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Background scene: phacelleGradBound 6.3 -> 7.0 from Libby's measured sup

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Libby measured sup |grad| 6.63 at |side| = 1.5, n = 0 (CultLib PR #1 head
990521b3); 7.0 adds margin. The shader passes roughness 0 as a literal, so no
1/(1-n) factor is needed; the comment records it. Pass 1 under SwiftShader:
terrain 288.8 ms vs 287.5 at 960x540 level 0, 75.3 vs 75.7 at level 3 (noise).

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
This commit is contained in:
Nibu 2026-11-01 06:37:01 +00:00
commit b2d6d32cc4
2 changed files with 9 additions and 9 deletions
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7
src/app/features/scene/README.md
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@ -38,10 +38,9 @@ computed from `SNOISE_LIPSCHITZ` (CultMath's constant for `snoise`) in `world.ts
envelope (fbm plus the erosion amplitude) the step uses the envelope's bound alone and Phacelle is
not evaluated.
- The Phacelle gradient bound `phacelleGradBound` (6.3) is **an empirical probe, not a proof**:
the maximum `|grad|` of the cos component over 4,194,304 random points (5.04) times 1.25
(`harness/scene/drive.cjs phacelle`). Replace it with Libby's bound; until then the march is
only as safe as that probe.
- The Phacelle gradient bound `phacelleGradBound` (7.0) is Libby's measured sup (6.63 at
|side| = 1.5, n = 0, CultLib PR #1 head 990521b3) plus margin: a measurement, not a proof.
The shader fixes roughness n = 0; a nonzero n needs the bound divided by (1 - n).
- The bound makes grazing rays crawl. A ray that exhausts its steps while still below the highest
terrain is ended as a distant surface (fog hides it). That is a visible approximation, not a
hit proven by the march.

11
src/app/features/scene/world.ts
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@ -23,11 +23,12 @@ export const WORLD = {
// The stripe wave vector and normalization the terrain feeds cultmath_phacelle.
erodeSide: [1.7, 0, 1] as const,
erodeNorm: 0.5,
// Lipschitz bound of the phasor's cos component, NOT a proof: max |grad| over 4,194,304 random
// points of the z = 0 slice with the side and norm above was 5.04 (`drive.cjs phacelle`,
// 2026-10-31), x 1.25. |value| <= 1 holds by construction (the output is a normalized phasor).
// Replace with the bound Libby supplies; until then the march is as safe as that probe.
phacelleGradBound: 6.3,
// Bound on |grad| of the phasor's cos component for the side and norm above. Libby measured a
// sup of 6.63 at |side| = 1.5, n = 0 (CultLib PR #1 head 990521b3); 7.0 adds margin. The
// shader passes roughness n = 0 as a literal, so the doc envelope max(10, 1.25|side|)/(1-n)
// needs no 1/(1-n) factor here; if n ever becomes nonzero, divide this bound by (1 - n).
// |value| <= 1 holds by construction (the output is a normalized phasor).
phacelleGradBound: 7.0,
// World tree at the origin.
tree: {
trunkHeight: 38,