 bytes .../mipmap-xxhdpi/ic_launcher_foreground.png | Bin 0 -> 903 bytes .../mipmap-xxhdpi/ic_launcher_round.png | Bin 0 -> 680 bytes .../android/mipmap-xxxhdpi/ic_launcher.png | Bin 0 -> 572 bytes .../mipmap-xxxhdpi/ic_launcher_foreground.png | Bin 0 -> 1357 bytes .../mipmap-xxxhdpi/ic_launcher_round.png | Bin 0 -> 911 bytes .../android/values/ic_launcher_background.xml | 4 + src-tauri/icons/icon.icns | Bin 0 -> 12672 bytes src-tauri/icons/icon.ico | Bin 0 -> 1965 bytes src-tauri/icons/icon.png | Bin 0 -> 1817 bytes src-tauri/icons/ios/AppIcon-20x20@1x.png | Bin 0 -> 91 bytes src-tauri/icons/ios/AppIcon-20x20@2x-1.png | Bin 0 -> 117 bytes src-tauri/icons/ios/AppIcon-20x20@2x.png | Bin 0 -> 117 bytes src-tauri/icons/ios/AppIcon-20x20@3x.png | Bin 0 -> 147 bytes src-tauri/icons/ios/AppIcon-29x29@1x.png | Bin 0 -> 105 bytes src-tauri/icons/ios/AppIcon-29x29@2x-1.png | Bin 0 -> 143 bytes src-tauri/icons/ios/AppIcon-29x29@2x.png | Bin 0 -> 143 bytes src-tauri/icons/ios/AppIcon-29x29@3x.png | Bin 0 -> 195 bytes src-tauri/icons/ios/AppIcon-40x40@1x.png | Bin 0 -> 117 bytes src-tauri/icons/ios/AppIcon-40x40@2x-1.png | Bin 0 -> 186 bytes src-tauri/icons/ios/AppIcon-40x40@2x.png | Bin 0 -> 186 bytes src-tauri/icons/ios/AppIcon-40x40@3x.png | Bin 0 -> 264 bytes src-tauri/icons/ios/AppIcon-512@2x.png | Bin 0 -> 5696 bytes src-tauri/icons/ios/AppIcon-60x60@2x.png | Bin 0 -> 264 bytes src-tauri/icons/ios/AppIcon-60x60@3x.png | Bin 0 -> 420 bytes src-tauri/icons/ios/AppIcon-76x76@1x.png | Bin 0 -> 180 bytes src-tauri/icons/ios/AppIcon-76x76@2x.png | Bin 0 -> 353 bytes src-tauri/icons/ios/AppIcon-83.5x83.5@2x.png | Bin 0 -> 389 bytes src-tauri/src/lib.rs | 8 + src-tauri/src/main.rs | 5 + src-tauri/tauri.conf.json | 56 + src/App.tsx | 48 +- src/ai/browserTransport.ts | 2 + src/board/sheetFile.ts | 181 + src/board/sheetTransfer.ts | 63 + src/components/Toolbar.tsx | 5 +- src/components/TopBar.tsx | 29 +- src/input/Composer.tsx | 2 +- src/lib/asset.ts | 19 + src/math/scene.ts | 2 +- src/ocr/comer/web.ts | 9 +- src/plot/PlotButton.tsx | 4 +- src/version.ts | 3 + vite.config.ts | 14 +- 91 files changed, 5911 insertions(+), 21 deletions(-) create mode 100644 .github/workflows/package-ios.yml create mode 100644 .github/workflows/package.yml create mode 100644 packaging/icon-source.png create mode 100644 packaging/icon-source.svg create mode 100644 rust-toolchain.toml create mode 100644 scripts/android-release-signing.mjs create mode 100644 scripts/checksum-artifacts.mjs create mode 100644 scripts/compact-debug-apk.py create mode 100644 scripts/make-icon.mjs create mode 100644 scripts/pack-smoke.ts create mode 100755 scripts/package-android.sh create mode 100755 scripts/package-ios.sh create mode 100755 scripts/package-windows.sh create mode 100644 scripts/verify-packaged-dist.mjs create mode 100644 src-tauri/Cargo.lock create mode 100644 src-tauri/Cargo.toml create mode 100644 src-tauri/build.rs create mode 100644 src-tauri/capabilities/default.json create mode 100644 src-tauri/icons/128x128.png create mode 100644 src-tauri/icons/128x128@2x.png create mode 100644 src-tauri/icons/32x32.png create mode 100644 src-tauri/icons/64x64.png create mode 100644 src-tauri/icons/Square107x107Logo.png create mode 100644 src-tauri/icons/Square142x142Logo.png create mode 100644 src-tauri/icons/Square150x150Logo.png create mode 100644 src-tauri/icons/Square284x284Logo.png create mode 100644 src-tauri/icons/Square30x30Logo.png create mode 100644 src-tauri/icons/Square310x310Logo.png create mode 100644 src-tauri/icons/Square44x44Logo.png create mode 100644 src-tauri/icons/Square71x71Logo.png create mode 100644 src-tauri/icons/Square89x89Logo.png create mode 100644 src-tauri/icons/StoreLogo.png create mode 100644 src-tauri/icons/android/mipmap-anydpi-v26/ic_launcher.xml create mode 100644 src-tauri/icons/android/mipmap-hdpi/ic_launcher.png create mode 100644 src-tauri/icons/android/mipmap-hdpi/ic_launcher_foreground.png create mode 100644 src-tauri/icons/android/mipmap-hdpi/ic_launcher_round.png create mode 100644 src-tauri/icons/android/mipmap-mdpi/ic_launcher.png create mode 100644 src-tauri/icons/android/mipmap-mdpi/ic_launcher_foreground.png create mode 100644 src-tauri/icons/android/mipmap-mdpi/ic_launcher_round.png create mode 100644 src-tauri/icons/android/mipmap-xhdpi/ic_launcher.png create mode 100644 src-tauri/icons/android/mipmap-xhdpi/ic_launcher_foreground.png create mode 100644 src-tauri/icons/android/mipmap-xhdpi/ic_launcher_round.png create mode 100644 src-tauri/icons/android/mipmap-xxhdpi/ic_launcher.png create mode 100644 src-tauri/icons/android/mipmap-xxhdpi/ic_launcher_foreground.png create mode 100644 src-tauri/icons/android/mipmap-xxhdpi/ic_launcher_round.png create mode 100644 src-tauri/icons/android/mipmap-xxxhdpi/ic_launcher.png create mode 100644 src-tauri/icons/android/mipmap-xxxhdpi/ic_launcher_foreground.png create mode 100644 src-tauri/icons/android/mipmap-xxxhdpi/ic_launcher_round.png create mode 100644 src-tauri/icons/android/values/ic_launcher_background.xml create mode 100644 src-tauri/icons/icon.icns create mode 100644 src-tauri/icons/icon.ico create mode 100644 src-tauri/icons/icon.png create mode 100644 src-tauri/icons/ios/AppIcon-20x20@1x.png create mode 100644 src-tauri/icons/ios/AppIcon-20x20@2x-1.png create mode 100644 src-tauri/icons/ios/AppIcon-20x20@2x.png create mode 100644 src-tauri/icons/ios/AppIcon-20x20@3x.png create mode 100644 src-tauri/icons/ios/AppIcon-29x29@1x.png create mode 100644 src-tauri/icons/ios/AppIcon-29x29@2x-1.png create mode 100644 src-tauri/icons/ios/AppIcon-29x29@2x.png create mode 100644 src-tauri/icons/ios/AppIcon-29x29@3x.png create mode 100644 src-tauri/icons/ios/AppIcon-40x40@1x.png create mode 100644 src-tauri/icons/ios/AppIcon-40x40@2x-1.png create mode 100644 src-tauri/icons/ios/AppIcon-40x40@2x.png create mode 100644 src-tauri/icons/ios/AppIcon-40x40@3x.png create mode 100644 src-tauri/icons/ios/AppIcon-512@2x.png create mode 100644 src-tauri/icons/ios/AppIcon-60x60@2x.png create mode 100644 src-tauri/icons/ios/AppIcon-60x60@3x.png create mode 100644 src-tauri/icons/ios/AppIcon-76x76@1x.png create mode 100644 src-tauri/icons/ios/AppIcon-76x76@2x.png create mode 100644 src-tauri/icons/ios/AppIcon-83.5x83.5@2x.png create mode 100644 src-tauri/src/lib.rs create mode 100644 src-tauri/src/main.rs create mode 100644 src-tauri/tauri.conf.json create mode 100644 src/board/sheetFile.ts create mode 100644 src/board/sheetTransfer.ts create mode 100644 src/lib/asset.ts create mode 100644 src/version.ts diff --git a/.github/workflows/package-ios.yml b/.github/workflows/package-ios.yml new file mode 100644 index 0000000..cb0b3e9 --- /dev/null +++ b/.github/workflows/package-ios.yml @@ -0,0 +1,57 @@ +name: package-ios + +# Manual only. A macOS runner is required and this file does not run on push. +on: + workflow_dispatch: + inputs: + target: + description: simulator builds a .app for the iOS Simulator. device exports an IPA only when signing secrets are set. + type: choice + options: + - simulator + - device + default: simulator + +permissions: + contents: read + +jobs: + ios: + runs-on: macos-latest + steps: + - uses: actions/checkout@v4 + - uses: dtolnay/rust-toolchain@stable + with: + toolchain: 1.90.0 + targets: aarch64-apple-ios,aarch64-apple-ios-sim,x86_64-apple-ios + - uses: actions/setup-node@v4 + with: + node-version: 22 + cache: npm + - uses: Swatinem/rust-cache@v2 + with: + workspaces: src-tauri + - name: CocoaPods + run: brew install cocoapods + - run: npm ci + - name: Simulator app + if: inputs.target == 'simulator' + run: bash scripts/package-ios.sh --simulator + - name: Signed IPA + if: inputs.target == 'device' + env: + IOS_CERTIFICATE: ${{ secrets.IOS_CERTIFICATE }} + IOS_CERTIFICATE_PASSWORD: ${{ secrets.IOS_CERTIFICATE_PASSWORD }} + IOS_MOBILE_PROVISION: ${{ secrets.IOS_MOBILE_PROVISION }} + APPLE_API_ISSUER: ${{ secrets.APPLE_API_ISSUER }} + APPLE_API_KEY: ${{ secrets.APPLE_API_KEY }} + APPLE_API_KEY_PATH: ${{ secrets.APPLE_API_KEY_PATH }} + run: bash scripts/package-ios.sh --device + - uses: actions/upload-artifact@v4 + if: always() && hashFiles('packaging/out/**') != '' + with: + name: mathscrap-ios + path: | + packaging/out/* + src-tauri/gen/apple/**/*.app + if-no-files-found: warn diff --git a/.github/workflows/package.yml b/.github/workflows/package.yml new file mode 100644 index 0000000..bede967 --- /dev/null +++ b/.github/workflows/package.yml @@ -0,0 +1,125 @@ +name: package + +on: + push: + branches: + - cursor/mathscrap-packaging-* + workflow_dispatch: + inputs: + sign_windows: + description: Import WINDOWS_CERTIFICATE and sign the EXE + type: boolean + default: false + sign_android: + description: Sign the release APK with ANDROID_KEY_* + type: boolean + default: false + +permissions: + contents: read + +concurrency: + group: package-${{ github.ref }} + cancel-in-progress: true + +jobs: + web: + runs-on: ubuntu-latest + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-node@v4 + with: + node-version: 22 + cache: npm + - run: npm ci + - run: npm run test:pack + - run: npm run pack:web + - uses: actions/upload-artifact@v4 + with: + name: mathscrap-web-dist + path: dist + if-no-files-found: error + + android: + runs-on: ubuntu-latest + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-java@v4 + with: + distribution: temurin + java-version: 17 + - uses: dtolnay/rust-toolchain@stable + with: + toolchain: 1.90.0 + targets: aarch64-linux-android,armv7-linux-androideabi,i686-linux-android,x86_64-linux-android + - uses: actions/setup-node@v4 + with: + node-version: 22 + cache: npm + - uses: Swatinem/rust-cache@v2 + with: + workspaces: src-tauri + - run: npm ci + - name: Debug APK + if: github.event_name != 'workflow_dispatch' || inputs.sign_android == false + run: bash scripts/package-android.sh --debug --install-sdk + - name: Release APK + if: github.event_name == 'workflow_dispatch' && inputs.sign_android + env: + ANDROID_KEY_ALIAS: ${{ secrets.ANDROID_KEY_ALIAS }} + ANDROID_KEY_PASSWORD: ${{ secrets.ANDROID_KEY_PASSWORD }} + ANDROID_KEY_BASE64: ${{ secrets.ANDROID_KEY_BASE64 }} + run: bash scripts/package-android.sh --release --install-sdk + - uses: actions/upload-artifact@v4 + with: + name: mathscrap-android + path: | + packaging/out/*.apk + packaging/out/SHA256SUMS + if-no-files-found: error + + windows: + runs-on: windows-latest + steps: + - uses: actions/checkout@v4 + - uses: dtolnay/rust-toolchain@stable + with: + toolchain: 1.90.0 + - uses: actions/setup-node@v4 + with: + node-version: 22 + cache: npm + - uses: Swatinem/rust-cache@v2 + with: + workspaces: src-tauri + - run: npm ci + - name: Import Authenticode certificate + if: github.event_name == 'workflow_dispatch' && inputs.sign_windows + shell: pwsh + env: + WINDOWS_CERTIFICATE: ${{ secrets.WINDOWS_CERTIFICATE }} + WINDOWS_CERTIFICATE_PASSWORD: ${{ secrets.WINDOWS_CERTIFICATE_PASSWORD }} + run: | + if ([string]::IsNullOrEmpty($env:WINDOWS_CERTIFICATE) -or [string]::IsNullOrEmpty($env:WINDOWS_CERTIFICATE_PASSWORD)) { + Write-Error "sign_windows was set but WINDOWS_CERTIFICATE or WINDOWS_CERTIFICATE_PASSWORD is empty." + exit 1 + } + New-Item -ItemType Directory -Force -Path certificate | Out-Null + Set-Content -Path certificate/tempCert.txt -Value $env:WINDOWS_CERTIFICATE + certutil -decode certificate/tempCert.txt certificate/certificate.pfx | Out-Null + Remove-Item certificate/tempCert.txt + $secure = ConvertTo-SecureString -String $env:WINDOWS_CERTIFICATE_PASSWORD -Force -AsPlainText + $imported = Import-PfxCertificate -FilePath certificate/certificate.pfx -CertStoreLocation Cert:\CurrentUser\My -Password $secure + "WINDOWS_CERTIFICATE_THUMBPRINT=$($imported.Thumbprint)" | Out-File -FilePath $env:GITHUB_ENV -Append -Encoding utf8 + Remove-Item -Recurse -Force certificate + - name: Unsigned or signed installer + shell: bash + run: bash scripts/package-windows.sh + - uses: actions/upload-artifact@v4 + with: + name: mathscrap-windows + path: | + packaging/out/*.exe + packaging/out/*.msi + packaging/out/SHA256SUMS + if-no-files-found: error diff --git a/.gitignore b/.gitignore index 523d259..e261fd1 100644 --- a/.gitignore +++ b/.gitignore @@ -34,3 +34,15 @@ ASTER_BG_TASK.md edge-mathscrap.png screen-check.png +# native shells (generated) and local package output +src-tauri/target +src-tauri/gen +packaging/out + +# signing material — never commit +*.keystore +*.jks +*.p12 +*.mobileprovision +keystore.properties + diff --git a/README.md b/README.md index 6619fe7..d228460 100644 --- a/README.md +++ b/README.md @@ -358,7 +358,7 @@ recognizeStrokes(strokes, encoder, decoder, vocab) → { text, latex, confidence 出处和 Apache-2.0 说明在 `public/models/comer/NOTICE.md` 与同目录的 `LICENSE`。预处理和 ink-on 一致:大约每 3px 重采样,黑底白字,内容缩放到大约 128px 高,放在高 256、宽为 64 的倍数(128–1024)的左上角。 -WASM 运行时不进 git。`npm install` 之后,开发服务器和 `vite preview` 从 `node_modules/onnxruntime-web/dist` 提供 `/ort/ort-wasm-simd-threaded.wasm`(约 12 MB)和对应的 `.mjs`。线程数设为 1,所以不需要跨域隔离。 +WASM 运行时不进 git。`npm install` 之后,开发服务器和 `vite preview` 从 `node_modules/onnxruntime-web/dist` 提供 `/ort/ort-wasm-simd-threaded.wasm` 和对应的 `.mjs`。`npm run build` 把同一批文件复制进 `dist/ort/`,安装包读的是这份副本,不再去 `node_modules`,也不打开 Vite。线程数设为 1,所以不需要跨域隔离。 ### 以后接到原生 ONNX Runtime @@ -403,7 +403,30 @@ scripts/e2e-plots.ts 浏览器:每个用例的图都真的画出来 scripts/e2e-sheet.ts 浏览器:在纸上写多个式子 → 同一个坐标系 ``` -纸面内容自动保存在 localStorage(`mathscrap.doc.v2`)里,第一次打开是空白纸。旧版本(`v1`)的卡片页不会自动迁移,原数据仍留在浏览器里。「清空这页」可以撤销。 +纸面内容自动保存在 localStorage(`mathscrap.doc.v2`)里,第一次打开是空白纸。桌面外壳和手机 WebView 各自把这份 localStorage 留在应用数据目录里。右上角菜单的「导出这一页 / 导入一页」读写 `mathscrap.sheet` JSON:只保留笔迹、式子和字条里的字符串和数字,不执行文件内容。旧版本(`v1`)的卡片页不会自动迁移,原数据仍留在浏览器里。「清空这页」和导入都可以撤销。 + +--- + +## 安装包 + +数学和手写识别仍走页面里的 Rust/WASM 与 CoMER ONNX。外壳是 [Tauri 2](https://v2.tauri.app/):它把 `dist/` 打进系统 WebView,不换成云端 OCR,也不在安装后去连 Vite 或公共 CDN。仓库里没有 MathScrap 标志,安装图标用的是纸面已有的牛皮色 `#c9a473`,不用 Vite 模板里的 `public/favicon.svg`。 + +| 命令 | 在哪台机器上 | 得到什么 | +| --- | --- | --- | +| `npm run pack:web` | 任何装了 Node 的机器 | `dist/`。这是被打进外壳的页面,不是安装包。 | +| `npm run pack:windows` | Windows 10 1803+,已装 WebView2、VS C++ 生成工具、Rust 1.90、Node | `packaging/out/` 里的 NSIS 安装程序和 `MathScrap.exe`。默认不签名,SmartScreen 会提示。 | +| `npm run pack:android` | Linux、macOS 或 Windows,JDK 17+、Android SDK、NDK、Rust Android 目标 | debug 签名的 APK,可以用 `adb install` 装到手机。不是 Play 商店包。 | +| `npm run pack:ios` | 只有 macOS + 完整 Xcode | 见下。 | + +版本号在 `package.json`、`src/version.ts` 和 `src-tauri/tauri.conf.json`,目前是 `0.1.0`。`npm run test:pack` 会核对这三处。 + +Windows 安装程序不附带 WebView2 下载器。Windows 11 和 2018 年之后更新过的 Windows 10 已经带有这个运行时。可选的代码签名只认环境变量 `WINDOWS_CERTIFICATE`(pfx 的 base64)和 `WINDOWS_CERTIFICATE_PASSWORD`,脚本不打印它们的值,也不在仓库里放证书。 + +Android 调试包由 SDK 的 debug keystore 签名,可以侧载,不能当作正式版。正式签名要已有的 keystore,变量名是 `ANDROID_KEY_ALIAS`、`ANDROID_KEY_PASSWORD`、`ANDROID_KEY_BASE64`。脚本不会自己生成 keystore。外壳编译需要 Rust 1.90(仓库根目录的 `rust-toolchain.toml`)。数学核心的测试也可以用这一版。 + +iOS 在非 Mac 上直接退出,不会造出一个 ipa 文件。模拟器产物是 `.app`,不能装到 iPhone。能装到别人手机上的 IPA 需要付费的 Apple Developer 证书和描述文件,变量名是 `IOS_CERTIFICATE`、`IOS_CERTIFICATE_PASSWORD`、`IOS_MOBILE_PROVISION`(或 `APPLE_API_ISSUER`、`APPLE_API_KEY`、`APPLE_API_KEY_PATH`)。最低系统是 iOS 16.4。本仓库不注册开发者账号,也不上传 TestFlight 或 App Store。 + +GitHub Actions:`.github/workflows/package.yml` 在打包分支上构建网页、debug APK 和未签名的 Windows 安装程序。`.github/workflows/package-ios.yml` 只在手动启动时使用 macOS runner。签名只在手动启动并且上面的 secrets 已配置时发生。这些 workflow 不创建 GitHub Release。 --- diff --git a/index.html b/index.html index 97d93c4..98e803b 100644 --- a/index.html +++ b/index.html @@ -3,7 +3,8 @@ - + + MathScrap diff --git a/package-lock.json b/package-lock.json index 1e9abaa..f555e0d 100644 --- a/package-lock.json +++ b/package-lock.json @@ -1,12 +1,12 @@ { "name": "mathscrap", - "version": "0.0.0", + "version": "0.1.0", "lockfileVersion": 3, "requires": true, "packages": { "": { "name": "mathscrap", - "version": "0.0.0", + "version": "0.1.0", "license": "Apache-2.0", "dependencies": { "@base-ui/react": "^1.9.0", @@ -14,6 +14,9 @@ "@fontsource/caveat": "^5.3.0", "@modelcontextprotocol/sdk": "^1.32.2", "@tailwindcss/vite": "^4.3.3", + "@tauri-apps/api": "2.12.4", + "@tauri-apps/plugin-dialog": "2.8.4", + "@tauri-apps/plugin-fs": "2.7.1", "class-variance-authority": "^0.7.1", "cn": "^0.5.1", "katex": "^0.19.1", @@ -29,6 +32,7 @@ "tw-animate-css": "^1.4.0" }, "devDependencies": { + "@tauri-apps/cli": "2.12.4", "@types/katex": "^0.16.8", "@types/node": "^24.19.2", "@types/plotly.js-dist-min": "^2.3.4", @@ -2553,6 +2557,251 @@ "vite": "^5.2.0 || ^6 || ^7 || ^8" } }, + "node_modules/@tauri-apps/api": { + "version": "2.12.4", + "resolved": "https://registry.npmjs.org/@tauri-apps/api/-/api-2.12.4.tgz", + "integrity": 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"sha512-4TBVjpi/q8PuNzjpkAc2iBGXMTLjOrAyfTiiOL8ORaJCZJRG3tjzmQ4sqs2CMG75FvLyRkOkERfP7AyY4iBNwQ==", + "license": "MIT OR Apache-2.0", + "dependencies": { + "@tauri-apps/api": "^2.12.0" + } + }, "node_modules/@ts-morph/common": { "version": "0.27.0", "resolved": "https://registry.npmjs.org/@ts-morph/common/-/common-0.27.0.tgz", diff --git a/package.json b/package.json index 36b4380..b98cb77 100644 --- a/package.json +++ b/package.json @@ -1,13 +1,20 @@ { "name": "mathscrap", "private": true, - "version": "0.0.0", + "version": "0.1.0", "type": "module", "scripts": { "dev": "vite", "build": "tsc -b && vite build", "lint": "oxlint", "preview": "vite preview", + "test:pack": "tsx scripts/pack-smoke.ts", + "pack:web": "tsc -b && vite build && node scripts/verify-packaged-dist.mjs", + "pack:desktop": "tauri build", + "pack:windows": "bash scripts/package-windows.sh", + "pack:android": "bash scripts/package-android.sh", + "pack:ios": "bash scripts/package-ios.sh", + "tauri": "tauri", "build:wasm": "cd crates/mathcore && wasm-pack build --target web --release --out-dir ../../src/wasm/pkg --out-name mathcore && rm -f ../../src/wasm/pkg/.gitignore", "test:rust": "cd crates/mathcore && cargo test", "smoke": "tsx scripts/smoke.ts", @@ -19,6 +26,9 @@ "e2e:sheet": "tsx scripts/e2e-sheet.ts" }, "dependencies": { + "@tauri-apps/api": "2.12.4", + "@tauri-apps/plugin-dialog": "2.8.4", + "@tauri-apps/plugin-fs": "2.7.1", "@base-ui/react": "^1.9.0", "@fontsource-variable/geist": "^5.3.0", "@fontsource/caveat": "^5.3.0", @@ -39,6 +49,7 @@ "tw-animate-css": "^1.4.0" }, "devDependencies": { + "@tauri-apps/cli": "2.12.4", "@types/katex": "^0.16.8", "@types/node": "^24.19.2", "@types/plotly.js-dist-min": "^2.3.4", diff --git a/packaging/icon-source.png b/packaging/icon-source.png new file mode 100644 index 0000000000000000000000000000000000000000..2977800e9c55f36de4adcb09205e6ce103c92155 GIT binary patch literal 5873 zcmeAS@N?(olHy`uVBq!ia0y~yU;#2&7&zE~RK2WrGXsN&n5T^H1*1j5Xi+d)6aYhDv?v%Y3Py{9(V}3qC>R|p z7#%qo9Y-46qiPS>Wsj>fFfdI6jS%MZ^LYS^Edd7C|L)(FuT+CFZ~=I*?;Ut#a4%?N xa0hr~@H=Q^@Buh|-vN(>jVc}u4XURNUgxb`_x&=K-2^5!22WQ%mvv4FO#okWsGtA< literal 0 HcmV?d00001 diff --git a/packaging/icon-source.svg b/packaging/icon-source.svg new file mode 100644 index 0000000..370d252 --- /dev/null +++ b/packaging/icon-source.svg @@ -0,0 +1,3 @@ + + + diff --git a/rust-toolchain.toml b/rust-toolchain.toml new file mode 100644 index 0000000..c3891f0 --- /dev/null +++ b/rust-toolchain.toml @@ -0,0 +1,3 @@ +[toolchain] +channel = "1.90.0" +profile = "minimal" diff --git a/scripts/android-release-signing.mjs b/scripts/android-release-signing.mjs new file mode 100644 index 0000000..4f304f0 --- /dev/null +++ b/scripts/android-release-signing.mjs @@ -0,0 +1,62 @@ +/** + * Write keystore.properties from ANDROID_KEY_* and point the generated Gradle + * release build at it. Does not create a keystore. Prints no secret values. + */ +import { existsSync, readFileSync, writeFileSync } from 'node:fs' +import path from 'node:path' + +const alias = process.env.ANDROID_KEY_ALIAS ?? '' +const password = process.env.ANDROID_KEY_PASSWORD ?? '' +const b64 = process.env.ANDROID_KEY_BASE64 ?? '' +if (!alias || !password || !b64) { + console.error('ANDROID_KEY_ALIAS, ANDROID_KEY_PASSWORD, and ANDROID_KEY_BASE64 are required.') + process.exit(2) +} + +const root = process.cwd() +const gen = path.join(root, 'src-tauri/gen/android') +const keystore = path.join(gen, 'upload-keystore.jks') +writeFileSync(keystore, Buffer.from(b64, 'base64'), { mode: 0o600 }) +writeFileSync( + path.join(gen, 'keystore.properties'), + `keyAlias=${alias}\npassword=${password}\nstoreFile=${keystore.replace(/\\/g, '/')}\n`, + { mode: 0o600 }, +) + +const gradle = path.join(gen, 'app/build.gradle.kts') +if (!existsSync(gradle)) { + console.error('Missing app/build.gradle.kts. Run tauri android init first.') + process.exit(1) +} +let text = readFileSync(gradle, 'utf8') +if (!text.includes('import java.io.FileInputStream') && !text.includes('java.io.FileInputStream')) { + text = `import java.io.FileInputStream\nimport java.util.Properties\n${text}` +} +if (!text.includes('signingConfigs')) { + const block = ` +signingConfigs { + create("release") { + val keystorePropertiesFile = rootProject.file("keystore.properties") + val keystoreProperties = Properties() + if (keystorePropertiesFile.exists()) { + keystoreProperties.load(FileInputStream(keystorePropertiesFile)) + } + keyAlias = keystoreProperties["keyAlias"] as String + keyPassword = keystoreProperties["password"] as String + storeFile = file(keystoreProperties["storeFile"] as String) + storePassword = keystoreProperties["password"] as String + } +} +` + const at = text.indexOf('buildTypes') + if (at < 0) { + console.error('build.gradle.kts has no buildTypes block; the Tauri Android template changed.') + process.exit(1) + } + text = `${text.slice(0, at)}${block}${text.slice(at)}` +} +if (!text.includes('signingConfig = signingConfigs.getByName("release")') && !text.includes('signingConfig = signingConfigs.getByName("release")')) { + text = text.replace(/getByName\("release"\)\s*\{/, 'getByName("release") {\n signingConfig = signingConfigs.getByName("release")') +} +writeFileSync(gradle, text) +console.log('Android release signing is wired to the supplied keystore. The keystore stays under src-tauri/gen and is gitignored.') diff --git a/scripts/checksum-artifacts.mjs b/scripts/checksum-artifacts.mjs new file mode 100644 index 0000000..28cdd44 --- /dev/null +++ b/scripts/checksum-artifacts.mjs @@ -0,0 +1,16 @@ +import { createHash } from 'node:crypto' +import { readdirSync, readFileSync, statSync, writeFileSync } from 'node:fs' +import path from 'node:path' + +const dir = path.resolve(process.argv[2] ?? 'packaging/out') +const names = readdirSync(dir) + .filter((name) => name !== 'SHA256SUMS') + .filter((name) => statSync(path.join(dir, name)).isFile()) + .sort() +const lines = names.map((name) => { + const file = path.join(dir, name) + const sha = createHash('sha256').update(readFileSync(file)).digest('hex') + return `${sha} ${name}` +}) +writeFileSync(path.join(dir, 'SHA256SUMS'), `${lines.join('\n')}\n`) +console.log(lines.join('\n')) diff --git a/scripts/compact-debug-apk.py b/scripts/compact-debug-apk.py new file mode 100644 index 0000000..eb2487d --- /dev/null +++ b/scripts/compact-debug-apk.py @@ -0,0 +1,21 @@ +"""Rewrite a debug APK without the large alignment padding Gradle sometimes leaves. + +The result is unsigned. The caller zip-aligns it and signs it with the Android +debug keystore. This does not create a release key. +""" +import sys +import zipfile +from pathlib import Path + +src = Path(sys.argv[1]) +dst = Path(sys.argv[2]) +with zipfile.ZipFile(src) as zin, zipfile.ZipFile(dst, "w") as zout: + for info in zin.infolist(): + data = zin.read(info.filename) + out = zipfile.ZipInfo(filename=info.filename, date_time=info.date_time) + if info.filename.endswith(".so"): + out.compress_type = zipfile.ZIP_STORED + else: + out.compress_type = zipfile.ZIP_DEFLATED + zout.writestr(out, data) +print(dst) diff --git a/scripts/make-icon.mjs b/scripts/make-icon.mjs new file mode 100644 index 0000000..ab0bf42 --- /dev/null +++ b/scripts/make-icon.mjs @@ -0,0 +1,20 @@ +/** + * Flat icon in the kraft color already used by `.kraft-page` (#c9a473). + * The repo has no MathScrap logomark. public/favicon.svg is the Vite template + * and is not reused here. + */ +import { PNG } from 'pngjs' +import { createWriteStream } from 'node:fs' +import path from 'node:path' +import { fileURLToPath } from 'node:url' + +const out = path.resolve(path.dirname(fileURLToPath(import.meta.url)), '../packaging/icon-source.png') +const size = 1024 +const png = new PNG({ width: size, height: size }) +for (let i = 0; i < png.data.length; i += 4) { + png.data[i] = 0xc9 + png.data[i + 1] = 0xa4 + png.data[i + 2] = 0x73 + png.data[i + 3] = 255 +} +png.pack().pipe(createWriteStream(out)).on('finish', () => console.log(out)) diff --git a/scripts/pack-smoke.ts b/scripts/pack-smoke.ts new file mode 100644 index 0000000..91e52f8 --- /dev/null +++ b/scripts/pack-smoke.ts @@ -0,0 +1,60 @@ +import { readFileSync } from 'node:fs' +import { assetUrl } from '../src/lib/asset.ts' +import { parseSheet, serializeSheet } from '../src/board/sheetFile.ts' +import { APP_VERSION } from '../src/version.ts' +import type { Doc } from '../src/board/types.ts' + +const pkg = JSON.parse(readFileSync(new URL('../package.json', import.meta.url), 'utf8')) as { version: string } +const tauri = JSON.parse(readFileSync(new URL('../src-tauri/tauri.conf.json', import.meta.url), 'utf8')) as { version: string; productName: string; identifier: string } + +function check(cond: unknown, message: string) { + if (!cond) throw new Error(message) +} + +check(pkg.version === APP_VERSION, `package.json version ${pkg.version} != ${APP_VERSION}`) +check(tauri.version === APP_VERSION, `tauri.conf.json version ${tauri.version} != ${APP_VERSION}`) +check(tauri.productName === 'MathScrap', 'product name must stay MathScrap') +check(tauri.identifier === 'app.mathscrap', `unexpected identifier ${tauri.identifier}`) + +check(assetUrl('models/comer/vocab.json', '/') === '/models/comer/vocab.json', 'absolute base') +check(assetUrl('/ort/', '/') === '/ort/', 'leading slash is stripped once') +check(assetUrl('ort/file.wasm', './') === './ort/file.wasm', 'relative base stays inside the bundle') +check(!assetUrl('models/comer/encoder_int8.onnx', '/').startsWith('http'), 'model URL is not a remote host') + +const doc: Doc = { + strokes: [{ id: 's1', pts: [1, 2, 0.5, 3, 4, 0.4], color: '#2b2118', width: 3, style: 'ink', createdAt: 1 }], + cards: [{ id: 'c1', x: 10, y: 20, text: 'y = x' }], + stickers: [], +} +const raw = serializeSheet(doc) +const back = parseSheet(raw) +check(back.cards[0]?.text === 'y = x' && back.strokes.length === 1, 'round trip') +check(parseSheet(JSON.stringify(doc)).cards[0]?.text === 'y = x', 'plain stored sheet') + +const kept = parseSheet('{"format":"mathscrap.sheet","version":1,"doc":{"strokes":[],"cards":[{"id":"c1","x":1,"y":2,"text":"y = x","__proto__":{"polluted":true}}],"stickers":[]}}') +check(kept.cards[0]?.text === 'y = x', 'extra card fields are not kept') +check(!('polluted' in {}), 'import does not pollute Object.prototype') + +const junk = [ + '{"format":"other","version":1,"doc":{}}', + '{"format":"mathscrap.sheet","version":99,"doc":{"strokes":[],"cards":[],"stickers":[]}}', + '{"strokes":[{"id":"s1","pts":[1,2],"color":"#fff","width":3,"style":"ink","createdAt":1}],"cards":[],"stickers":[]}', + '{"strokes":[{"id":"s1","pts":[1,2,0],"color":"javascript:alert(1)","width":3,"style":"ink","createdAt":1}],"cards":[],"stickers":[]}', + '{"strokes":[],"cards":[{"id":"c1","x":1,"y":2,"text":' + JSON.stringify('x'.repeat(9000)) + '}],"stickers":[]}', + '[]', + '"y = x"', +] +for (const sample of junk) { + let threw = false + try { + parseSheet(sample) + } catch { + threw = true + } + check(threw, `should reject ${sample.slice(0, 60)}`) +} + +const withProto = parseSheet('{"strokes":[],"cards":[{"id":"c1","x":1,"y":2,"text":"y = 1"}],"stickers":[],"__proto__":{"admin":true},"eval":"process.exit(1)"}') +check(withProto.cards.length === 1 && !('eval' in withProto), 'unknown fields are dropped') + +console.log(`pack-smoke ok ${APP_VERSION}`) diff --git a/scripts/package-android.sh b/scripts/package-android.sh new file mode 100755 index 0000000..0c2dc54 --- /dev/null +++ b/scripts/package-android.sh @@ -0,0 +1,136 @@ +#!/usr/bin/env bash +# Android APK. Default is a debug-signed APK (sideload with adb). It is not a Play release. +# Release signing inputs, values never printed: +# ANDROID_KEY_ALIAS ANDROID_KEY_PASSWORD ANDROID_KEY_BASE64 +set -euo pipefail +cd "$(dirname "$0")/.." + +mode="debug" +install_sdk=0 +for arg in "$@"; do + case "$arg" in + --debug) mode="debug" ;; + --release) mode="release" ;; + --install-sdk) install_sdk=1 ;; + *) + echo "Unknown argument: $arg" >&2 + echo "Usage: scripts/package-android.sh [--debug|--release] [--install-sdk]" >&2 + exit 2 + ;; + esac +done + +NDK_VERSION="${ANDROID_NDK_VERSION:-27.2.12479018}" +PLATFORM="${ANDROID_PLATFORM:-android-35}" +BUILD_TOOLS="${ANDROID_BUILD_TOOLS:-35.0.0}" +CMDLINE_URL="${ANDROID_CMDLINE_TOOLS_URL:-https://dl.google.com/android/repository/commandlinetools-linux-13114758_latest.zip}" + +if [[ "$install_sdk" -eq 1 ]]; then + sdk="${ANDROID_HOME:-$HOME/android-sdk}" + mkdir -p "$sdk/cmdline-tools" + if [[ ! -x "$sdk/cmdline-tools/latest/bin/sdkmanager" ]]; then + tmp="$(mktemp)" + curl -fsSL -o "$tmp" "$CMDLINE_URL" + rm -rf "$sdk/cmdline-tools/latest" + unzip -q "$tmp" -d "$sdk/cmdline-tools" + mv "$sdk/cmdline-tools/cmdline-tools" "$sdk/cmdline-tools/latest" + rm -f "$tmp" + fi + export ANDROID_HOME="$sdk" + export ANDROID_SDK_ROOT="$sdk" + yes | "$sdk/cmdline-tools/latest/bin/sdkmanager" --sdk_root="$sdk" --licenses >/dev/null || true + "$sdk/cmdline-tools/latest/bin/sdkmanager" --sdk_root="$sdk" "platform-tools" "platforms;${PLATFORM}" "build-tools;${BUILD_TOOLS}" "ndk;${NDK_VERSION}" +fi + +missing=0 +if ! command -v java >/dev/null 2>&1; then + echo "JDK 17 or newer is not on PATH." + missing=1 +fi +if [[ -z "${ANDROID_HOME:-}${ANDROID_SDK_ROOT:-}" && -d "$HOME/android-sdk" ]]; then + export ANDROID_HOME="$HOME/android-sdk" + export ANDROID_SDK_ROOT="$HOME/android-sdk" +fi +if [[ -z "${ANDROID_HOME:-}${ANDROID_SDK_ROOT:-}" ]]; then + echo "ANDROID_HOME is unset. Re-run with --install-sdk or point it at an Android SDK." + missing=1 +else + export ANDROID_HOME="${ANDROID_HOME:-$ANDROID_SDK_ROOT}" + export ANDROID_SDK_ROOT="${ANDROID_SDK_ROOT:-$ANDROID_HOME}" +fi +if [[ -z "${NDK_HOME:-}" && -n "${ANDROID_HOME:-}" && -d "${ANDROID_HOME}/ndk/${NDK_VERSION}" ]]; then + export NDK_HOME="${ANDROID_HOME}/ndk/${NDK_VERSION}" +fi +if [[ -z "${NDK_HOME:-}" || ! -d "${NDK_HOME}" ]]; then + echo "NDK_HOME is unset. Expected ${ANDROID_HOME:-ANDROID_HOME}/ndk/${NDK_VERSION}." + missing=1 +fi +( + cd src-tauri + rustup show active-toolchain >/dev/null + rustup target add aarch64-linux-android armv7-linux-androideabi i686-linux-android x86_64-linux-android +) +if [[ "$missing" -ne 0 ]]; then + echo "Android prerequisites are incomplete. No APK was produced." + exit 3 +fi + +version="$(node -p "require('./package.json').version")" +if [[ ! -d src-tauri/gen/android ]]; then + npx tauri android init --ci +fi + +mkdir -p packaging/out +if [[ "$mode" == "release" ]]; then + if [[ -z "${ANDROID_KEY_ALIAS:-}" || -z "${ANDROID_KEY_PASSWORD:-}" || -z "${ANDROID_KEY_BASE64:-}" ]]; then + echo "Release APK needs ANDROID_KEY_ALIAS, ANDROID_KEY_PASSWORD, and ANDROID_KEY_BASE64." >&2 + echo "This script does not generate a keystore. No release APK was produced." >&2 + exit 2 + fi + node scripts/android-release-signing.mjs + npx tauri android build --apk --target aarch64 --split-per-abi --ci + label="release-signed" +else + # Keep the debug APK installable without embedding full Rust debuginfo. + # The signature is still the Android debug keystore, not a Play release key. + CARGO_PROFILE_DEV_DEBUG=0 CARGO_PROFILE_DEV_STRIP=symbols \ + npx tauri android build --debug --apk --target aarch64 --split-per-abi --ci + label="debug-signed" +fi + +copied=0 +while IFS= read -r file; do + kind="$(basename "$(dirname "$file")")" + abi="$(basename "$(dirname "$(dirname "$file")")")" + if [[ "$kind" != debug && "$kind" != release ]]; then + abi="$kind" + fi + dest="packaging/out/MathScrap-${version}-android-${abi}-${label}.apk" + cp "$file" "$dest" + echo "artifact $dest" + copied=1 +done < <(find src-tauri/gen/android -type f -name '*.apk' ! -name '*-unsigned.apk' | sort) +if [[ "$mode" == "debug" && -f "$HOME/.android/debug.keystore" ]]; then + tools="$(find "$ANDROID_HOME/build-tools" -mindepth 1 -maxdepth 1 -type d | sort | tail -1)" + for apk in packaging/out/MathScrap-"${version}"-android-*-debug-signed.apk; do + [[ -f "$apk" ]] || continue + tmp="${apk}.unaligned" + python3 scripts/compact-debug-apk.py "$apk" "$tmp" + "$tools/zipalign" -f -p 4 "$tmp" "${apk}.aligned" + "$tools/apksigner" sign --ks "$HOME/.android/debug.keystore" --ks-pass pass:android --key-pass pass:android --ks-key-alias androiddebugkey "${apk}.aligned" + mv "${apk}.aligned" "$apk" + rm -f "$tmp" "${apk}.idsig" + done +fi +if [[ "$copied" -ne 1 ]]; then + echo "The Android build finished but no APK was found." >&2 + exit 1 +fi +node scripts/checksum-artifacts.mjs packaging/out +if [[ "$label" == "debug-signed" ]]; then + echo "This APK is signed with the Android debug keystore. It can be sideloaded with adb install." + echo "It is not a Play Store release and the debug certificate is not a production key." +else + echo "This APK is signed with the keystore supplied through ANDROID_KEY_BASE64." + echo "It was not uploaded to Play." +fi diff --git a/scripts/package-ios.sh b/scripts/package-ios.sh new file mode 100755 index 0000000..4f7a7a2 --- /dev/null +++ b/scripts/package-ios.sh @@ -0,0 +1,112 @@ +#!/usr/bin/env bash +# iOS Simulator .app, or a signed IPA when Apple signing inputs are present. +# This script never enrolls in the Apple Developer Program and never creates a certificate. +set -euo pipefail +cd "$(dirname "$0")/.." + +target="simulator" +for arg in "$@"; do + case "$arg" in + --simulator) target="simulator" ;; + --device) target="device" ;; + *) + echo "Unknown argument: $arg" >&2 + echo "Usage: scripts/package-ios.sh [--simulator|--device]" >&2 + exit 2 + ;; + esac +done + +if [[ "$(uname -s)" != "Darwin" ]]; then + cat <<'EOF' +This machine is not macOS. No IPA and no iOS Simulator build were produced. + +An installable iPhone package needs all of the following, which are not on this Linux builder: + +1. A Mac with macOS 12 or newer. +2. Full Xcode 15 or newer (the App Store app, not only Command Line Tools). + Open Xcode once, then: sudo xcodebuild -license accept + xcode-select -s /Applications/Xcode.app/Contents/Developer +3. Rust iOS targets: + rustup target add aarch64-apple-ios aarch64-apple-ios-sim x86_64-apple-ios +4. CocoaPods: brew install cocoapods +5. Node 22 and this repo: npm ci + +What each command actually produces: + +- npm run pack:ios -- --simulator + Runs `tauri ios build --debug` for the Apple silicon simulator. + Output is a .app for the iOS Simulator. It is not an IPA and will not install on an iPhone. + +- A development install on your own phone uses a free Apple ID added in + Xcode > Settings > Accounts, with automatic signing on Personal Team. + That signature lasts about 7 days and is not a distributable IPA. + This repository does not collect that Apple ID. + +- A distributable IPA (Ad Hoc, TestFlight, or App Store) needs the paid + Apple Developer Program, which this task does not enroll in or purchase. + When you already have the certificate and profile, put only these names + in the CI environment or your shell. Do not commit the values: + IOS_CERTIFICATE base64 of the .p12 exported from Keychain + IOS_CERTIFICATE_PASSWORD + IOS_MOBILE_PROVISION base64 of the .mobileprovision + Optional automatic signing instead of the three above: + APPLE_API_ISSUER + APPLE_API_KEY + APPLE_API_KEY_PATH path to the AuthKey .p8 already on that Mac + Then: npm run pack:ios -- --device + +Minimum OS for the packaged shell is iOS 16.4 (WebAssembly SIMD for CoMER). +The bundle id is app.mathscrap. It must match the App ID inside the profile. +EOF + exit 3 +fi + +if ! command -v xcodebuild >/dev/null 2>&1; then + echo "xcodebuild is missing. Install full Xcode and point xcode-select at it." >&2 + exit 3 +fi +rustup target add aarch64-apple-ios aarch64-apple-ios-sim x86_64-apple-ios +if [[ ! -d src-tauri/gen/apple ]]; then + npx tauri ios init --ci +fi + +version="$(node -p "require('./package.json').version")" +mkdir -p packaging/out + +if [[ "$target" == "simulator" ]]; then + npx tauri ios build --debug --target aarch64-sim --ci + echo "Simulator build finished. Search src-tauri/gen/apple for the .app." + echo "This is not an IPA and is not installable on an iPhone." + find src-tauri/gen/apple -name '*.app' -type d | head -20 + exit 0 +fi + +signed=0 +if [[ -n "${IOS_CERTIFICATE:-}" && -n "${IOS_CERTIFICATE_PASSWORD:-}" && -n "${IOS_MOBILE_PROVISION:-}" ]]; then + signed=1 +elif [[ -n "${APPLE_API_ISSUER:-}" && -n "${APPLE_API_KEY:-}" && -n "${APPLE_API_KEY_PATH:-}" ]]; then + signed=1 +fi +if [[ "$signed" -ne 1 ]]; then + echo "Refusing to export an IPA. Signing inputs are absent, so the result would not be an installable device package." >&2 + echo "See the prerequisite list printed on a non-Mac run of this script." >&2 + exit 2 +fi + +method="${IOS_EXPORT_METHOD:-release-testing}" +case "$method" in + app-store-connect|release-testing|debugging) ;; + *) + echo "IOS_EXPORT_METHOD must be app-store-connect, release-testing, or debugging." >&2 + exit 2 + ;; +esac +npx tauri ios build --export-method "$method" --ci +while IFS= read -r file; do + dest="packaging/out/MathScrap-${version}-ios-$(basename "$file")" + cp "$file" "$dest" + echo "artifact $dest" +done < <(find src-tauri/gen/apple -type f -name '*.ipa' | sort) +node scripts/checksum-artifacts.mjs packaging/out +echo "If an IPA was copied above, it was signed with the provided profile. It was not uploaded to App Store Connect or TestFlight." diff --git a/scripts/package-windows.sh b/scripts/package-windows.sh new file mode 100755 index 0000000..1281b05 --- /dev/null +++ b/scripts/package-windows.sh @@ -0,0 +1,49 @@ +#!/usr/bin/env bash +# Unsigned Windows NSIS installer and MathScrap.exe, built on Windows. +# Optional Authenticode inputs (never printed): WINDOWS_CERTIFICATE, WINDOWS_CERTIFICATE_PASSWORD. +# When those are imported into the runner certificate store, also set WINDOWS_CERTIFICATE_THUMBPRINT. +set -euo pipefail +cd "$(dirname "$0")/.." + +os="$(uname -s)" +case "$os" in + MINGW*|MSYS*|CYGWIN*) ;; + *) + echo "This machine is ${os}. A Windows EXE was not built here." + echo "Build on Windows with: npm run pack:windows" + echo "CI job: package.yml / windows, runner windows-latest." + echo "The installer is unsigned unless a manual run imports WINDOWS_CERTIFICATE." + echo "WebView2 must already be on the machine (Windows 11, and Windows 10 from version 1803). This package does not download it." + exit 3 + ;; +esac + +version="$(node -p "require('./package.json').version")" +mkdir -p packaging/out +args=(build --bundles nsis --ci) +if [[ -n "${WINDOWS_CERTIFICATE_THUMBPRINT:-}" ]]; then + args+=(--config "{\"bundle\":{\"windows\":{\"certificateThumbprint\":\"${WINDOWS_CERTIFICATE_THUMBPRINT}\",\"digestAlgorithm\":\"sha256\",\"timestampUrl\":\"http://timestamp.digicert.com\"}}}") + label="signed" +else + label="unsigned" + echo "No WINDOWS_CERTIFICATE_THUMBPRINT. Building an unsigned installer. Windows SmartScreen will warn." +fi + +npx tauri "${args[@]}" + +copied=0 +while IFS= read -r file; do + base="$(basename "$file")" + dest="packaging/out/MathScrap-${version}-windows-x64-${label}-${base}" + cp "$file" "$dest" + echo "artifact $dest" + copied=1 +done < <(find src-tauri/target/release/bundle/nsis src-tauri/target/release -maxdepth 3 -type f \( -name '*.exe' -o -name '*.msi' \) 2>/dev/null || true) +if [[ "$copied" -ne 1 ]]; then + echo "tauri build finished but no EXE was found." >&2 + exit 1 +fi +node scripts/checksum-artifacts.mjs packaging/out +echo "Windows ${label} package is in packaging/out." +echo "Installable: yes, as an unsigned desktop program, unless label is signed." +echo "Not a Store submission." diff --git a/scripts/verify-packaged-dist.mjs b/scripts/verify-packaged-dist.mjs new file mode 100644 index 0000000..07d3a65 --- /dev/null +++ b/scripts/verify-packaged-dist.mjs @@ -0,0 +1,61 @@ +import { createHash } from 'node:crypto' +import { existsSync, readdirSync, readFileSync, statSync } from 'node:fs' +import path from 'node:path' + +const root = process.cwd() +const dist = path.join(root, 'dist') +const lines = [] + +function fail(message) { + console.error(`verify-packaged-dist: ${message}`) + process.exit(1) +} + +function need(rel, minBytes) { + const file = path.join(dist, rel) + if (!existsSync(file)) fail(`missing ${rel}`) + const size = statSync(file).size + if (size < minBytes) fail(`${rel} is ${size} bytes, expected at least ${minBytes}`) + const sha = createHash('sha256').update(readFileSync(file)).digest('hex') + lines.push(`${sha} ${rel} ${size}`) +} + +if (!existsSync(dist)) fail('dist/ is missing. Run npm run build first. This check does not start Vite.') + +need('index.html', 100) +need('models/comer/encoder_int8.onnx', 1_000_000) +need('models/comer/decoder_int8.onnx', 1_000_000) +need('models/comer/vocab.json', 100) +need('models/comer/LICENSE', 100) +need('models/comer/NOTICE.md', 50) +need('favicon.svg', 50) + +const ortDir = path.join(dist, 'ort') +if (!existsSync(ortDir)) fail('dist/ort is missing. ONNX Runtime WASM was not copied into the bundle.') +const ort = readdirSync(ortDir) +for (const name of ['ort-wasm-simd-threaded.wasm', 'ort-wasm-simd-threaded.mjs']) { + if (!ort.includes(name)) fail(`dist/ort/${name} was not bundled`) + need(path.posix.join('ort', name), name.endsWith('.wasm') ? 1_000_000 : 100) +} +if (!ort.some((name) => name === 'ort-wasm-simd.wasm')) { + console.log('note: ort-wasm-simd.wasm (non-threaded) is not in this onnxruntime-web build; the threaded file is the one the page requests with numThreads = 1') +} + +const assets = path.join(dist, 'assets') +const wasm = existsSync(assets) ? readdirSync(assets).filter((name) => name.endsWith('.wasm')) : [] +if (!wasm.length) fail('mathcore WASM was not emitted under dist/assets') +for (const name of wasm) need(path.posix.join('assets', name), 100_000) + +const html = readFileSync(path.join(dist, 'index.html'), 'utf8') +if (/47321|47322|fonts\.googleapis|cdn\.jsdelivr|unpkg\.com|esm\.sh/.test(html)) 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Packaged shells never call it. + if (!import.meta.env.DEV) return return startBrowserBridge((name, args) => bridge.call(name, args)) }, [bridge]) + const exportPage = useCallback(() => { + void exportSheetFile(docRef.current) + .then((kind) => { + if (kind === 'cancelled') return + toast.success(kind === 'shared' ? '已交给系统分享' : '已导出这一页') + }) + .catch((e: unknown) => toast(e instanceof Error ? e.message : '没能导出')) + }, [docRef]) + + const importPage = useCallback( + async (file: File | undefined) => { + if (!file) return + try { + const next = parseSheet(await readSheetFile(file)) + commit(next) + setSelected(null) + toast.success('已导入这一页', { action: { label: '撤销', onClick: undo } }) + } catch (e) { + toast(e instanceof Error ? e.message : '没能导入') + } + }, + [commit, undo], + ) + const anchor = composer.at ? { left: composer.at.x * view.scale + view.x, top: composer.at.y * view.scale + view.y } : null const showHints = prefs.showHints && composer.open && composerFocused && (!compact || !composerText) const floated = plot.open && !plot.details && !plot.full @@ -458,8 +487,23 @@ export default function App() { onClear={() => setConfirmClear(true)} onSettings={() => setSettingsOpen(true)} onAssist={() => setAssistOpen(true)} + onExport={exportPage} + onImport={() => importRef.current?.click()} onSample={writeSample} /> + { + const file = e.target.files?.[0] + e.target.value = '' + void importPage(file) + }} + /> @@ -470,7 +514,9 @@ export default function App() { data-no-board className={cn( 'absolute z-30 overflow-hidden rounded-2xl opacity-80 shadow-[0_10px_28px_rgba(60,40,20,0.22)]', - compact ? 'right-3 bottom-[calc(132px+env(safe-area-inset-bottom))] h-[200px] w-[min(300px,78vw)]' : 'right-5 bottom-[4.75rem] h-[240px] w-[360px]', + compact + ? 'right-[max(0.75rem,env(safe-area-inset-right))] bottom-[calc(132px+env(safe-area-inset-bottom))] h-[200px] w-[min(300px,78vw)]' + : 'right-[max(1.25rem,env(safe-area-inset-right))] bottom-[max(4.75rem,calc(4.75rem+env(safe-area-inset-bottom)))] h-[240px] w-[360px]', )} > diff --git a/src/ai/browserTransport.ts b/src/ai/browserTransport.ts index 8869b42..7dc65a4 100644 --- a/src/ai/browserTransport.ts +++ b/src/ai/browserTransport.ts @@ -8,6 +8,8 @@ import { directTransport, type AiTransport } from './client' */ export function browserTransport(): AiTransport { const direct = directTransport() + // The packaged shell has no Vite forwarder. Call the address the person typed. + if (import.meta.env.PROD) return direct return { async request(url, init) { try { diff --git a/src/board/sheetFile.ts b/src/board/sheetFile.ts new file mode 100644 index 0000000..de2d0b3 --- /dev/null +++ b/src/board/sheetFile.ts @@ -0,0 +1,181 @@ +import type { Card, Doc, PenStyle, Sticker, Stroke } from './types' + +export const SHEET_FORMAT = 'mathscrap.sheet' +export const SHEET_VERSION = 1 + +const MAX_BYTES = 8_000_000 +const MAX_STROKES = 4_000 +const MAX_CARDS = 2_000 +const MAX_STICKERS = 500 +const MAX_NUMBERS = 2_000_000 +const MAX_TEXT = 8_000 +const MAX_STICKER_TEXT = 400 +const ID = /^[A-Za-z0-9_-]{1,40}$/ +const COLOR = /^#(?:[0-9a-fA-F]{3}|[0-9a-fA-F]{6}|[0-9a-fA-F]{8})$/ +const STYLES = new Set(['ink', 'dashed', 'dotted', 'pencil', 'washi', 'marker']) + +export function serializeSheet(doc: Doc): string { + const body = { + format: SHEET_FORMAT, + version: SHEET_VERSION, + doc: copyDoc(doc), + } + const text = JSON.stringify(body) + if (text.length > MAX_BYTES) throw new Error('这一页太大,没法导出') + return text +} + +/** + * Accept only a MathScrap sheet envelope, or the same `{strokes,cards,stickers}` + * object the page already stores. Fields are copied one by one. Strings stay + * data; nothing in the file is evaluated. + */ +export function parseSheet(raw: string): Doc { + if (raw.length > MAX_BYTES) throw new Error('文件太大') + let parsed: unknown + try { + parsed = JSON.parse(raw) + } catch { + throw new Error('这不是 JSON 文件') + } + const root = record(parsed) + if (!root) throw new Error('文件内容不是一张纸') + if ('format' in root || 'version' in root || 'doc' in root) { + if (root.format !== SHEET_FORMAT) throw new Error('这不是 MathScrap 的纸') + if (root.version !== SHEET_VERSION) throw new Error('这张纸的版本读不了') + return copyDoc(asDoc(root.doc)) + } + return copyDoc(asDoc(root)) +} + +function copyDoc(doc: Doc): Doc { + return { + strokes: doc.strokes.map(copyStroke), + cards: doc.cards.map(copyCard), + stickers: doc.stickers.map(copySticker), + } +} + +function asDoc(value: unknown): Doc { + const src = record(value) + if (!src || !Array.isArray(src.strokes) || !Array.isArray(src.cards)) throw new Error('文件里没有笔迹和式子') + if (src.strokes.length > MAX_STROKES || src.cards.length > MAX_CARDS) throw new Error('这一页的内容太多') + const stickers = src.stickers == null ? [] : src.stickers + if (!Array.isArray(stickers) || stickers.length > MAX_STICKERS) throw new Error('这一页的内容太多') + let numbers = 0 + const strokes = src.strokes.map((item) => { + const stroke = copyStroke(asStroke(item)) + numbers += stroke.pts.length + if (numbers > MAX_NUMBERS) throw new Error('笔迹太长') + return stroke + }) + return { + strokes, + cards: src.cards.map((item) => copyCard(asCard(item))), + stickers: stickers.map((item) => copySticker(asSticker(item))), + } +} + +function asStroke(value: unknown): Stroke { + const src = record(value) + if (!src) throw new Error('有一笔读不出来') + const pts = src.pts + if (!Array.isArray(pts) || pts.length % 3 !== 0) throw new Error('有一笔的点不对') + const style = src.style + if (typeof style !== 'string' || !STYLES.has(style as PenStyle | 'marker')) throw new Error('有一笔的笔触不对') + return { + id: idOf(src.id), + pts: pts.map(num), + color: colorOf(src.color), + width: widthOf(src.width), + style: style as PenStyle | 'marker', + recognized: src.recognized === undefined ? undefined : bool(src.recognized), + createdAt: num(src.createdAt), + } +} + +function copyStroke(stroke: Stroke): Stroke { + const next: Stroke = { + id: idOf(stroke.id), + pts: stroke.pts.map(num), + color: colorOf(stroke.color), + width: widthOf(stroke.width), + style: stroke.style, + createdAt: num(stroke.createdAt), + } + if (!STYLES.has(next.style)) throw new Error('有一笔的笔触不对') + if (next.pts.length % 3 !== 0) throw new Error('有一笔的点不对') + if (stroke.recognized !== undefined) next.recognized = bool(stroke.recognized) + return next +} + +function asCard(value: unknown): Card { + const src = record(value) + if (!src) throw new Error('有一个式子读不出来') + return copyCard({ id: idOf(src.id), x: num(src.x), y: num(src.y), text: textOf(src.text, MAX_TEXT) }) +} + +function copyCard(card: Card): Card { + return { id: idOf(card.id), x: num(card.x), y: num(card.y), text: textOf(card.text, MAX_TEXT) } +} + +function asSticker(value: unknown): Sticker { + const src = record(value) + if (!src) throw new Error('有一张字条读不出来') + return copySticker({ + id: idOf(src.id), + x: num(src.x), + y: num(src.y), + text: textOf(src.text, MAX_STICKER_TEXT), + size: widthOf(src.size), + rot: num(src.rot), + }) +} + +function copySticker(sticker: Sticker): Sticker { + return { + id: idOf(sticker.id), + x: num(sticker.x), + y: num(sticker.y), + text: textOf(sticker.text, MAX_STICKER_TEXT), + size: widthOf(sticker.size), + rot: num(sticker.rot), + } +} + +function record(value: unknown): Record | null { + if (!value || typeof value !== 'object' || Array.isArray(value)) return null + return value as Record +} + +function idOf(value: unknown): string { + if (typeof value !== 'string' || !ID.test(value)) throw new Error('有一条内容的编号不对') + return value +} + +function num(value: unknown): number { + if (typeof value !== 'number' || !Number.isFinite(value)) throw new Error('有一个数字读不出来') + return value +} + +function widthOf(value: unknown): number { + const n = num(value) + if (n <= 0 || n > 256) throw new Error('有一笔太粗或太细') + return n +} + +function colorOf(value: unknown): string { + if (typeof value !== 'string' || !COLOR.test(value)) throw new Error('有一笔的颜色不对') + return value +} + +function textOf(value: unknown, max: number): string { + if (typeof value !== 'string') throw new Error('有一段文字读不出来') + if (value.length > max) throw new Error('有一段文字太长') + return value +} + +function bool(value: unknown): boolean { + if (typeof value !== 'boolean') throw new Error('有一个开关读不出来') + return value +} diff --git a/src/board/sheetTransfer.ts b/src/board/sheetTransfer.ts new file mode 100644 index 0000000..a2d1ede --- /dev/null +++ b/src/board/sheetTransfer.ts @@ -0,0 +1,63 @@ +import { serializeSheet } from './sheetFile' +import type { Doc } from './types' + +function suggestedName(): string { + const now = new Date() + const p = (n: number) => String(n).padStart(2, '0') + return `mathscrap-sheet-${now.getFullYear()}${p(now.getMonth() + 1)}${p(now.getDate())}-${p(now.getHours())}${p(now.getMinutes())}.json` +} + +function inTauri(): boolean { + return typeof window !== 'undefined' && '__TAURI_INTERNALS__' in window +} + +/** Write the sheet to a place the person picks. Falls back to a browser download. */ +export async function exportSheetFile(doc: Doc): Promise<'saved' | 'shared' | 'downloaded' | 'cancelled'> { + const text = serializeSheet(doc) + const name = suggestedName() + if (inTauri()) { + try { + const saved = await saveWithDialog(text, name) + if (saved !== 'unsupported') return saved + } catch { + /* the shell refused the folder; try the other two paths */ + } + } + const file = new File([text], name, { type: 'application/json' }) + if (typeof navigator !== 'undefined' && navigator.canShare?.({ files: [file] })) { + await navigator.share({ files: [file], title: 'MathScrap' }) + return 'shared' + } + downloadBlob(file, name) + return 'downloaded' +} + +async function saveWithDialog(text: string, name: string): Promise<'saved' | 'cancelled' | 'unsupported'> { + const dialog = await import('@tauri-apps/plugin-dialog') + const fs = await import('@tauri-apps/plugin-fs') + if (typeof dialog.save !== 'function' || typeof fs.writeTextFile !== 'function') return 'unsupported' + const path = await dialog.save({ + defaultPath: name, + filters: [{ name: 'MathScrap sheet', extensions: ['json'] }], + }) + if (path == null) return 'cancelled' + await fs.writeTextFile(path, text) + return 'saved' +} + +function downloadBlob(file: File, name: string) { + const url = URL.createObjectURL(file) + const a = document.createElement('a') + a.href = url + a.download = name + a.rel = 'noopener' + document.body.appendChild(a) + a.click() + a.remove() + setTimeout(() => URL.revokeObjectURL(url), 1500) +} + +export async function readSheetFile(file: File): Promise { + if (file.size > 8_000_000) throw new Error('文件太大') + return file.text() +} diff --git a/src/components/Toolbar.tsx b/src/components/Toolbar.tsx index 4dabaed..9259560 100644 --- a/src/components/Toolbar.tsx +++ b/src/components/Toolbar.tsx @@ -97,7 +97,10 @@ export function Toolbar({ tool, setTool, pen, setPen, compact, onRecognize }: Pr const sep =
    return (

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z>Lo^tk5JAv{kFekwCiJqU`FPNB3Upi`&1$L_nAVhUnM`sDm?N+A-E*sr6R=+NpZfy zIxM9bWL$+A5}a-@>32H)k~I*&L%F}tnqs0e#W~)v8A@NFeZu8g4s?I#Ua<@~`-;7n rwaKd&nPkwG-vq)I!K*!)Z0H2r*JBzkUGS<&rWgikep$t1vxNT#61I Date: Mon, 2 Nov 2026 19:24:32 +0800 Subject: [PATCH 100/123] =?UTF-8?q?feat:=20ETC=20X361=E2=80=93X367=20Yff?= =?UTF-8?q?=20isoscelizer=20+=20sqrt-side=20band?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(361)–X(367) (X266-Ceva of I, congruent-circum / equal-perimeter / Wabash equal-area isoscelizers, trilinear√ / √a / crosspoint(I,X366)); document skip of X(368)–X(370) (no closed barycentrics in ETC). --- crates/mathcore/src/geometry.rs | 244 ++++++++++++++++++++++++++++++++ 1 file changed, 244 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 101847e..2d77bbd 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -13247,6 +13247,166 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] // X(359)/X(360) dual-labeled in the Hofstadter block above (Hf_1 / Hf_0). } + // X(361)–X(370): Yff isoscelizer / sqrt-side band (ETC). + // X(361)=X(266)-Ceva conjugate of X(1); bary sin A(csc B/2+csc C/2−csc A/2). + // X(362)=congruent-circumcircles isoscelizer; bary a(b cos B/2+c cos C/2−a cos A/2). + // X(363)=equal-perimeters isoscelizer; bary a(b/(1+sin B/2)+c/(1+sin C/2)−a/(1+sin A/2)). + // X(364)=Wabash=equal-areas isoscelizer; bary a(√b+√c−√a); =X(366)-Ceva conjugate of X(1). + // X(365)=trilinear square-roots; bary a^{3/2}; isogonal of X(366); crosssum(X1,X364). + // X(366)=isogonal(X365); bary √a; cevapoint(X1,X364). + // X(367)=crosspoint(X1,X366); bary a(√b+√c); =crosssum(X1,X365). + // X(368) equi-Brocard / X(369) 1st trisected-perimeter / X(370) equilateral-cevian: + // no closed barycentrics in ETC (certified ETC also omits); skip this round. + { + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(361): X(266)-Ceva conjugate of I; isoscelizer au=bv=cw + { + let f = |saa: f64, aa: f64, bb: f64, cc_: f64| { + let ha = (aa / 2.0).sin(); + let hb = (bb / 2.0).sin(); + let hc = (cc_ / 2.0).sin(); + if ha.abs() < 1e-12 || hb.abs() < 1e-12 || hc.abs() < 1e-12 { + return f64::NAN; + } + saa * (1.0 / hb + 1.0 / hc - 1.0 / ha) + }; + push_bary( + &mut out, + "等腰化点", + "X_{361}", + "X(361) = X(266)\\text{-Ceva conj. of }X_1;\\ \\sin A(\\csc\\tfrac{B}{2}+\\csc\\tfrac{C}{2}-\\csc\\tfrac{A}{2})", + "X(361):X(266) 对内心的 Ceva 共轭(等腰化点)", + "X361", + f(sa, g[0], g[1], g[2]), + f(sb, g[1], g[2], g[0]), + f(sc, g[2], g[0], g[1]), + ); + } + // X(362): congruent circumcircles isoscelizer + { + let f = |aa: f64, bb: f64, cc_: f64, ang_a: f64, ang_b: f64, ang_c: f64| { + aa * (bb * (ang_b / 2.0).cos() + cc_ * (ang_c / 2.0).cos() - aa * (ang_a / 2.0).cos()) + }; + push_bary( + &mut out, + "等外接圆等腰化", + "X_{362}", + "X(362) = \\mathrm{isoscelizer};\\ a(b\\cos\\tfrac{B}{2}+c\\cos\\tfrac{C}{2}-a\\cos\\tfrac{A}{2})", + "X(362):等外接圆等腰化点", + "X362", + f(a, b, c, g[0], g[1], g[2]), + f(b, c, a, g[1], g[2], g[0]), + f(c, a, b, g[2], g[0], g[1]), + ); + } + // X(363): equal-perimeters isoscelizer + { + let f = |aa: f64, bb: f64, cc_: f64, ang_a: f64, ang_b: f64, ang_c: f64| { + aa * (bb / (1.0 + (ang_b / 2.0).sin()) + + cc_ / (1.0 + (ang_c / 2.0).sin()) + - aa / (1.0 + (ang_a / 2.0).sin())) + }; + push_bary( + &mut out, + "等周长等腰化", + "X_{363}", + "X(363) = \\mathrm{isoscelizer};\\ a\\big(\\tfrac{b}{1+\\sin B/2}+\\tfrac{c}{1+\\sin C/2}-\\tfrac{a}{1+\\sin A/2}\\big)", + "X(363):等周长等腰化点", + "X363", + f(a, b, c, g[0], g[1], g[2]), + f(b, c, a, g[1], g[2], g[0]), + f(c, a, b, g[2], g[0], g[1]), + ); + } + // X(364): Wabash = equal-areas isoscelizer + { + let f = |aa: f64, bb: f64, cc_: f64| aa * (bb.sqrt() + cc_.sqrt() - aa.sqrt()); + push_bary( + &mut out, + "Wabash点", + "X_{364}", + "X(364) = X(366)\\text{-Ceva conj. of }X_1;\\ a(\\sqrt{b}+\\sqrt{c}-\\sqrt{a})", + "X(364):Wabash 点(等面积等腰化点)", + "X364", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(365): trilinear square-roots; bary a^{3/2}; isogonal of X(366) + { + let f = |aa: f64| aa * aa.sqrt(); + push_bary( + &mut out, + "边根等角", + "X_{365}", + "X(365) = \\mathrm{isogonal}(X_{366})=\\mathrm{crosssum}(X_1,X_{364});\\ a^{3/2}", + "X(365):边长平方根三线坐标点(X(366) 的等角共轭)", + "X365", + f(a), + f(b), + f(c), + ); + } + // X(366): isogonal of X(365); bary √a; cevapoint(I, X364) + { + let f = |aa: f64| aa.sqrt(); + push_bary( + &mut out, + "边根点", + "X_{366}", + "X(366) = \\mathrm{isogonal}(X_{365})=\\mathrm{cevapoint}(X_1,X_{364});\\ \\sqrt{a}", + "X(366):边长平方根重心坐标点(X(365) 的等角共轭)", + "X366", + f(a), + f(b), + f(c), + ); + } + // X(367): crosspoint(I, X366); bary a(√b+√c) + { + let f = |aa: f64, bb: f64, cc_: f64| aa * (bb.sqrt() + cc_.sqrt()); + push_bary( + &mut out, + "X1X366交点", + "X_{367}", + "X(367) = \\mathrm{crosspoint}(X_1,X_{366})=\\mathrm{crosssum}(X_1,X_{365});\\ a(\\sqrt{b}+\\sqrt{c})", + "X(367):内心与 X(366) 的交点", + "X367", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(368)/X(369)/X(370): deferred — no closed barycentrics in ETC. + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. @@ -19958,6 +20118,90 @@ mod tests { } + + #[test] + fn x361_to_x367_isoscelizer_sqrt_side_band() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("等腰化点", "X_{361}", 5.0999110570327515, 2.653978761539622), + ("等外接圆等腰化", "X_{362}", 4.224941270860307, 1.7406232496876568), + ("等周长等腰化", "X_{363}", 4.254362495787133, 1.7084322657787965), + ("Wabash点", "X_{364}", 4.289582048035992, 1.6850063075553896), + ("边根等角", "X_{365}", 4.603067268271407, 2.0596746496290916), + ("边根点", "X_{366}", 4.389105555973576, 1.8145279194492863), + ("X1X366交点", "X_{367}", 4.44793644473969, 1.8742668386531587), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + // X368–X370 deferred (no closed barycentrics). + for lab in ["X_{368}", "X_{369}", "X_{370}"] { + assert!(fs.iter().all(|f| f.label != lab), "{} should be skipped", lab); + } + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: all finite in this band. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs3.iter().any(|f| f.group == grp && f.label == lab), + "equil missing {} {}", + grp, + lab + ); + } + + // Right 3-4-5: all finite. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 417a64ad4121b8b6ea82d8f5b2b68fd1813ce53a Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:25:01 +0800 Subject: [PATCH 101/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X361=E2=80=93X367=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 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CVo7EI From 65414879412fd6bb39a0c8f216a71518c6705159 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:28:10 +0800 Subject: [PATCH 102/123] =?UTF-8?q?feat:=20ETC=20X371=E2=80=93X380=20Kenmo?= =?UTF-8?q?tu=20mates=20+=20pedal=20centroids=20+=20Euler=20intercepts?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(371)–X(380): Kenmotu dual-label X371, harmonic mate X372, pedal centroids of G/X9/X10 (X373–X375), reflection of G in O (X376), Euler intercepts X7X8/X6X7 (X377/X379), reflection of Exeter in O (X378; skip right), and X1X19∩X9X55 (X380). --- crates/mathcore/src/geometry.rs | 310 ++++++++++++++++++++++++++++++++ 1 file changed, 310 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 2d77bbd..ae37887 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -2291,6 +2291,18 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] y: km[1], label: "Km 肯莫图".into(), })); + out.push(fact( + "肯莫图点", + "X_{371}", + pt(km[0], km[1]), + None, + "X(371) = a\\cos(A-\\pi/4):\\cdots = \\mathrm{isogonal}(X_{485})", + "X(371):肯莫图点(全等正方形点)", + ).with(Shape::Point { + x: km[0], + y: km[1], + label: "X371".into(), + })); let edge_den = a * a + b * b + c * c + 4.0 * area; if edge_den > 1e-12 { let edge = std::f64::consts::SQRT_2 * a * b * c / edge_den; @@ -13407,6 +13419,209 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] // X(368)/X(369)/X(370): deferred — no closed barycentrics in ETC. } + // X(371)–X(380): Kenmotu mates / pedal-centroids / Euler intercepts (ETC). + // X(371)=Kenmotu: dual-labeled earlier as Km; bary a cos(A−π/4)=isogonal(X485). + // X(372)={X3,X6}-harmonic of X371; bary a cos(A+π/4)=isogonal(X486); Brocard-inverse of X371. + // X(373)=centroid of pedal(G); bary 2abc+ca²cos C+ba²cos B (= a²(b⁴+c⁴−a²b²−a²c²−6b²c²)). + // X(374)=centroid of pedal(X9); bary a(2b+2c−3a+(c+a)cos C+(b+a)cos B). + // X(375)=centroid of pedal(X10); bary a(2bc(b+c)+ca(c+a)cos C+ab(a+b)cos B); =midpoint(X51,X210). + // X(376)=centroid of antipedal(G)=reflection(G in O)=midpoint(G,X20); bary 5sin2A−sin2B−sin2C. + // X(377)=Euler intercept of X7X8; bary b⁴+c⁴−a⁴−2b²c²−2abc(a+b+c). + // X(378)=reflection(X22 in O); bary tan A+sin2A; skip right (tan undefined). + // X(379)=Euler intercept of X6X7; bary a⁵+(b+c)(bca²−(bc+ca+ab)(b−c)²). + // X(380)=X1X19 ∩ X9X55; bary a(b+c−a)[3a³+(b+c)(3a²+(b−c)²+a(b+c))]. + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let right = ca.abs() < 1e-12 || cb.abs() < 1e-12 || cc.abs() < 1e-12; + let pi4 = std::f64::consts::FRAC_PI_4; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(371): dual-labeled in the Kenmotu block above (Km / X_{371}). + // X(372): {X3,X6}-harmonic conjugate of Kenmotu + { + let f = |aa: f64, ang: f64| aa * (ang + pi4).cos(); + push_bary( + &mut out, + "肯莫图谐共轭", + "X_{372}", + "X(372) = \\{X_3,X_6\\}\\text{-harmonic of }X_{371};\\ a\\cos(A+\\pi/4)", + "X(372):{X(3),X(6)} 关于肯莫图点的调和共轭(等角共轭于 X(486))", + "X372", + f(a, g[0]), + f(b, g[1]), + f(c, g[2]), + ); + } + // X(373): centroid of pedal triangle of G + { + let f = |aa: f64, bb: f64, cc_: f64, ang_b: f64, ang_c: f64| { + 2.0 * aa * bb * cc_ + cc_ * aa * aa * ang_c.cos() + bb * aa * aa * ang_b.cos() + }; + push_bary( + &mut out, + "重心垂足重心", + "X_{373}", + "X(373) = \\mathrm{centroid}(\\mathrm{pedal}(G));\\ 2abc+ca^2\\cos C+ba^2\\cos B", + "X(373):重心的垂足三角形的重心", + "X373", + f(a, b, c, g[1], g[2]), + f(b, c, a, g[2], g[0]), + f(c, a, b, g[0], g[1]), + ); + } + // X(374): centroid of pedal triangle of Mittenpunkt X(9) + { + let f = |aa: f64, bb: f64, cc_: f64, ang_b: f64, ang_c: f64| { + aa * (2.0 * bb + 2.0 * cc_ - 3.0 * aa + + (cc_ + aa) * ang_c.cos() + + (bb + aa) * ang_b.cos()) + }; + push_bary( + &mut out, + "X9垂足重心", + "X_{374}", + "X(374) = \\mathrm{centroid}(\\mathrm{pedal}(X_9));\\ a(2b+2c-3a+\\cdots)", + "X(374):米滕蓬特 X(9) 的垂足三角形的重心", + "X374", + f(a, b, c, g[1], g[2]), + f(b, c, a, g[2], g[0]), + f(c, a, b, g[0], g[1]), + ); + } + // X(375): centroid of pedal triangle of Spieker X(10); = midpoint(X51,X210) + { + let f = |aa: f64, bb: f64, cc_: f64, ang_b: f64, ang_c: f64| { + aa * (2.0 * bb * cc_ * (bb + cc_) + + cc_ * aa * (cc_ + aa) * ang_c.cos() + + aa * bb * (aa + bb) * ang_b.cos()) + }; + push_bary( + &mut out, + "X10垂足重心", + "X_{375}", + "X(375) = \\mathrm{centroid}(\\mathrm{pedal}(X_{10}))=\\mathrm{midpoint}(X_{51},X_{210})", + "X(375):斯皮克点 X(10) 的垂足三角形的重心", + "X375", + f(a, b, c, g[1], g[2]), + f(b, c, a, g[2], g[0]), + f(c, a, b, g[0], g[1]), + ); + } + // X(376): reflection of G in O (= midpoint(G, X20)) + { + let f = |ang_a: f64, ang_b: f64, ang_c: f64| { + 5.0 * (2.0 * ang_a).sin() - (2.0 * ang_b).sin() - (2.0 * ang_c).sin() + }; + push_bary( + &mut out, + "重心反足重心", + "X_{376}", + "X(376) = 2O-G = \\mathrm{midpoint}(G,X_{20});\\ 5\\sin 2A-\\sin 2B-\\sin 2C", + "X(376):重心关于外心的反射(重心的反足三角形的重心)", + "X376", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(377): Euler-line intercept of X(7)X(8) + { + let f = |aa: f64, bb: f64, cc_: f64| { + bb.powi(4) + cc_.powi(4) - aa.powi(4) - 2.0 * bb * bb * cc_ * cc_ + - 2.0 * aa * bb * cc_ * (aa + bb + cc_) + }; + push_bary( + &mut out, + "X7X8欧拉截", + "X_{377}", + "X(377) = X_7X_8 \\cap \\mathrm{Euler};\\ b^4+c^4-a^4-2b^2c^2-2abc(a+b+c)", + "X(377):X(7)X(8) 与欧拉线的交点", + "X377", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(378): reflection of Exeter X(22) in O; skip right + if !right { + let f = |ang: f64| ang.tan() + (2.0 * ang).sin(); + push_bary( + &mut out, + "X22外心反射", + "X_{378}", + "X(378) = 2O-X_{22};\\ \\tan A+\\sin 2A", + "X(378):埃克塞特点关于外心的反射(跳过直角)", + "X378", + f(g[0]), + f(g[1]), + f(g[2]), + ); + } + // X(379): Euler-line intercept of X(6)X(7) + { + let f = |aa: f64, bb: f64, cc_: f64| { + aa.powi(5) + + (bb + cc_) + * (bb * cc_ * aa * aa + - (bb * cc_ + cc_ * aa + aa * bb) * (bb - cc_).powi(2)) + }; + push_bary( + &mut out, + "X6X7欧拉截", + "X_{379}", + "X(379) = X_6X_7 \\cap \\mathrm{Euler};\\ a^5+(b+c)(bca^2-(bc+ca+ab)(b-c)^2)", + "X(379):X(6)X(7) 与欧拉线的交点", + "X379", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(380): X(1)X(19) ∩ X(9)X(55) + { + let f = |aa: f64, bb: f64, cc_: f64| { + let s = bb + cc_; + aa * (s - aa) + * (3.0 * aa.powi(3) + s * (3.0 * aa * aa + (bb - cc_).powi(2) + aa * s)) + }; + push_bary( + &mut out, + "X1X19交X9X55", + "X_{380}", + "X(380) = X_1X_{19}\\cap X_9X_{55};\\ a(b+c-a)[3a^3+(b+c)(3a^2+(b-c)^2+a(b+c))]", + "X(380):X(1)X(19) 与 X(9)X(55) 的交点", + "X380", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. @@ -20202,6 +20417,101 @@ mod tests { } + #[test] + fn x371_to_x380_kenmotu_pedal_euler_band() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("肯莫图点", "X_{371}", 4.451520875906775, 1.7771279955358747), + ("肯莫图谐共轭", "X_{372}", 5.536930298223856, 3.566426083563593), + ("重心垂足重心", "X_{373}", 4.440104166666667, 1.9734732849164527), + ("X9垂足重心", "X_{374}", 4.328343531468532, 1.8573561960778358), + ("X10垂足重心", "X_{375}", 4.37109375, 1.9213628319075857), + ("重心反足重心", "X_{376}", 3.7291666666666665, 0.3711609040115441), + ("X7X8欧拉截", "X_{377}", 4.344031531531532, 1.873250390986583), + ("X22外心反射", "X_{378}", 4.595135908440629, 2.4866880197108565), + ("X6X7欧拉截", "X_{379}", 4.533564305616659, 2.3362711353139662), + ("X1X19交X9X55", "X_{380}", 4.43520575654077, 1.7328059090328471), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + // Km dual-label agrees with X371. + let km = fs.iter().find(|f| f.group == "肯莫图点" && f.label == "Km").expect("Km"); + let x371 = fs.iter().find(|f| f.group == "肯莫图点" && f.label == "X_{371}").expect("X371"); + assert_eq!(ptxy(km), ptxy(x371)); + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: all finite; X371=X372=G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs3.iter().any(|f| f.group == grp && f.label == lab), + "equil missing {} {}", + grp, + lab + ); + } + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let x371e = fs3.iter().find(|f| f.group == "肯莫图点" && f.label == "X_{371}").unwrap(); + let x372e = fs3.iter().find(|f| f.group == "肯莫图谐共轭" && f.label == "X_{372}").unwrap(); + assert_eq!(ptxy(x371e), ptxy(g3)); + assert!((ptxy(x372e).0 - ptxy(g3).0).abs() < 1e-9 && (ptxy(x372e).1 - ptxy(g3).1).abs() < 1e-9); + + // Right 3-4-5: skip X378 (tan); keep the rest. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().all(|f| f.label != "X_{378}"), "X378 skip right"); + for (grp, lab, ..) in want { + if lab == "X_{378}" { + continue; + } + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 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z*+OoC@WTZ%O$?Mwk5ztiWv($p6?WT(!^S*W!WM*0H{mJfU+k{!zSl#tYFfr26rT_o2c<%oM?bUIx9r2|F0(irZU4j?s5Tq1X6|i< zC@U@6W9)Bx4dD7M5Su=?uN3-15sH`xe+bH#BfqU?CqC9*qoJ_S(uuuh6*kV^CcC21 z%2IE_zOYxJ;B96Q<=tlbvGMi~J@mXOn_%BB)@U)Bx6NF`CfX%~kx&?Y`K=kJO|nmd zk~R+-PJ`_bZzkJU)8Ko?3SBVjDfSraafv%1a!j??pc8i-0d#Q(-ffy4;@%&L8eM1Ehvy!VzqcFZ)v(!=xeF?gjP{tm z3m!db=#kFoIreUzmo96$py$%MG_x+7XRkzSXJcrU-H_hrV;H6#hC*3yH~9Yod#I2@ zU*q-b0|6J>%ZoO$Lm3RV$o`&1VcUI=NQmRR%_{0*e5h0yS>e7YXsiB7GA0uNC1ogM z1mZSoe6qwo!)=8X1!&72vlG<)e0$BAY^nWyTJi>{A^k*wDyupW|5CSSh5B7l`f%cn@VR6w3a7!n|t)jd8%+qYO z{WS{y&QYRp`~bmBBmE;4&yzi! zTt~_Qvyz%(x3oxSplQ;32Vg2&Z|@_yv@Y@w2eF}YjqkzT&+ zPY;`ou$c)RElrmXn>zdiHxC01x8n^x+K&T5#}0efhGGyrJydtXI&#lgsUdS0#ipC( zSeo5SWunY<*u8h-=@NO09fg3lCwBo2SiKhm?-6Gx zNFCc4O6{)W=G)2%kyWwly`V8|GS z;6N1Kz)o95vQ3Pis%Px8ubHK7LI5~R$>+>!2nqnv=*WJskG1HO6r$hz!R*S;+aoM7 z{L&9FBm8Lpz!Qrg81~@v=DX~IU22hTX?*PjEO6nkrQ*V9bkW`;yS@&s_>z4Jf~b6r zj%5C1*0W!>*KAl8!tyb!a2X|W#XiVA*i$Z=^+mjygBtz>d-zq#{K>4NUb9nTYqJJ@ zc)@&wT?c(>KL$kizy;GEd>j4gz@Twc)r)3L$1ir)dtl^Ed;jbP-_U-wkI#O7+1VK& z*0=2a}*i%u!nYABw`OjAK77* zvBQX!lmeUR??7!>Mnc|{tSn+sB;?dT> Date: Mon, 2 Nov 2026 19:16:40 +0800 Subject: [PATCH 096/123] =?UTF-8?q?feat:=20ETC=20X341=E2=80=93X350=20isoto?= =?UTF-8?q?mics=20+=20Hirst/cevapoints?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(341)–X(350) as isotomics of X(269)/X(271)/X(275)/X(277)/X(278)/ X(279)/X(280)/X(281)/X(284)/X(291), with cevapoint/crosspoint/Hirst identities where ETC lists them; right/equilateral guards for sec and a²−bc. --- crates/mathcore/src/geometry.rs | 333 ++++++++++++++++++++++++++++++++ 1 file changed, 333 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 3f0d639..a125a7c 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -12794,6 +12794,246 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] + + // X(341)–X(350): continue isotomic / Hirst / cevapoint band (ETC). + // X(341)=isotomic(X269); bary bc(b+c−a)². + // X(342)=isotomic(X271)=cevapoint(X208,X223); bary (sec A tan A/2)(1+cos A−cos B−cos C); skip right. + // X(343)=isotomic(X275)=crosspoint(X69,X76); bary cos A cos(B−C). + // X(344)=isotomic(X277); bary a²+b²+c²−2ab−2ac [=sin A·csc²(A/2)(cos⁴(B/2)+cos⁴(C/2)−cos⁴(A/2))]. + // X(345)=isotomic(X278); bary 1/(1−sec A); skip right. + // X(346)=isotomic(X279)=crosspoint(X312,X341); bary (b+c−a)². + // X(347)=isotomic(X280)=cevapoint(X40,X223); bary a(−1−cos A+cos B+cos C)sec²(A/2). + // X(348)=isotomic(X281)=cevapoint(X2,X347); bary 1/(1+sec A); skip right. + // X(349)=isotomic(X284)=cevapoint(X226,X307); bary (cos B+cos C)csc² A. + // X(350)=isotomic(X291)=X(2)-Hirst of X(75); bary bc(a²−bc); skip equil. + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let equil = (a - b).abs() < 1e-12 && (b - c).abs() < 1e-12; + let right = ca.abs() < 1e-9 || cb.abs() < 1e-9 || cc.abs() < 1e-9; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(341): isotomic of X(269); bary bc(b+c−a)² + { + let f = |aa: f64, bb: f64, cc_: f64| bb * cc_ * (bb + cc_ - aa).powi(2); + push_bary( + &mut out, + "X269等截", + "X_{341}", + "X(341) = \\mathrm{isotomic}(X_{269});\\ bc(b+c-a)^2", + "X(341):X(269) 的等截共轭", + "X341", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(342): isotomic of X(271)=cevapoint(X208,X223); skip right (sec A → ∞) + if !right { + let f = |aa: f64, caa: f64, cbb: f64, ccc: f64| { + if caa.abs() < 1e-12 { + return f64::NAN; + } + let th = (aa * 0.5).tan(); + (1.0 / caa) * th * (1.0 + caa - cbb - ccc) + }; + push_bary( + &mut out, + "X208X223截点", + "X_{342}", + "X(342) = \\mathrm{isotomic}(X_{271})=\\mathrm{cevapoint}(X_{208},X_{223});\\ (\\sec A\\tan\\tfrac{A}{2})(1+\\cos A-\\cdots)", + "X(342):X(271) 的等截共轭(X(208) 与 X(223) 的截点)", + "X342", + f(g[0], ca, cb, cc), + f(g[1], cb, cc, ca), + f(g[2], cc, ca, cb), + ); + } + // X(343): isotomic of X(275)=crosspoint(X69,X76); bary cos A cos(B−C) + { + let f = |caa: f64, bb: f64, cc_: f64| caa * (bb - cc_).cos(); + push_bary( + &mut out, + "X69X76交点", + "X_{343}", + "X(343) = \\mathrm{isotomic}(X_{275})=\\mathrm{crosspoint}(X_{69},X_{76});\\ \\cos A\\cos(B-C)", + "X(343):X(275) 的等截共轭(X(69) 与 X(76) 的交点)", + "X343", + f(ca, g[1], g[2]), + f(cb, g[2], g[0]), + f(cc, g[0], g[1]), + ); + } + // X(344): isotomic of X(277); bary a²+b²+c²−2ab−2ac + { + let f = |aa: f64, bb: f64, cc_: f64| { + aa * aa + bb * bb + cc_ * cc_ - 2.0 * aa * bb - 2.0 * aa * cc_ + }; + push_bary( + &mut out, + "X277等截", + "X_{344}", + "X(344) = \\mathrm{isotomic}(X_{277});\\ a^2+b^2+c^2-2ab-2ac", + "X(344):X(277) 的等截共轭", + "X344", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(345): isotomic of X(278); bary 1/(1−sec A); skip right + if !right { + let f = |caa: f64| { + if caa.abs() < 1e-12 { + return f64::NAN; + } + let den = 1.0 - 1.0 / caa; + if den.abs() < 1e-14 { + return f64::NAN; + } + 1.0 / den + }; + push_bary( + &mut out, + "X278等截", + "X_{345}", + "X(345) = \\mathrm{isotomic}(X_{278});\\ 1/(1-\\sec A)", + "X(345):X(278) 的等截共轭", + "X345", + f(ca), + f(cb), + f(cc), + ); + } + // X(346): isotomic of X(279)=crosspoint(X312,X341); bary (b+c−a)² + { + let f = |aa: f64, bb: f64, cc_: f64| (bb + cc_ - aa).powi(2); + push_bary( + &mut out, + "X312X341交点", + "X_{346}", + "X(346) = \\mathrm{isotomic}(X_{279})=\\mathrm{crosspoint}(X_{312},X_{341});\\ (b+c-a)^2", + "X(346):X(279) 的等截共轭(X(312) 与 X(341) 的交点)", + "X346", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(347): isotomic of X(280)=cevapoint(X40,X223) + { + let f = |side: f64, aa: f64, caa: f64, cbb: f64, ccc: f64| { + let cah = (aa * 0.5).cos(); + if cah.abs() < 1e-12 { + return f64::NAN; + } + side * (-1.0 - caa + cbb + ccc) / (cah * cah) + }; + push_bary( + &mut out, + "X40X223截点", + "X_{347}", + "X(347) = \\mathrm{isotomic}(X_{280})=\\mathrm{cevapoint}(X_{40},X_{223});\\ a(-1-\\cos A+\\cdots)\\sec^2\\tfrac{A}{2}", + "X(347):X(280) 的等截共轭(X(40) 与 X(223) 的截点)", + "X347", + f(a, g[0], ca, cb, cc), + f(b, g[1], cb, cc, ca), + f(c, g[2], cc, ca, cb), + ); + } + // X(348): isotomic of X(281)=cevapoint(G,X347); bary 1/(1+sec A); skip right + if !right { + let f = |caa: f64| { + if caa.abs() < 1e-12 { + return f64::NAN; + } + let den = 1.0 + 1.0 / caa; + if den.abs() < 1e-14 { + return f64::NAN; + } + 1.0 / den + }; + push_bary( + &mut out, + "重心X347截点", + "X_{348}", + "X(348) = \\mathrm{isotomic}(X_{281})=\\mathrm{cevapoint}(X_2,X_{347});\\ 1/(1+\\sec A)", + "X(348):X(281) 的等截共轭(重心与 X(347) 的截点)", + "X348", + f(ca), + f(cb), + f(cc), + ); + } + // X(349): isotomic of X(284)=cevapoint(X226,X307); bary (cos B+cos C)csc² A + { + let f = |saa: f64, cbb: f64, ccc: f64| { + if saa.abs() < 1e-14 { + return f64::NAN; + } + (cbb + ccc) / (saa * saa) + }; + push_bary( + &mut out, + "X226X307截点", + "X_{349}", + "X(349) = \\mathrm{isotomic}(X_{284})=\\mathrm{cevapoint}(X_{226},X_{307});\\ (\\cos B+\\cos C)\\csc^2 A", + "X(349):X(284) 的等截共轭(X(226) 与 X(307) 的截点)", + "X349", + f(sa, cb, cc), + f(sb, cc, ca), + f(sc, ca, cb), + ); + } + // X(350): isotomic of X(291)=X(2)-Hirst of X(75); bary bc(a²−bc); skip equil + if !equil { + let f = |aa: f64, bb: f64, cc_: f64| { + let d = aa * aa - bb * cc_; + if d.abs() < 1e-14 { + return f64::NAN; + } + bb * cc_ * d + }; + push_bary( + &mut out, + "X75重心Hirst", + "X_{350}", + "X(350) = \\mathrm{isotomic}(X_{291})=X(2)\\text{-Hirst of }X(75);\\ bc(a^2-bc)", + "X(350):X(291) 的等截共轭(重心对摩西点 X(75) 的 Hirst 逆)", + "X350", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + } + + + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -19321,6 +19561,99 @@ mod tests { + + #[test] + fn x341_to_x350_isotomics_hirst_cevapoint() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("X269等截", "X_{341}", 3.0069444444444446, 0.6723929420498987), + ("X208X223截点", "X_{342}", 4.220788526733359, 0.38378533239463564), + ("X69X76交点", "X_{343}", 3.5879381258941345, 0.9126652010845535), + ("X277等截", "X_{344}", 4.81706204379562, 2.1891543640287363), + ("X278等截", "X_{345}", 2.9102272727272727, 0.4621173310815668), + ("X312X341交点", "X_{346}", 3.305241935483871, 0.8198855874027797), + ("X40X223截点", "X_{347}", 3.695389291257113, 0.1656737250075146), + ("重心X347截点", "X_{348}", 3.916828370030097, 1.0652928115365186), + ("X226X307截点", "X_{349}", 4.086802409438044, 1.6166629514227433), + ("X75重心Hirst", "X_{350}", -32.6402027027027, -31.736219953466517), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + + // Isosceles 5-5-6: all finite in this band. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: skip X350 (a²−bc → 0); keep X341–X349. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.label != "X_{350}"), "X350 should skip equil"); + for (grp, lab, ..) in want { + if lab == "X_{350}" { + continue; + } + assert!( + fs3.iter().any(|f| f.group == grp && f.label == lab), + "equil missing {} {}", + grp, + lab + ); + } + + // Right 3-4-5: skip X342/X345/X348 (sec); keep others. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for lab in ["X_{342}", "X_{345}", "X_{348}"] { + assert!(fs4.iter().all(|f| f.label != lab), "{} should skip right", lab); + } + for (grp, lab, ..) in want { + if matches!(lab, "X_{341}" | "X_{343}" | "X_{344}" | "X_{346}" | "X_{347}" | "X_{349}" | "X_{350}") { + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + } + + + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 558706d765279f6e49f3502686006861d4705749 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 19:16:57 +0800 Subject: [PATCH 097/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X341=E2=80=93X350=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 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J3pEp!{|~t>y%7Ka From d6d95b71e5dc55bb916280cc6dc8f0f21c7e2acb Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 18:54:09 +0800 Subject: [PATCH 082/123] =?UTF-8?q?feat:=20ETC=20X271=E2=80=93X280=20isogo?= =?UTF-8?q?nals=20and=20cevapoint?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land X(271)–X(280) in geometry.rs: isogonals of X208/X209/X212/X213/ X216–X220, cevapoint(H,K) as X(275), Hofstadter −2 as X(276), and X(1)-cross of Nagel as X(280). Right guards for X271/X273/X275/X276/X278. --- crates/mathcore/src/geometry.rs | 328 ++++++++++++++++++++++++++++++++ 1 file changed, 328 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 23a0632..327823e 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -11058,6 +11058,247 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + + // X(271)–X(280): continue isogonal / cevapoint band (ETC). + // X(271)=isog(X208)=isotomic(X342); bary (sin A)(cot A cot A/2)/(-1-cos A+cos B+cos C); skip right. + // X(272)=isog(X209); bary (sin A)/[(sin A+sin(A−B)+sin(A−C))(sin B+sin C)]. + // X(273)=isog(X212)=isotomic(X78)=polar(X9); bary tan A sec²(A/2); skip right. + // X(274)=isog(X213)=isotomic(X37); bary bc/(b+c). + // X(275)=cevapoint(H,K)=isog(X216)=polar(X5); bary sec A sec(B−C); skip right. + // X(276)=isog(X217)=Hofstadter −2; bary csc² A sec A sec(B−C); skip right. + // X(277)=isog(X218); bary 1/(a²+b²+c²−2ab−2ac). + // X(278)=isog(X219); bary 1−sec A [= tan A tan(A/2)]; skip right. + // X(279)=isog(X220); bary tan²(A/2). + // X(280)=X(1)-cross of X(8)=isog(X221); bary (sin A)csc²(A/2)/(-1-cos A+cos B+cos C). + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let right = ca.abs() < 1e-9 || cb.abs() < 1e-9 || cc.abs() < 1e-9; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(271): skip right (cot A → ∞) + if !right { + let f = |aa: f64, bb: f64, cc: f64| { + let den = -1.0 - aa.cos() + bb.cos() + cc.cos(); + if den.abs() < 1e-12 { + return f64::NAN; + } + let half = aa * 0.5; + if half.tan().abs() < 1e-14 { + return f64::NAN; + } + // (sin A)(cot A cot A/2)/den = cos A · cot(A/2) / den + aa.cos() / half.tan() / den + }; + push_bary( + &mut out, + "X208等角", + "X_{271}", + "X(271) = \\mathrm{isog}(X_{208});\\ (\\sin A)(\\cot A\\cot\\tfrac{A}{2})/(-1-\\cos A+\\cdots)", + "X(271):X(208) 的等角共轭(X(342) 等截)", + "X271", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(272) + { + let f = |aa: f64, bb: f64, cc: f64| { + let num = aa.sin() + (aa - bb).sin() + (aa - cc).sin(); + let den = (bb.sin() + cc.sin()) * num; + if den.abs() < 1e-14 { + return f64::NAN; + } + aa.sin() / den + }; + push_bary( + &mut out, + "X209等角", + "X_{272}", + "X(272) = \\mathrm{isog}(X_{209});\\ (\\sin A)/[(\\sin A+\\sin(A-B)+\\sin(A-C))(\\sin B+\\sin C)]", + "X(272):X(209) 的等角共轭", + "X272", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(273): skip right (tan A → ∞) + if !right { + let f = |aa: f64| { + let c_half = (aa * 0.5).cos(); + if c_half.abs() < 1e-14 { + return f64::NAN; + } + aa.tan() / (c_half * c_half) + }; + push_bary( + &mut out, + "X212等角", + "X_{273}", + "X(273) = \\mathrm{isog}(X_{212})=\\mathrm{isotomic}(X_{78});\\ \\tan A\\sec^2\\tfrac{A}{2}", + "X(273):X(212) 的等角共轭(X(78) 等截 / X(9) 极共轭)", + "X273", + f(g[0]), + f(g[1]), + f(g[2]), + ); + } + // X(274) + { + push_bary( + &mut out, + "X213等角", + "X_{274}", + "X(274) = \\mathrm{isog}(X_{213})=\\mathrm{isotomic}(X_{37});\\ bc/(b+c)", + "X(274):X(213) 的等角共轭(X(37) 等截)", + "X274", + b * c / (b + c), + c * a / (c + a), + a * b / (a + b), + ); + } + // X(275): skip right (sec A → ∞); cevapoint of H and K + if !right { + let f = |aa: f64, bb: f64, cc: f64| { + let cbc = (bb - cc).cos(); + if aa.cos().abs() < 1e-14 || cbc.abs() < 1e-14 { + return f64::NAN; + } + 1.0 / (aa.cos() * cbc) + }; + push_bary( + &mut out, + "垂心勒莫恩截点", + "X_{275}", + "X(275) = \\mathrm{cevapoint}(H,K)=\\mathrm{isog}(X_{216});\\ \\sec A\\sec(B-C)", + "X(275):垂心与勒莫恩点的截点(X(216) 等角 / X(5) 极共轭)", + "X275", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(276): skip right (sec A → ∞); Hofstadter −2 + if !right { + let f = |aa: f64, bb: f64, cc: f64| { + let saa = aa.sin(); + let caa = aa.cos(); + let cbc = (bb - cc).cos(); + if saa.abs() < 1e-14 || caa.abs() < 1e-14 || cbc.abs() < 1e-14 { + return f64::NAN; + } + 1.0 / (saa * saa * caa * cbc) + }; + push_bary( + &mut out, + "X217等角", + "X_{276}", + "X(276) = \\mathrm{isog}(X_{217});\\ \\csc^2 A\\sec A\\sec(B-C)", + "X(276):X(217) 的等角共轭(Hofstadter −2 点)", + "X276", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + // X(277) + { + let f = |aa: f64, bb: f64, cc: f64| { + let den = aa * aa + bb * bb + cc * cc - 2.0 * aa * bb - 2.0 * aa * cc; + if den.abs() < 1e-14 { + return f64::NAN; + } + 1.0 / den + }; + push_bary( + &mut out, + "X218等角", + "X_{277}", + "X(277) = \\mathrm{isog}(X_{218});\\ 1/(a^2+b^2+c^2-2ab-2ac)", + "X(277):X(218) 的等角共轭", + "X277", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(278): skip right (sec A → ∞) + if !right { + push_bary( + &mut out, + "X219等角", + "X_{278}", + "X(278) = \\mathrm{isog}(X_{219});\\ 1-\\sec A\\ [=\\tan A\\tan\\tfrac{A}{2}]", + "X(278):X(219) 的等角共轭", + "X278", + 1.0 - 1.0 / ca, + 1.0 - 1.0 / cb, + 1.0 - 1.0 / cc, + ); + } + // X(279) + { + push_bary( + &mut out, + "X220等角", + "X_{279}", + "X(279) = \\mathrm{isog}(X_{220});\\ \\tan^2\\tfrac{A}{2}", + "X(279):X(220) 的等角共轭", + "X279", + (g[0] * 0.5).tan().powi(2), + (g[1] * 0.5).tan().powi(2), + (g[2] * 0.5).tan().powi(2), + ); + } + // X(280) + { + let f = |aa: f64, bb: f64, cc: f64| { + let den = -1.0 - aa.cos() + bb.cos() + cc.cos(); + let s_half = (aa * 0.5).sin(); + if den.abs() < 1e-12 || s_half.abs() < 1e-14 { + return f64::NAN; + } + aa.sin() / (s_half * s_half) / den + }; + push_bary( + &mut out, + "内心奈格尔交叉共轭", + "X_{280}", + "X(280) = X(1)\\text{-cross of }X(8)=\\mathrm{isog}(X_{221});\\ (\\sin A)\\csc^2\\tfrac{A}{2}/(-1-\\cos A+\\cdots)", + "X(280):内心对奈格尔点的交叉共轭(X(221) 等角)", + "X280", + f(g[0], g[1], g[2]), + f(g[1], g[2], g[0]), + f(g[2], g[0], g[1]), + ); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -16949,6 +17190,93 @@ mod tests { } } + #[test] + fn x271_to_x280_isogonals_cevapoint() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("X208等角", "X_{271}", 4.569633883704235, 3.829888413065841), + ("X209等角", "X_{272}", 0.7199770872986051, 0.18117854313016454), + ("X212等角", "X_{273}", 4.87699699243971, 3.3047981376409314), + ("X213等角", "X_{274}", 4.135283025518117, 1.5802419096832656), + ("垂心勒莫恩截点", "X_{275}", 4.749702779383263, 2.6734750735796546), + ("X217等角", "X_{276}", 4.385508246326592, 2.1596621974365897), + ("X218等角", "X_{277}", 3.5721756890576, 1.2223724154554005), + ("X219等角", "X_{278}", 4.9566122071516645, 3.5163083231866197), + ("X220等角", "X_{279}", 4.889986493974234, 2.7947888291577954), + ("内心奈格尔交叉共轭", "X_{280}", 4.756291946308725, 4.475700133725433), + ]; + for (grp, lab, ex, ey) in want { + let f = fs + .iter() + .find(|f| f.group == grp && f.label == lab) + .unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!( + (x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, + "{} {:?} want {:?}", + lab, + (x, y), + (ex, ey) + ); + } + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs2.iter().any(|f| f.group == grp && f.label == lab), + "isos missing {} {}", + grp, + lab + ); + } + + // Equilateral: all finite for this band. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + for (grp, lab, ..) in want { + assert!( + fs3.iter().any(|f| f.group == grp && f.label == lab), + "equil missing {} {}", + grp, + lab + ); + } + + // Right 3-4-5: X271/X273/X275/X276/X278 skip (cot/tan/sec); others finite. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for skip in ["X_{271}", "X_{273}", "X_{275}", "X_{276}", "X_{278}"] { + assert!(fs4.iter().all(|f| f.label != skip), "{} should skip right", skip); + } + for (grp, lab, ..) in want { + if matches!(lab, "X_{271}" | "X_{273}" | "X_{275}" | "X_{276}" | "X_{278}") { + continue; + } + assert!( + fs4.iter().any(|f| f.group == grp && f.label == lab), + "right missing {} {}", + grp, + lab + ); + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 7b1c4b2e734262f5442ec3b704e563a3bc24a764 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 18:54:09 +0800 Subject: [PATCH 083/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X271=E2=80=93X280=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 820512 -> 824707 bytes 1 file changed, 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From a62fc61a5149795364fa47a67d3836becc98a067 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 18:32:16 +0800 Subject: [PATCH 070/123] =?UTF-8?q?feat:=20ETC=20X211=E2=80=93X220=20class?= =?UTF-8?q?ical=20Ceva-conjugate=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Fill next contiguous classical band after X210: X(211) H-Ceva of Brocard mid X39; X(212) Mittenpunkt-Ceva of X41; X(213) K-Ceva of X42 (=cross of K,X31); X(214) G-Ceva of X44 (=mid(I,X100)=comp X80; skip equil); X(215) I-Ceva of X50 (skip equil); X(216) N-Ceva of X51; X(217) K-Ceva of X51; X(218) Ge-Ceva of X55; X(219) Na-Ceva of X55; X(220) Mittenpunkt-Ceva of X55 (=bary-square of X9). Acute/right/equilateral/isosceles guards; prefer centers not already in geometry.rs. --- crates/mathcore/src/geometry.rs | 365 ++++++++++++++++++++++++++++++++ 1 file changed, 365 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index a320d09..b8574df 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -9333,6 +9333,294 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(211)–X(220): next classical Ceva-conjugate band (ETC). + // X(211)=X(4)-Ceva of X(39); bary a⁴(b²+c²)(a²b²−b⁴+a²c²+b²c²−c⁴). + // X(212)=X(9)-Ceva of X(41); bary (sin 2A)(1+cos A). + // X(213)=X(6)-Ceva of X(42); bary (b+c)a³. + // X(214)=X(2)-Ceva of X(44)=mid(I,X100)=comp(X80); bary a(b+c−2a)(b²+c²−a²−bc); skip equil. + // X(215)=X(1)-Ceva of X(50); bary (sin A)(sin 3A)(sin 3B+sin 3C−sin 3A); skip equil. + // X(216)=X(5)-Ceva of X(51); bary (sin A)(sin 2A)cos(B−C). + // X(217)=X(6)-Ceva of X(51); bary a⁴(a²−b²−c²)(a²b²−b⁴+a²c²+2b²c²−c⁴). + // X(218)=X(7)-Ceva of X(55); bary a²(a²+b²+c²−2ab−2ac). + // X(219)=X(8)-Ceva of X(55); bary sin 2A·cot(A/2)=2 cos A(1+cos A). + // X(220)=X(9)-Ceva of X(55)=bary-square of X(9); bary a²(b+c−a)². + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let equil = (a - b).abs() < 1e-12 && (b - c).abs() < 1e-12; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(211) + { + let f = |aa: f64, bb: f64, cc: f64| { + let a2 = aa * aa; + let b2 = bb * bb; + let c2 = cc * cc; + let a4 = a2 * a2; + a4 * (b2 + c2) * (a2 * b2 - b2 * b2 + a2 * c2 + b2 * c2 - c2 * c2) + }; + let wa = f(a, b, c); + let wb = f(b, c, a); + let wc = f(c, a, b); + push_bary( + &mut out, + "垂心布罗卡中点塞瓦", + "X_{211}", + "X(211) = X(4)\\text{-Ceva of }X(39);\\ a^4(b^2+c^2)(a^2b^2-b^4+a^2c^2+b^2c^2-c^4)", + "X(211):垂心对布罗卡中点的塞瓦共轭", + "X211", + wa, + wb, + wc, + ); + } + // X(212) + { + let wa = (2.0 * g[0]).sin() * (1.0 + ca); + let wb = (2.0 * g[1]).sin() * (1.0 + cb); + let wc = (2.0 * g[2]).sin() * (1.0 + cc); + push_bary( + &mut out, + "米滕第二幂截点塞瓦", + "X_{212}", + "X(212) = X(9)\\text{-Ceva of }X(41);\\ (\\sin 2A)(1+\\cos A)", + "X(212):米滕阿列夫点对第二幂截点的塞瓦共轭", + "X212", + wa, + wb, + wc, + ); + } + // X(213) + { + let wa = (b + c) * a * a * a; + let wb = (c + a) * b * b * b; + let wc = (a + b) * c * c * c; + push_bary( + &mut out, + "勒莫恩内心勒莫恩截点塞瓦", + "X_{213}", + "X(213) = X(6)\\text{-Ceva of }X(42);\\ (b+c)a^3", + "X(213):勒莫恩点对内心–勒莫恩截点的塞瓦共轭(K 与 X(31) 的截点)", + "X213", + wa, + wb, + wc, + ); + } + // X(214): also mid(I, X100) = complement of X(80) + { + let wa = a * (b + c - 2.0 * a) * (b * b + c * c - a * a - b * c); + let wb = b * (c + a - 2.0 * b) * (c * c + a * a - b * b - c * a); + let wc = c * (a + b - 2.0 * c) * (a * a + b * b - c * c - a * b); + push_bary( + &mut out, + "重心X44塞瓦", + "X_{214}", + "X(214) = X(2)\\text{-Ceva of }X(44) = \\mathrm{mid}(I,X_{100});\\ a(b+c-2a)(b^2+c^2-a^2-bc)", + "X(214):重心对 X(44) 的塞瓦共轭(内心与 X(100) 中点;X(80) 的补点)", + "X214", + wa, + wb, + wc, + ); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if let Some(x100) = out + .iter() + .rev() + .find(|f| f.label == "X_{100}") + .and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some([*x, *y]), + _ => None, + }) + { + let mid = [(inc[0] + x100[0]) / 2.0, (inc[1] + x100[1]) / 2.0]; + if dist2(xy, mid) < 1e-6 * (1.0 + rr) { + out.push(fact( + "重心X44塞瓦", + "X_{214}=\\mathrm{mid}(I,X_{100})", + "\\text{中点}".into(), + None, + "X(214) = \\mathrm{mid}(X(1),X(100))", + "X(214) 是内心与 X(100) 的中点", + )); + } + } + if let Some(x80) = out + .iter() + .rev() + .find(|f| f.label == "X_{80}") + .and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some([*x, *y]), + _ => None, + }) + { + let comp = [ + (3.0 * centroid[0] - x80[0]) / 2.0, + (3.0 * centroid[1] - x80[1]) / 2.0, + ]; + if dist2(xy, comp) < 1e-6 * (1.0 + rr) { + out.push(fact( + "重心X44塞瓦", + "X_{214}=\\mathrm{comp}(X_{80})", + "\\text{补点}".into(), + None, + "X(214) = (3G - X(80))/2", + "X(214) 是 X(80) 关于重心的补点", + )); + } + } + } + } + // X(215): skip equilateral (sin 3A = 0) + if !equil { + let s3a = (3.0 * g[0]).sin(); + let s3b = (3.0 * g[1]).sin(); + let s3c = (3.0 * g[2]).sin(); + let wa = sa * s3a * (s3b + s3c - s3a); + let wb = sb * s3b * (s3c + s3a - s3b); + let wc = sc * s3c * (s3a + s3b - s3c); + push_bary( + &mut out, + "内心三倍角正弦塞瓦", + "X_{215}", + "X(215) = X(1)\\text{-Ceva of }X(50);\\ (\\sin A)(\\sin 3A)(\\sin 3B+\\sin 3C-\\sin 3A)", + "X(215):内心对三倍角正弦点的塞瓦共轭", + "X215", + wa, + wb, + wc, + ); + } + // X(216) + { + let wa = sa * (2.0 * g[0]).sin() * (g[1] - g[2]).cos(); + let wb = sb * (2.0 * g[1]).sin() * (g[2] - g[0]).cos(); + let wc = sc * (2.0 * g[2]).sin() * (g[0] - g[1]).cos(); + push_bary( + &mut out, + "九点垂足重心塞瓦", + "X_{216}", + "X(216) = X(5)\\text{-Ceva of }X(51);\\ (\\sin A)(\\sin 2A)\\cos(B-C)", + "X(216):九点中心对垂足三角形重心的塞瓦共轭(O 与 K 的截点)", + "X216", + wa, + wb, + wc, + ); + } + // X(217) + { + let f = |aa: f64, bb: f64, cc: f64| { + let a2 = aa * aa; + let b2 = bb * bb; + let c2 = cc * cc; + let a4 = a2 * a2; + a4 * (a2 - b2 - c2) * (a2 * b2 - b2 * b2 + a2 * c2 + 2.0 * b2 * c2 - c2 * c2) + }; + let wa = f(a, b, c); + let wb = f(b, c, a); + let wc = f(c, a, b); + push_bary( + &mut out, + "勒莫恩垂足重心塞瓦", + "X_{217}", + "X(217) = X(6)\\text{-Ceva of }X(51);\\ a^4(a^2-b^2-c^2)(\\cdots)", + "X(217):勒莫恩点对垂足三角形重心的塞瓦共轭(K 与 X(184) 的截点)", + "X217", + wa, + wb, + wc, + ); + } + // X(218) + { + let f = |aa: f64, bb: f64, cc: f64| { + let a2 = aa * aa; + a2 * (a2 + bb * bb + cc * cc - 2.0 * aa * bb - 2.0 * aa * cc) + }; + let wa = f(a, b, c); + let wb = f(b, c, a); + let wc = f(c, a, b); + push_bary( + &mut out, + "格尔巩外接内切相似塞瓦", + "X_{218}", + "X(218) = X(7)\\text{-Ceva of }X(55);\\ a^2(a^2+b^2+c^2-2ab-2ac)", + "X(218):格尔巩点对 X(55) 的塞瓦共轭", + "X218", + wa, + wb, + wc, + ); + } + // X(219) + { + let wa = 2.0 * ca * (1.0 + ca); + let wb = 2.0 * cb * (1.0 + cb); + let wc = 2.0 * cc * (1.0 + cc); + push_bary( + &mut out, + "奈格尔外接内切相似塞瓦", + "X_{219}", + "X(219) = X(8)\\text{-Ceva of }X(55);\\ \\sin 2A\\cot\\tfrac{A}{2}=2\\cos A(1+\\cos A)", + "X(219):奈格尔点对 X(55) 的塞瓦共轭", + "X219", + wa, + wb, + wc, + ); + } + // X(220): barycentric square of Mittenpunkt X(9) + { + let wa = a * a * (b + c - a) * (b + c - a); + let wb = b * b * (c + a - b) * (c + a - b); + let wc = c * c * (a + b - c) * (a + b - c); + push_bary( + &mut out, + "米滕外接内切相似塞瓦", + "X_{220}", + "X(220) = X(9)\\text{-Ceva of }X(55) = X(9)^2;\\ a^2(b+c-a)^2", + "X(220):米滕阿列夫点对 X(55) 的塞瓦共轭(X(9) 的重心平方)", + "X220", + wa, + wb, + wc, + ); + } + } + + + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. @@ -14680,6 +14968,83 @@ mod tests { } } + #[test] + fn x211_to_x220_ceva_conjugates() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("垂心布罗卡中点塞瓦", "X_{211}", 5.3174323110483765, 3.5273321313623947), + ("米滕第二幂截点塞瓦", "X_{212}", 3.799729364005413, 0.8385349599366532), + ("勒莫恩内心勒莫恩截点塞瓦", "X_{213}", 4.793033065723228, 2.301971867768948), + ("重心X44塞瓦", "X_{214}", 2.75, 2.9047375096555625), + ("内心三倍角正弦塞瓦", "X_{215}", 3.118293471234648, 3.204536963894954), + ("九点垂足重心塞瓦", "X_{216}", 4.153027823240589, 1.2850620179944163), + ("勒莫恩垂足重心塞瓦", "X_{217}", 4.634208909592487, 1.7187829379619926), + ("格尔巩外接内切相似塞瓦", "X_{218}", 5.0863099374565675, 2.6677561450735174), + ("奈格尔外接内切相似塞瓦", "X_{219}", 3.5044852627082443, 0.6948539108958203), + ("米滕外接内切相似塞瓦", "X_{220}", 3.8901257770709847, 1.1758370720016735), + ]; + for (grp, lab, ex, ey) in want { + let f = fs.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!((x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, "{} {:?} want {:?}", lab, (x, y), (ex, ey)); + } + assert!(fs.iter().any(|f| f.group == "重心X44塞瓦" && f.label.contains("mid"))); + assert!(fs.iter().any(|f| f.group == "重心X44塞瓦" && f.label.contains("comp"))); + // mid(I,X100) Cartesian. + let i = fs.iter().find(|f| f.group == "特殊点" && f.label == "I").expect("I"); + let x100 = fs.iter().find(|f| f.label == "X_{100}").expect("X100"); + let x214 = fs.iter().find(|f| f.group == "重心X44塞瓦" && f.label == "X_{214}").unwrap(); + let (ix, iy) = ptxy(i); + let (p100x, p100y) = ptxy(x100); + let (p214x, p214y) = ptxy(x214); + assert!((p214x - (ix + p100x) / 2.0).abs() < 1e-6 && (p214y - (iy + p100y) / 2.0).abs() < 1e-6); + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!(fs2.iter().any(|f| f.group == grp && f.label == lab), "isos missing {} {}", grp, lab); + } + + // Equilateral: X215 skips; others → G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (gx3, gy3) = ptxy(g3); + assert!(fs3.iter().all(|f| f.group != "内心三倍角正弦塞瓦"), "X215 should skip equil"); + // X214 bary vanishes identically on equilateral (b+c−2a=0). + assert!(fs3.iter().all(|f| !(f.group == "重心X44塞瓦" && f.label == "X_{214}")), "X214 should skip equil"); + for (grp, lab, ..) in want { + if grp == "内心三倍角正弦塞瓦" || grp == "重心X44塞瓦" { + continue; + } + let f = fs3.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("equil missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!((x - gx3).abs() < 1e-5 && (y - gy3).abs() < 1e-5, "equilateral {} != G {:?}", lab, (x, y)); + } + + // Right 3-4-5: all finite in this band. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + for (grp, lab, ..) in want { + assert!(fs4.iter().any(|f| f.group == grp && f.label == lab), "right missing {} {}", grp, lab); + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From b3d5aef965b9d7858c46787ececb925911e74750 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 18:32:16 +0800 Subject: [PATCH 071/123] =?UTF-8?q?chore:=20refresh=20mathcore=20WASM=20af?= =?UTF-8?q?ter=20X211=E2=80=93X220=20ETC=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/wasm/pkg/mathcore_bg.wasm | Bin 793650 -> 798123 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/src/wasm/pkg/mathcore_bg.wasm b/src/wasm/pkg/mathcore_bg.wasm index 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z`e-XceG+L5p!dbgB8`b~j(n&hYz5$FO^q6~q*XyvV}$KDT^l^g?aH{Ivw_4dFY4fS zjku(1=H$)GI%zj8cq`nJNF?v{ADmOByuO(c_3~96Xkg=-&XQ;h^STc7_l6GCC^xBy z_LS;CQwqv-*1unR#w{wNt=qarb0}k?f7k6+i`knSb>L1#XOC@eXxbn8W+mR|-5l37 wH*)CXQ5{+s*_5mvk^k;tQcL4qxUav61-prO|JIV){ej-g1SBu1Jkyl_3zY(;f&c&j From fa04dfea25866e490a32c738aec4382f884bf3cf Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 18:37:11 +0800 Subject: [PATCH 072/123] =?UTF-8?q?feat:=20ETC=20X221=E2=80=93X230=20class?= =?UTF-8?q?ical=20Ceva-conjugate=20centers?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Land next ETC band in geometry.rs: I/Ge/G Ceva of X(56)/X(57), Ge-Ceva of X(63), H/Ge/Spieker Ceva of X(65), O-Ceva of X(71), Ge-Ceva of X(81), G-Ceva of X(114); acute/right/equilateral guards and complement/midpoint identities where applicable. --- crates/mathcore/src/geometry.rs | 411 ++++++++++++++++++++++++++++++++ 1 file changed, 411 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index b8574df..6fcd053 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -9619,6 +9619,336 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(221)–X(230): next classical Ceva-conjugate band (ETC). + // X(221)=X(1)-Ceva of X(56); bary (sin A) sin²(A/2)(cos B+cos C−cos A−1); skip right (∞). + // X(222)=X(7)-Ceva of X(56); bary a² cos A/(1+cos A) [= a²/(1+sec A)]. + // X(223)=X(2)-Ceva of X(57)=comp(X189); bary (sin A) tan(A/2)(cos B+cos C−cos A−1). + // X(224)=X(7)-Ceva of X(63); bary (sin A)[cot B cos²(B/2)+cot C cos²(C/2)−cot A cos²(A/2)] cot A. + // X(225)=X(4)-Ceva of X(65); bary tan A(cos B+cos C); skip right. + // X(226)=X(7)-Ceva of X(65)=comp(X63); bary (b+c)/(b+c−a). + // X(227)=X(10)-Ceva of X(65); bary a(b+c)(cos B+cos C−cos A−1) tan(A/2). + // X(228)=X(3)-Ceva of X(71); bary (sin A sin 2A)(sin B+sin C). + // X(229)=X(7)-Ceva of X(81)=mid(I,X267); u=a(b+c−a)/(b+c), bary a(v+w−u)/(b+c). + // X(230)=X(2)-Ceva of X(114)=mid(X115,X187)=comp(X325); bary a·bc[a²(2a²−b²−c²)+(b²−c²)²]; skip equil. + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let equil = (a - b).abs() < 1e-12 && (b - c).abs() < 1e-12; + let right = ca.abs() < 1e-9 || cb.abs() < 1e-9 || cc.abs() < 1e-9; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(221): skip right (Σbary → 0 / ∞) + if !right { + let f = |ang: f64, cb_: f64, cc_: f64, ca_: f64| { + let s_half = (ang * 0.5).sin(); + s_half * s_half * (cb_ + cc_ - ca_ - 1.0) + }; + let wa = sa * f(g[0], cb, cc, ca); + let wb = sb * f(g[1], cc, ca, cb); + let wc = sc * f(g[2], ca, cb, cc); + push_bary( + &mut out, + "内心外接内切外相似塞瓦", + "X_{221}", + "X(221) = X(1)\\text{-Ceva of }X(56);\\ (\\sin A)\\sin^2\\tfrac{A}{2}(\\cos B+\\cos C-\\cos A-1)", + "X(221):内心对 X(56) 的塞瓦共轭", + "X221", + wa, + wb, + wc, + ); + } + // X(222) + { + let wa = a * a * ca / (1.0 + ca); + let wb = b * b * cb / (1.0 + cb); + let wc = c * c * cc / (1.0 + cc); + push_bary( + &mut out, + "格尔巩外接内切外相似塞瓦", + "X_{222}", + "X(222) = X(7)\\text{-Ceva of }X(56);\\ a^2\\cos A/(1+\\cos A)", + "X(222):格尔巩点对 X(56) 的塞瓦共轭", + "X222", + wa, + wb, + wc, + ); + } + // X(223): also complement of X(189) + { + let f = |ang: f64, cb_: f64, cc_: f64, ca_: f64| { + (ang * 0.5).tan() * (cb_ + cc_ - ca_ - 1.0) + }; + let wa = sa * f(g[0], cb, cc, ca); + let wb = sb * f(g[1], cc, ca, cb); + let wc = sc * f(g[2], ca, cb, cc); + push_bary( + &mut out, + "重心外接内切内相似塞瓦", + "X_{223}", + "X(223) = X(2)\\text{-Ceva of }X(57) = \\mathrm{comp}(X_{189});\\ (\\sin A)\\tan\\tfrac{A}{2}(\\cos B+\\cos C-\\cos A-1)", + "X(223):重心对 X(57) 的塞瓦共轭(X(189) 的补点)", + "X223", + wa, + wb, + wc, + ); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if let Some(x189) = out + .iter() + .rev() + .find(|f| f.label == "X_{189}") + .and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some([*x, *y]), + _ => None, + }) + { + let comp = [ + (3.0 * centroid[0] - x189[0]) / 2.0, + (3.0 * centroid[1] - x189[1]) / 2.0, + ]; + if dist2(xy, comp) < 1e-6 * (1.0 + rr) { + out.push(fact( + "重心外接内切内相似塞瓦", + "X_{223}=\\mathrm{comp}(X_{189})", + "\\text{补点}".into(), + None, + "X(223) = (3G - X(189))/2", + "X(223) 是 X(189) 关于重心的补点", + )); + } + } + } + } + // X(224) + { + let cot = |t: f64| t.cos() / t.sin(); + let f = |aa: f64, bb: f64, cc: f64| { + (cot(bb) * (bb * 0.5).cos().powi(2) + + cot(cc) * (cc * 0.5).cos().powi(2) + - cot(aa) * (aa * 0.5).cos().powi(2)) + * cot(aa) + }; + let wa = sa * f(g[0], g[1], g[2]); + let wb = sb * f(g[1], g[2], g[0]); + let wc = sc * f(g[2], g[0], g[1]); + push_bary( + &mut out, + "格尔巩克劳森等角塞瓦", + "X_{224}", + "X(224) = X(7)\\text{-Ceva of }X(63);\\ (\\sin A)[\\cot B\\cos^2\\tfrac{B}{2}+\\cdots]\\cot A", + "X(224):格尔巩点对克劳森等角点的塞瓦共轭", + "X224", + wa, + wb, + wc, + ); + } + // X(225): skip right (tan A → ∞) + if !right { + let wa = g[0].tan() * (cb + cc); + let wb = g[1].tan() * (cc + ca); + let wc = g[2].tan() * (ca + cb); + push_bary( + &mut out, + "垂心内心奈格尔截点塞瓦", + "X_{225}", + "X(225) = X(4)\\text{-Ceva of }X(65);\\ \\tan A(\\cos B+\\cos C)", + "X(225):垂心对内心–奈格尔截点的塞瓦共轭", + "X225", + wa, + wb, + wc, + ); + } + // X(226): also complement of X(63) + { + let wa = (b + c) / (b + c - a); + let wb = (c + a) / (c + a - b); + let wc = (a + b) / (a + b - c); + push_bary( + &mut out, + "格尔巩内心奈格尔截点塞瓦", + "X_{226}", + "X(226) = X(7)\\text{-Ceva of }X(65) = \\mathrm{comp}(X_{63});\\ (b+c)/(b+c-a)", + "X(226):格尔巩点对内心–奈格尔截点的塞瓦共轭(X(63) 的补点)", + "X226", + wa, + wb, + wc, + ); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if let Some(x63) = out + .iter() + .rev() + .find(|f| f.label == "X_{63}") + .and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some([*x, *y]), + _ => None, + }) + { + let comp = [ + (3.0 * centroid[0] - x63[0]) / 2.0, + (3.0 * centroid[1] - x63[1]) / 2.0, + ]; + if dist2(xy, comp) < 1e-6 * (1.0 + rr) { + out.push(fact( + "格尔巩内心奈格尔截点塞瓦", + "X_{226}=\\mathrm{comp}(X_{63})", + "\\text{补点}".into(), + None, + "X(226) = (3G - X(63))/2", + "X(226) 是 X(63) 关于重心的补点", + )); + } + } + } + } + // X(227) + { + let wa = a * (b + c) * (cb + cc - ca - 1.0) * (g[0] * 0.5).tan(); + let wb = b * (c + a) * (cc + ca - cb - 1.0) * (g[1] * 0.5).tan(); + let wc = c * (a + b) * (ca + cb - cc - 1.0) * (g[2] * 0.5).tan(); + push_bary( + &mut out, + "斯皮克内心奈格尔截点塞瓦", + "X_{227}", + "X(227) = X(10)\\text{-Ceva of }X(65);\\ a(b+c)(\\cos B+\\cos C-\\cos A-1)\\tan\\tfrac{A}{2}", + "X(227):斯皮克点对内心–奈格尔截点的塞瓦共轭", + "X227", + wa, + wb, + wc, + ); + } + // X(228) + { + let wa = (sa * (2.0 * g[0]).sin()) * (sb + sc); + let wb = (sb * (2.0 * g[1]).sin()) * (sc + sa); + let wc = (sc * (2.0 * g[2]).sin()) * (sa + sb); + push_bary( + &mut out, + "外心X71塞瓦", + "X_{228}", + "X(228) = X(3)\\text{-Ceva of }X(71);\\ (\\sin A\\sin 2A)(\\sin B+\\sin C)", + "X(228):外心对 X(71) 的塞瓦共轭", + "X228", + wa, + wb, + wc, + ); + } + // X(229) + { + let ua = a * (b + c - a) / (b + c); + let ub = b * (c + a - b) / (c + a); + let uc = c * (a + b - c) / (a + b); + let wa = a * (ub + uc - ua) / (b + c); + let wb = b * (uc + ua - ub) / (c + a); + let wc = c * (ua + ub - uc) / (a + b); + push_bary( + &mut out, + "格尔巩X81塞瓦", + "X_{229}", + "X(229) = X(7)\\text{-Ceva of }X(81) = \\mathrm{mid}(I,X_{267});\\ a(v+w-u)/(b+c)", + "X(229):格尔巩点对 X(81) 的塞瓦共轭(内心与 X(267) 中点)", + "X229", + wa, + wb, + wc, + ); + } + // X(230): skip equilateral (weights vanish); also mid(X115,X187) + if !equil { + let f = |aa: f64, bb: f64, cc: f64| { + let a2 = aa * aa; + let b2 = bb * bb; + let c2 = cc * cc; + bb * cc * (a2 * (2.0 * a2 - b2 - c2) + (b2 - c2) * (b2 - c2)) + }; + let wa = a * f(a, b, c); + let wb = b * f(b, c, a); + let wc = c * f(c, a, b); + push_bary( + &mut out, + "重心基伯特对跖塞瓦", + "X_{230}", + "X(230) = X(2)\\text{-Ceva of }X(114) = \\mathrm{mid}(X_{115},X_{187});\\ a\\cdot bc[a^2(2a^2-b^2-c^2)+(b^2-c^2)^2]", + "X(230):重心对基伯特对跖点的塞瓦共轭(X(115) 与 X(187) 中点)", + "X230", + wa, + wb, + wc, + ); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + let x115 = out.iter().rev().find(|f| f.label == "X_{115}").and_then(|f| { + match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some([*x, *y]), + _ => None, + } + }); + let x187 = out.iter().rev().find(|f| f.label == "X_{187}").and_then(|f| { + match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some([*x, *y]), + _ => None, + } + }); + if let (Some(p115), Some(p187)) = (x115, x187) { + let mid = [(p115[0] + p187[0]) / 2.0, (p115[1] + p187[1]) / 2.0]; + if dist2(xy, mid) < 1e-6 * (1.0 + rr) { + out.push(fact( + "重心基伯特对跖塞瓦", + "X_{230}=\\mathrm{mid}(X_{115},X_{187})", + "\\text{中点}".into(), + None, + "X(230) = \\mathrm{mid}(X(115),X(187))", + "X(230) 是 X(115) 与 X(187) 的中点", + )); + } + } + } + } + } @@ -15045,6 +15375,87 @@ mod tests { } } + #[test] + fn x221_to_x230_ceva_conjugates() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("内心外接内切外相似塞瓦", "X_{221}", 4.299465240641711, 0.24853369066571662), + ("格尔巩外接内切外相似塞瓦", "X_{222}", 4.443778110944527, 1.4632560768279894), + ("重心外接内切内相似塞瓦", "X_{223}", 3.999165275459098, 0.2036710774716755), + ("格尔巩克劳森等角塞瓦", "X_{224}", 7.940993788819878, 3.331727909625635), + ("垂心内心奈格尔截点塞瓦", "X_{225}", 4.925313706563707, 3.4080197326122943), + ("格尔巩内心奈格尔截点塞瓦", "X_{226}", 4.5498670212765955, 2.1090248407871504), + ("斯皮克内心奈格尔截点塞瓦", "X_{227}", 3.862864077669903, 0.18330867779379764), + ("外心X71塞瓦", "X_{228}", 4.150208623087622, 1.120417991670574), + ("格尔巩X81塞瓦", "X_{229}", 4.685504847481674, 2.3948572831242365), + ("重心基伯特对跖塞瓦", "X_{230}", 8.295973047538201, 6.302331054746105), + ]; + for (grp, lab, ex, ey) in want { + let f = fs.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!((x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, "{} {:?} want {:?}", lab, (x, y), (ex, ey)); + } + assert!(fs.iter().any(|f| f.group == "重心外接内切内相似塞瓦" && f.label.contains("comp"))); + assert!(fs.iter().any(|f| f.group == "格尔巩内心奈格尔截点塞瓦" && f.label.contains("comp"))); + assert!(fs.iter().any(|f| f.group == "重心基伯特对跖塞瓦" && f.label.contains("mid"))); + // mid(X115,X187) Cartesian. + let x115 = fs.iter().find(|f| f.label == "X_{115}").expect("X115"); + let x187 = fs.iter().find(|f| f.label == "X_{187}").expect("X187"); + let x230 = fs.iter().find(|f| f.group == "重心基伯特对跖塞瓦" && f.label == "X_{230}").unwrap(); + let (p115x, p115y) = ptxy(x115); + let (p187x, p187y) = ptxy(x187); + let (p230x, p230y) = ptxy(x230); + assert!((p230x - (p115x + p187x) / 2.0).abs() < 1e-6 && (p230y - (p115y + p187y) / 2.0).abs() < 1e-6); + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!(fs2.iter().any(|f| f.group == grp && f.label == lab), "isos missing {} {}", grp, lab); + } + + // Equilateral: X230 skips; others → G. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (gx3, gy3) = ptxy(g3); + assert!(fs3.iter().all(|f| !(f.group == "重心基伯特对跖塞瓦" && f.label == "X_{230}")), "X230 should skip equil"); + for (grp, lab, ..) in want { + if grp == "重心基伯特对跖塞瓦" { + continue; + } + let f = fs3.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("equil missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!((x - gx3).abs() < 1e-5 && (y - gy3).abs() < 1e-5, "equilateral {} != G {:?}", lab, (x, y)); + } + + // Right 3-4-5: X221 (∞) and X225 (tan) skip; others finite. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().all(|f| !(f.group == "内心外接内切外相似塞瓦" && f.label == "X_{221}")), "X221 should skip right"); + assert!(fs4.iter().all(|f| !(f.group == "垂心内心奈格尔截点塞瓦" && f.label == "X_{225}")), "X225 should skip right"); + for (grp, lab, ..) in want { + if grp == "内心外接内切外相似塞瓦" || grp == "垂心内心奈格尔截点塞瓦" { + continue; + } + assert!(fs4.iter().any(|f| f.group == grp && f.label == lab), "right missing {} {}", grp, lab); + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 9ac5a66d1402e34dc94793568bafceb77955fdce Mon Sep 17 00:00:00 2001 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Content-Transfer-Encoding: 8bit Land X(231)–X(240) in geometry.rs: X(2)-Ceva of X128/X132/X140/X188, X(7)-Ceva of X177, X(4)-Ceva of X185 (=mid(H,X24)), and line conjugates X237–X240 (O-line of G; I-line of X37/X42/X48). Equilateral/right guards and complement/midpoint/Euler identities match prior bands. --- crates/mathcore/src/geometry.rs | 417 +++++++++++++++++++++++++++++++- 1 file changed, 416 insertions(+), 1 deletion(-) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 6fcd053..20ee323 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -9950,7 +9950,334 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } - + // X(231)–X(240): next classical Ceva / line-conjugate band (ETC). + // X(231)=X(2)-Ceva of X(128); bary poly in a⁸…; skip equil (weights→0). + // X(232)=X(2)-Ceva of X(132); bary a²(a²+b²−c²)(a²−b²+c²)(a²b²−b⁴+a²c²−c⁴); skip equil. + // X(233)=X(2)-Ceva of X(140)=comp(X95); bary (a²(b²+c²)−(b²−c²)²)(2a⁴−3a²(b²+c²)+(b²−c²)²). + // X(234)=X(7)-Ceva of X(177); bary (sin A)(cos B/2+cos C/2)(cos B/2 cos C/2)². + // X(235)=X(4)-Ceva of X(185)=mid(H,X24); bary a(sec A−cos(B−C)); skip right (sec/den). + // X(236)=X(2)-Ceva of X(188); bary a(1+sin(A/2))/sin A (Iliev). + // X(237)=X(3)-line conjugate of G; bary a⁴(a²b²−b⁴+a²c²−c⁴); skip equil; on Euler. + // X(238)=X(1)-line conjugate of X(37); bary a(a²−bc); skip equil. + // X(239)=X(1)-line conjugate of X(42); bary a²−bc; skip equil. + // X(240)=X(1)-line conjugate of X(48); bary tan A cos(A+ω); skip right/equil. + { + let (ca, cb, cc) = (g[0].cos(), g[1].cos(), g[2].cos()); + let (sa, sb, sc) = (g[0].sin(), g[1].sin(), g[2].sin()); + let equil = (a - b).abs() < 1e-12 && (b - c).abs() < 1e-12; + let right = ca.abs() < 1e-9 || cb.abs() < 1e-9 || cc.abs() < 1e-9; + let push_bary = |out: &mut Vec, + group: &str, + label: &str, + tip: &str, + zh: &str, + tag: &str, + wa: f64, + wb: f64, + wc: f64| { + let den = wa + wb + wc; + if den.abs() > 1e-12 && wa.is_finite() && wb.is_finite() && wc.is_finite() { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if xy[0].is_finite() && xy[1].is_finite() { + out.push( + fact(group, label, pt(xy[0], xy[1]), None, tip, zh).with(Shape::Point { + x: xy[0], + y: xy[1], + label: tag.into(), + }), + ); + } + } + }; + // X(231): skip equilateral + if !equil { + let f = |aa: f64, bb: f64, cc: f64| { + let (a2, b2, c2) = (aa * aa, bb * bb, cc * cc); + let (a4, b4, c4) = (a2 * a2, b2 * b2, c2 * c2); + let (a6, b6, c6) = (a4 * a2, b4 * b2, c4 * c2); + let (a8, b8, c8) = (a4 * a4, b4 * b4, c4 * c4); + 2.0 * a8 - 4.0 * a6 * b2 + 3.0 * a4 * b4 - 2.0 * a2 * b6 + b8 + - 4.0 * a6 * c2 + 2.0 * a2 * b4 * c2 - 4.0 * b6 * c2 + + 3.0 * a4 * c4 + 2.0 * a2 * b2 * c4 + 6.0 * b4 * c4 + - 2.0 * a2 * c6 - 4.0 * b2 * c6 + c8 + }; + push_bary( + &mut out, + "重心X128塞瓦", + "X_{231}", + "X(231) = X(2)\\text{-Ceva of }X(128);\\ \\text{bary poly }a^8\\cdots", + "X(231):重心对 X(128) 的塞瓦共轭", + "X231", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(232): skip equilateral + if !equil { + let f = |aa: f64, bb: f64, cc: f64| { + let a2 = aa * aa; + let b2 = bb * bb; + let c2 = cc * cc; + a2 * (a2 + b2 - c2) + * (a2 - b2 + c2) + * (a2 * b2 - b2 * b2 + a2 * c2 - c2 * c2) + }; + push_bary( + &mut out, + "重心X132塞瓦", + "X_{232}", + "X(232) = X(2)\\text{-Ceva of }X(132);\\ a^2(a^2+b^2-c^2)(a^2-b^2+c^2)(\\cdots)", + "X(232):重心对 X(132) 的塞瓦共轭", + "X232", + f(a, b, c), + f(b, c, a), + f(c, a, b), + ); + } + // X(233): also complement of X(95) + { + let f = |aa: f64, bb: f64, cc: f64| { + let a2 = aa * aa; + let b2 = bb * bb; + let c2 = cc * cc; + let d = (b2 - c2) * (b2 - c2); + (a2 * (b2 + c2) - d) * (2.0 * a2 * a2 - 3.0 * a2 * (b2 + c2) + d) + }; + let wa = f(a, b, c); + let wb = f(b, c, a); + let wc = f(c, a, b); + push_bary( + &mut out, + "重心X140塞瓦", + "X_{233}", + "X(233) = X(2)\\text{-Ceva of }X(140) = \\mathrm{comp}(X_{95})", + "X(233):重心对 X(140) 的塞瓦共轭(X(95) 的补点)", + "X233", + wa, + wb, + wc, + ); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + if let Some(x95) = out + .iter() + .rev() + .find(|f| f.label == "X_{95}") + .and_then(|f| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some([*x, *y]), + _ => None, + }) + { + let comp = [ + (3.0 * centroid[0] - x95[0]) / 2.0, + (3.0 * centroid[1] - x95[1]) / 2.0, + ]; + if dist2(xy, comp) < 1e-6 * (1.0 + rr) { + out.push(fact( + "重心X140塞瓦", + "X_{233}=\\mathrm{comp}(X_{95})", + "\\text{补点}".into(), + None, + "X(233) = (3G - X(95))/2", + "X(233) 是 X(95) 关于重心的补点", + )); + } + } + } + } + // X(234) + { + let f = |_aa: f64, bb: f64, cc: f64| { + let cbh = (bb * 0.5).cos(); + let cch = (cc * 0.5).cos(); + (cbh + cch) * (cbh * cch).powi(2) + }; + push_bary( + &mut out, + "格尔巩X177塞瓦", + "X_{234}", + "X(234) = X(7)\\text{-Ceva of }X(177);\\ (\\sin A)(\\cos\\tfrac{B}{2}+\\cos\\tfrac{C}{2})(\\cos\\tfrac{B}{2}\\cos\\tfrac{C}{2})^2", + "X(234):格尔巩点对 X(177) 的塞瓦共轭", + "X234", + sa * f(g[0], g[1], g[2]), + sb * f(g[1], g[2], g[0]), + sc * f(g[2], g[0], g[1]), + ); + } + // X(235): skip right; also mid(H,X24) when both present + if !right { + let f = |aa: f64, bb: f64, cc: f64| { + let a2 = aa * aa; + let b2 = bb * bb; + let c2 = cc * cc; + let d = (b2 - c2) * (b2 - c2); + let num = a2 * a2 * (b2 + c2) - 2.0 * a2 * d + d * (b2 + c2); + let den = a2 - b2 - c2; + num / den + }; + let wa = f(a, b, c); + let wb = f(b, c, a); + let wc = f(c, a, b); + push_bary( + &mut out, + "垂心X185塞瓦", + "X_{235}", + "X(235) = X(4)\\text{-Ceva of }X(185) = \\mathrm{mid}(H,X_{24});\\ a(\\sec A-\\cos(B-C))", + "X(235):垂心对 X(185) 的塞瓦共轭(H 与 X(24) 中点)", + "X235", + wa, + wb, + wc, + ); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + let x24 = out.iter().rev().find(|f| f.label == "X_{24}").and_then(|f| { + match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => Some([*x, *y]), + _ => None, + } + }); + if let (Some(p24), true) = (x24, orth[0].is_finite() && orth[1].is_finite()) { + let mid = [(orth[0] + p24[0]) / 2.0, (orth[1] + p24[1]) / 2.0]; + if dist2(xy, mid) < 1e-6 * (1.0 + rr) { + out.push(fact( + "垂心X185塞瓦", + "X_{235}=\\mathrm{mid}(H,X_{24})", + "\\text{中点}".into(), + None, + "X(235) = \\mathrm{mid}(H,X(24))", + "X(235) 是垂心与 X(24) 的中点", + )); + } + } + } + } + // X(236) + { + let wa = a * (1.0 + (g[0] * 0.5).sin()) / sa; + let wb = b * (1.0 + (g[1] * 0.5).sin()) / sb; + let wc = c * (1.0 + (g[2] * 0.5).sin()) / sc; + push_bary( + &mut out, + "重心X188塞瓦", + "X_{236}", + "X(236) = X(2)\\text{-Ceva of }X(188);\\ a(1+\\sin\\tfrac{A}{2})/\\sin A", + "X(236):重心对 X(188) 的塞瓦共轭", + "X236", + wa, + wb, + wc, + ); + } + // X(237): skip equilateral; on Euler + if !equil { + let f = |aa: f64, bb: f64, cc: f64| { + let a2 = aa * aa; + let b2 = bb * bb; + let c2 = cc * cc; + a2 * a2 * (a2 * b2 - b2 * b2 + a2 * c2 - c2 * c2) + }; + let wa = f(a, b, c); + let wb = f(b, c, a); + let wc = f(c, a, b); + push_bary( + &mut out, + "外心重心线共轭", + "X_{237}", + "X(237) = X(3)\\text{-line conjugate of }X(2);\\ a^4(a^2b^2-b^4+a^2c^2-c^4)", + "X(237):外心对重心的线共轭(欧拉线上)", + "X237", + wa, + wb, + wc, + ); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let xy = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + let cross = (centroid[0] - circ[0]) * (xy[1] - circ[1]) + - (centroid[1] - circ[1]) * (xy[0] - circ[0]); + let scale = (centroid[0] - circ[0]).abs() + + (centroid[1] - circ[1]).abs() + + (xy[0] - circ[0]).abs() + + (xy[1] - circ[1]).abs() + + 1e-12; + if cross.abs() / scale < 1e-5 { + out.push(fact( + "外心重心线共轭", + "X_{237}\\in\\text{Euler}", + "\\text{共线}".into(), + None, + "X(237)\\in OH", + "X(237) 在欧拉线上", + )); + } + } + } + // X(238): skip equilateral + if !equil { + push_bary( + &mut out, + "内心X37线共轭", + "X_{238}", + "X(238) = X(1)\\text{-line conjugate of }X(37);\\ a(a^2-bc)", + "X(238):内心对 X(37) 的线共轭", + "X238", + a * (a * a - b * c), + b * (b * b - c * a), + c * (c * c - a * b), + ); + } + // X(239): skip equilateral + if !equil { + push_bary( + &mut out, + "内心X42线共轭", + "X_{239}", + "X(239) = X(1)\\text{-line conjugate of }X(42);\\ a^2-bc", + "X(239):内心对 X(42) 的线共轭", + "X239", + a * a - b * c, + b * b - c * a, + c * c - a * b, + ); + } + // X(240): skip right (tan) and equilateral (cos(A+ω)→0) + if !right && !equil && area > 1e-12 { + let sum_sq = a * a + b * b + c * c; + let tan_w = (4.0 * area) / sum_sq; + let cos_w = 1.0 / (1.0 + tan_w * tan_w).sqrt(); + let sin_w = tan_w * cos_w; + let wa = g[0].tan() * (ca * cos_w - sa * sin_w); + let wb = g[1].tan() * (cb * cos_w - sb * sin_w); + let wc = g[2].tan() * (cc * cos_w - sc * sin_w); + push_bary( + &mut out, + "内心X48线共轭", + "X_{240}", + "X(240) = X(1)\\text{-line conjugate of }X(48);\\ \\tan A\\cos(A+\\omega)", + "X(240):内心对 X(48) 的线共轭", + "X240", + wa, + wb, + wc, + ); + } + } // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. @@ -15456,6 +15783,94 @@ mod tests { } } + #[test] + fn x231_to_x240_ceva_line_conjugates() { + let ptxy = |f: &Fact| match f.shape.as_ref() { + Some(Shape::Point { x, y, .. }) => (*x, *y), + _ => panic!("missing point shape for {}", f.label), + }; + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let want = [ + ("重心X128塞瓦", "X_{231}", 8.79269284386617, 6.099003920714991), + ("重心X132塞瓦", "X_{232}", 5.881308260081088, 7.290749222310604), + ("重心X140塞瓦", "X_{233}", 4.344833517179783, 1.8457230145462953), + ("格尔巩X177塞瓦", "X_{234}", 4.669908110357883, 2.314192564857007), + ("垂心X185塞瓦", "X_{235}", 5.04625, 3.588741126138643), + ("重心X188塞瓦", "X_{236}", 4.37076736265419, 1.8247014772360928), + ("外心重心线共轭", "X_{237}", 8.863779033270559, 12.91480698998983), + ("内心X37线共轭", "X_{238}", 14.333333333333334, 14.200938936093863), + ("内心X42线共轭", "X_{239}", 37.958333333333336, 37.27746470724639), + ("内心X48线共轭", "X_{240}", 6.520821842250415, 8.289102939394008), + ]; + for (grp, lab, ex, ey) in want { + let f = fs.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!((x - ex).abs() < 1e-6 && (y - ey).abs() < 1e-6, "{} {:?} want {:?}", lab, (x, y), (ex, ey)); + } + assert!(fs.iter().any(|f| f.group == "重心X140塞瓦" && f.label.contains("comp"))); + assert!(fs.iter().any(|f| f.group == "垂心X185塞瓦" && f.label.contains("mid"))); + assert!(fs.iter().any(|f| f.group == "外心重心线共轭" && f.label.contains("Euler"))); + // mid(H,X24) + let h = fs.iter().find(|f| f.group == "特殊点" && f.label == "H").expect("H"); + let x24 = fs.iter().find(|f| f.label == "X_{24}").expect("X24"); + let x235 = fs.iter().find(|f| f.group == "垂心X185塞瓦" && f.label == "X_{235}").unwrap(); + let (hx, hy) = ptxy(h); + let (p24x, p24y) = ptxy(x24); + let (p235x, p235y) = ptxy(x235); + assert!((p235x - (hx + p24x) / 2.0).abs() < 1e-6 && (p235y - (hy + p24y) / 2.0).abs() < 1e-6); + // comp(X95) + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let x95 = fs.iter().find(|f| f.label == "X_{95}").expect("X95"); + let x233 = fs.iter().find(|f| f.group == "重心X140塞瓦" && f.label == "X_{233}").unwrap(); + let (gx, gy) = ptxy(g); + let (p95x, p95y) = ptxy(x95); + let (p233x, p233y) = ptxy(x233); + assert!((p233x - (3.0 * gx - p95x) / 2.0).abs() < 1e-6 && (p233y - (3.0 * gy - p95y) / 2.0).abs() < 1e-6); + + // Isosceles 5-5-6: all finite. + let k2 = TriangleKnown { a: Some(5.0), b: Some(5.0), c: Some(6.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + for (grp, lab, ..) in want { + assert!(fs2.iter().any(|f| f.group == grp && f.label == lab), "isos missing {} {}", grp, lab); + } + + // Equilateral: X231/232/237/238/239/240 skip; X233/234/236 → G; X235 finite on Euler. + let k3 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + let g3 = fs3.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let (gx3, gy3) = ptxy(g3); + for skip in ["X_{231}", "X_{232}", "X_{237}", "X_{238}", "X_{239}", "X_{240}"] { + assert!(fs3.iter().all(|f| f.label != skip), "{} should skip equil", skip); + } + for (grp, lab) in [("重心X140塞瓦", "X_{233}"), ("格尔巩X177塞瓦", "X_{234}"), ("重心X188塞瓦", "X_{236}")] { + let f = fs3.iter().find(|f| f.group == grp && f.label == lab).unwrap_or_else(|| panic!("equil missing {} {}", grp, lab)); + let (x, y) = ptxy(f); + assert!((x - gx3).abs() < 1e-5 && (y - gy3).abs() < 1e-5, "equilateral {} != G {:?}", lab, (x, y)); + } + + // Right 3-4-5: X235/X240 skip; others that are non-equil-only remain finite. + let k4 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r4 = triangle_solve(&k4); + assert!(r4.error.is_none(), "{:?}", r4.error); + let fs4 = &r4.cases[0].facts; + assert!(fs4.iter().all(|f| !(f.group == "垂心X185塞瓦" && f.label == "X_{235}")), "X235 should skip right"); + assert!(fs4.iter().all(|f| !(f.group == "内心X48线共轭" && f.label == "X_{240}")), "X240 should skip right"); + for (grp, lab, ..) in want { + if grp == "垂心X185塞瓦" || grp == "内心X48线共轭" { + continue; + } + assert!(fs4.iter().any(|f| f.group == grp && f.label == lab), "right missing {} {}", grp, lab); + } + } + #[test] fn etc_dual_labels_steiner_tarry_parry() { let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; From 17aeb07a2c9d093acb313934a090513f725277a9 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Mon, 2 Nov 2026 18:41:37 +0800 Subject: [PATCH 075/123] 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z%VfK2Z*-V3F_vImtbwe((R65zOjn+*6lQyYF3&^2x#?V4MdVbX^trNq>Rr&QfNuo) zkDW^^<~^H<`(WK={V?%dKc=g5Wm448%3;RRI|eD11X~tTw&JrZQ_?)yE-n|CE%y$j z+^)+=c?rLc6rz}K@jOITOuh;+Va5(=HuCu)&sU-|^YBjmRnV&gv(;hEe>Fyr`AGhx zRDP~nm=WLX03tWs#NBWoX*_tPVQ&wu-+RyiBrw}H+kBK@cVrdh+YQyydw(KBYm37j zC}ST6?nVdNx=$v@H|Q8<^i3+#I27O)#{Jy=hV^w18rHYpyY5WT`B_stQq+FD0G|)c aySr5#^^W`HLREafYD)1DNySG>t@wXKK&zMl From 516d6bd1733fa40f58a511973c4f555a8f8cc886 Mon Sep 17 00:00:00 2001 From: DNT_OF <3174600270@qq.com> Date: Sun, 1 Nov 2026 16:18:13 +0800 Subject: [PATCH 034/123] feat: orthic-of-orthic X24, Lemoine-Ceva X43, line-conj X44, Clawson-isog X63 X24 acute-only (tan A cos 2A); X44 skips equilateral (weights vanish); X63 bary cos A pairs with Clawson X19 and X48. --- crates/mathcore/src/geometry.rs | 158 ++++++++++++++++++++++++++++++++ src/wasm/pkg/mathcore_bg.wasm | Bin 641680 -> 643906 bytes 2 files changed, 158 insertions(+) diff --git a/crates/mathcore/src/geometry.rs b/crates/mathcore/src/geometry.rs index 116208e..33286f4 100644 --- a/crates/mathcore/src/geometry.rs +++ b/crates/mathcore/src/geometry.rs @@ -3607,6 +3607,117 @@ fn triangle_derived(s: [f64; 3], g: [f64; 3], v: [[f64; 2]; 3], names: [&str; 3] } } + // X(24): perspector of ABC and the orthic-of-orthic triangle. + // Bary tan A cos 2A = tan A − sin 2A; skip right/obtuse (tan undefined / sign issues). + { + let cosines = [g[0].cos(), g[1].cos(), g[2].cos()]; + let acute = cosines.iter().all(|&c| c > 1e-9) + && g.iter().all(|&ang| ang > 1e-9 && ang < std::f64::consts::FRAC_PI_2 - 1e-9); + if acute { + let wa = g[0].tan() - (2.0 * g[0]).sin(); + let wb = g[1].tan() - (2.0 * g[1]).sin(); + let wc = g[2].tan() - (2.0 * g[2]).sin(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x24 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "二重垂足透视", + "X_{24}", + pt(x24[0], x24[1]), + None, + "X(24) = (\\tan A\\cos 2A:\\cdots) = (\\tan A-\\sin 2A:\\cdots)", + "X(24):ABC 与二重垂足三角形的透视中心(锐角)", + ).with(Shape::Point { + x: x24[0], + y: x24[1], + label: "X24".into(), + })); + } + } + } + + // X(43): X(6)-Ceva conjugate of I; bary a(ab+ac−bc). + { + let wa = a * (a * b + a * c - b * c); + let wb = b * (b * c + b * a - c * a); + let wc = c * (c * a + c * b - a * b); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x43 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "勒莫恩Ceva", + "X_{43}", + pt(x43[0], x43[1]), + None, + "X(43) = \\bigl(a(ab+ac-bc):\\cdots\\bigr)", + "X(43):勒莫恩点对内心的 Ceva 共轭", + ).with(Shape::Point { + x: x43[0], + y: x43[1], + label: "X43".into(), + })); + } + } + + // X(44): X(6)-line conjugate of I; bary a(b+c−2a). Skip equilateral (all weights 0). + { + let wa = a * (b + c - 2.0 * a); + let wb = b * (c + a - 2.0 * b); + let wc = c * (a + b - 2.0 * c); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x44 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "勒莫恩线共轭", + "X_{44}", + pt(x44[0], x44[1]), + None, + "X(44) = \\bigl(a(b+c-2a):\\cdots\\bigr)", + "X(44):勒莫恩点对内心的线共轭(等边时退化)", + ).with(Shape::Point { + x: x44[0], + y: x44[1], + label: "X44".into(), + })); + } + } + + // X(63): isogonal conjugate of Clawson X(19); bary cos A : cos B : cos C. + // Always finite (Σ cos = 1+r/R > 0); equals G on equilateral. + { + let wa = g[0].cos(); + let wb = g[1].cos(); + let wc = g[2].cos(); + let den = wa + wb + wc; + if den.abs() > 1e-12 { + let x63 = [ + (wa * pa[0] + wb * pb[0] + wc * pc[0]) / den, + (wa * pa[1] + wb * pb[1] + wc * pc[1]) / den, + ]; + out.push(fact( + "克劳森等角", + "X_{63}", + pt(x63[0], x63[1]), + None, + "X(63) = (\\cos A:\\cos B:\\cos C)", + "X(63):克劳森点的等角共轭(亦为 X(48) 的截线伴点)", + ).with(Shape::Point { + x: x63[0], + y: x63[1], + label: "X63".into(), + })); + } + } + // Ceva: concurrent cevians AD, BE, CF satisfy (BD/DC)(CE/EA)(AF/FB) = 1. // Emit the classical families that are always concurrent from three sides alone. { @@ -7116,6 +7227,53 @@ mod tests { assert!(fs3.iter().any(|f| f.group == "截线交点" && f.label == "X_{38}")); } + #[test] + fn x24_x43_x44_x63() { + // Scalene acute 6-7-8. + let k = TriangleKnown { a: Some(6.0), b: Some(7.0), c: Some(8.0), ..Default::default() }; + let r = triangle_solve(&k); + assert!(r.error.is_none(), "{:?}", r.error); + let fs = &r.cases[0].facts; + let x24 = fs.iter().find(|f| f.group == "二重垂足透视" && f.label == "X_{24}").expect("X24"); + let x43 = fs.iter().find(|f| f.group == "勒莫恩Ceva" && f.label == "X_{43}").expect("X43"); + let x44 = fs.iter().find(|f| f.group == "勒莫恩线共轭" && f.label == "X_{44}").expect("X44"); + let x63 = fs.iter().find(|f| f.group == "克劳森等角" && f.label == "X_{63}").expect("X63"); + let g = fs.iter().find(|f| f.group == "特殊点" && f.label == "G").expect("G"); + let o = fs.iter().find(|f| f.group == "特殊点" && f.label == "O").expect("O"); + let i = fs.iter().find(|f| f.group == "特殊点" && f.label == "I").expect("I"); + assert_ne!(x24.value, g.value); + assert_ne!(x24.value, o.value); + assert_ne!(x43.value, i.value); + assert_ne!(x43.value, x44.value); + assert_ne!(x63.value, o.value); // cos A ≠ a² cos A + assert_ne!(x63.value, g.value); + assert_ne!(x44.value, x63.value); + + // Equilateral: X24 present (=G); X44 skipped; X43=X63=G. + let k2 = TriangleKnown { a: Some(2.0), b: Some(2.0), c: Some(2.0), ..Default::default() }; + let r2 = triangle_solve(&k2); + assert!(r2.error.is_none(), "{:?}", r2.error); + let fs2 = &r2.cases[0].facts; + let g2 = fs2.iter().find(|f| f.group == "特殊点" && f.label == "G").unwrap(); + let x24e = fs2.iter().find(|f| f.group == "二重垂足透视" && f.label == "X_{24}").unwrap(); + assert_eq!(x24e.value, g2.value); + assert!(fs2.iter().all(|f| f.group != "勒莫恩线共轭"), "X44 skip equilateral"); + let x43e = fs2.iter().find(|f| f.group == "勒莫恩Ceva" && f.label == "X_{43}").unwrap(); + let x63e = fs2.iter().find(|f| f.group == "克劳森等角" && f.label == "X_{63}").unwrap(); + assert_eq!(x43e.value, g2.value); + assert_eq!(x63e.value, g2.value); + + // Right 3-4-5: X24 skipped (tan∞); X43/X44/X63 present. + let k3 = TriangleKnown { a: Some(3.0), b: Some(4.0), c: Some(5.0), ..Default::default() }; + let r3 = triangle_solve(&k3); + assert!(r3.error.is_none(), "{:?}", r3.error); + let fs3 = &r3.cases[0].facts; + assert!(fs3.iter().all(|f| f.group != "二重垂足透视"), "X24 skip right"); + assert!(fs3.iter().any(|f| f.group == "勒莫恩Ceva" && f.label == "X_{43}")); + assert!(fs3.iter().any(|f| f.group == "勒莫恩线共轭" && f.label == "X_{44}")); + assert!(fs3.iter().any(|f| f.group == "克劳森等角" && f.label == "X_{63}")); + } + #[test] fn british_flag_on_rectangle() { let pts = vec![ diff --git 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