Lipschitz gyroid#90
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The gyroid implicit function
g(p) = sin(kx·x)·cos(ky·y) + sin(ky·y)·cos(kz·z) + sin(kz·z)·cos(kx·x)
is not a true SDF: its gradient has magnitude up to √3·max(kᵢ), so
unrescaled it overstates 3D distance by that factor. The octree
marching-cubes renderer's |sdf(center)| ≥ half-diagonal pruning then
skips cubes that contain the gyroid surface, producing holes.
GyroidSDF3 grows an invStretch field set at construction:
invStretch = 1 / (√3 · max(|kx|, |ky|, |kz|))
Evaluate multiplies its result by invStretch, giving a Lipschitz-1
scalar field with the same zero level set — safe for octree pruning.
render/gyroid_test.go: watertight tests on box-clipped gyroid at four
scale configurations (isotropic 2 and 3, anisotropic 2-3-4, fine 1) at
80 cells, asserting zero boundary edges.
8 scale configurations (isotropic from 0.7 to 5, plus 3 anisotropic including an extreme case where one axis dominates kMax) clipped by a Box3D — exercises the √3·max(kᵢ) bound across the full range of gyroid frequencies. Plus a separate test that fixes the gyroid scale and varies the clipping shape (sphere, rounded box, cylinder, shell-via-difference) so the gyroid surface meets different boundary geometries. All assert zero boundary edges from the octree at cells=80.
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Fix Gyroid3D Lipschitz under-correction
Fixes one of the bugs in #85.
The bug
Gyroid3Dreturns the gyroid implicit functionwhich is not a signed distance function —
|∇g|is bounded by√3·max(kᵢ)(tight for isotropic scales), not by 1. The octreemarching-cubes renderer treats
Evaluateas a Lipschitz-1 distanceestimator and prunes cubes via
|sdf(center)| ≥ half-diagonal. Becausegis up to√3·max(kᵢ)larger than the true distance, the pruningrule wrongly skips cubes that contain the gyroid surface, producing
holes.
The uniform renderer is fine — it evaluates every cube — so the bug
only shows up under octree.
The fix
GyroidSDF3grows aninvStretch float64field set at construction:Evaluatemultiplies its result byinvStretch, producing aLipschitz-1 scalar field with the same zero level set — the gyroid
surface is unchanged, just the magnitudes scale down enough that
octree pruning becomes sound.
Tests
render/gyroid_test.goclips the (infinite) gyroid with a 10×10×10box and renders via the octree at 80 cells, asserting zero boundary
edges across four scale configurations:
isotropic_2,isotropic_3— symmetric scalesanisotropic_2_3_4— non-isotropic, exerciseskMaxselectionfine_1— high-frequency case wherekMaxis largeAll pass on macOS.
Architecture-specific note
Same family of bug as the high-taper screw rendering issue from #84 —
non-1-Lipschitz SDF that the octree's
isEmptyrule wrongly trusts.The conservative
√3·max(kᵢ)bound is loose enough to absorb 1-ulpFMA/FTZ rounding differences between architectures, so this should
pass equally on x86_64 and Apple Silicon.