levelset(): a solid from a grid or a function(x,y,z)

[revarbat]

// from a grid you built
levelset(field, bounds=[[-25,-25,-25],[25,25,25]], isovalue=20);

// or straight from a function
levelset(function(x,y,z) sqrt(x*x+y*y+z*z),
         bounds=[[-30,-30,-30],[30,30,30]], isovalue=20, edge=1.2);

Implicit surfaces — metaballs, gyroids, anything from a formula or sampled data — previously meant meshing them yourself. BOSL2 does exactly that: isosurface.scad is 217 KB of marching cubes written in the language.

Two intakes, and neither is simply better

	sampling	parallel	accuracy	ceiling
grid field[i][j][k]	0.41 µs	yes	capped by the grid	~550 MB at 200³
function(x,y,z)	0.96 µs	no	Manifold snaps toward the true surface	none

Measured at matched resolution, sphere against analytic:

	grid	function
50³	0.23 s, −0.244%	0.32 s, −0.103%
100³	1.06 s, −0.059%	1.91 s, −0.025%

The function form is ~1.5× slower and ~2.4× more accurate — because Manifold picks its own sample points on a body-centred cubic lattice and can snap toward the surface, where a grid can only be interpolated. That accuracy advantage was not obvious up front and is the reason to offer both rather than pick one.

canParallel is the crux, not a tuning knob: true for a grid because the lambda is pure C++, false for a function because it re-enters the evaluator. Manifold warns that parallel policies "will crash language runtimes with runtime locks that expect to not be called back by unregistered threads."

Against BOSL2, same field

grid	levelset	BOSL2 isosurface()
50³	0.26 s	2.07 s	8.0×
100³	1.15 s	14.59 s	12.7×

Correctness

Sphere volume converging with resolution: −1.04% → −0.24% → −0.09%, genus 0 throughout.

Sixteen tests, including the ones volume alone can't catch: a torus → genus 1, two disjoint blobs → genus −1, and a deliberately asymmetric field for axis order — bounding box comes out exactly [[-5,-10,-20],[5,10,20]], where a symmetric field would pass even with the axes transposed.

Also pinned: an isovalue nothing reaches → empty, and one everything satisfies → the whole bounding box. They look alike from outside and mean opposite things; my first version of that test asserted the wrong one.

Two limits stated rather than glossed

Memory — ~67 bytes/cell on the grid path, so 200³ ≈ 550 MB. The function path has no ceiling.

Accuracy on the grid path is bounded by your grid, not by Manifold. Hence tolerance = -1 is forced (a positive value would make Manifold do extra evaluations that only re-interpolate data already used) and edgeLength defaults to the grid spacing.

The function form requires edge= explicitly: there's no grid to infer it from and the cost is cubic in it, so a silent default would give either a useless mesh or a ten-minute one.

Also fixes UB I introduced while wiring the second intake: the grid lambda's ScalarField& was bound to a null pointer on the function path. Never dereferenced, still undefined, and exactly the kind of thing that works until a sanitizer disagrees.

1062 tests pass under both engines. Version 0.49.0 → 0.50.0.

Not included, deliberately: 2D (CrossSection has no equivalent), adaptive sampling, and BOSL2's metaball specs — this is a primitive for isosurface() to sit on, not a replacement.

🤖 Generated with Claude Code