levelset: 2D contours and bounded isovalue ranges

[revarbat]

// bounded range -> a shell
levelset(function(x,y,z) sqrt(x*x+y*y+z*z), bounds=[[-30,-30,-30],[30,30,30]],
         isovalue=[15,20], edge=1);

// 2D -- bounds with 2-vector corners gives a section
levelset(function(x,y) sqrt(x*x+y*y), bounds=[[-30,-30],[30,30]],
         isovalue=[15,20], edge=0.5);      // an annulus

Ranges

isovalue is now a band: a scalar v means [-INF, v] (at or below — the distance-field reading), a range means between, and [lo, INF] is BOSL2's "at or above" idiom. Code forwarding BOSL2's own isovalue argument therefore gets BOSL2's own semantics, with no translation and no invert.

One LevelSet pass either way. A bounded range could be difference(levelset(hi), levelset(lo)) — that works and gives the same answer — but it meshes twice and then booleans.

2D

CrossSection has no contour extraction, only construction from polygons, so this is marching squares. Three details carry the correctness:

• Saddles (cases 5/10) resolved by the cell-centre average. Picking wrong changes the topology — two touching blobs versus one pinched shape — not just the shape.
• Vertices keyed on edge identity, never on float coordinates, so loops close exactly rather than nearly.
• Padding with an outside ring so no contour runs off the box.

Dimension comes from bounds, not from guessing at the field.

Two bugs measurement caught that passing tests would not have

The 2D grid intake never ran. The array was parsed as 3D before bounds was read, so every 2D grid was rejected before the 2D path existed. Parsing is now deferred until the dimension is known.

Padding inflated anything touching the box edge. A half-plane came out 0.9 × spacing too large along every side it touched — an O(h) error, where a closed contour is O(h²) — because the contour landed out in the pad ring:

                before-clip      after-clip
edge=1          872.76           800.000000000
edge=0.5        836.21           800.000000000
edge=0.25       818.06           800.000000000     (analytic 800)

I only found it because the disc converged beautifully while the half-plane didn't — the shape of the error, O(h) versus O(h²), is what pointed at the boundary rather than at the algorithm.

Verified against analytic values

	got	analytic
disc	1256.48	1256.64
annulus	549.782	549.779 — and 2 contours, a real hole
two blobs	401.811	402.124 — and 2 contours
half-plane	800.000000000	800
asymmetric rect	bbox x±5, y±15	pins i→x, j→y

Nineteen new tests. 1075 pass under both engines.

Version 0.50.1 → 0.51.0.

🤖 Generated with Claude Code