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cultmath: span stage value and gradient against an independent octave assembly

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SpanStageGradientMatchesDifferences now also compares field.w and field.xyz with an octave sum assembled
in the test from Stage.Point and snoise_grad, so shift, offset, octaveStep, M, lacunarity and gain are pinned
numerically, which a value/gradient self-consistency check cannot do.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
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Meta Vens 2026-10-14 20:53:37 +02:00
commit 6a3132f139
1 changed files with 22 additions and 0 deletions
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packages/cultmath/tests/CultMath.Tests/SpanStageTests.cs
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@ -217,6 +217,28 @@ public sealed class SpanStageTests
var span = Span.Draw(random, q, 0.1f, 0.1f);
SpanNoise At(float3 p) => ridged ? stage.Ridged(p, span.Velocity, span.Speed, span.AccelerationBound, span.HalfLength) : stage.Fbm(p, span.Velocity, span.Speed, span.AccelerationBound, span.HalfLength);
var centre = At(q);
// The value and gradient from an independent assembly of the octaves: pins shift, offset, octaveStep,
// M, lacunarity and gain themselves, which a value/gradient self-consistency check cannot see.
var matrix = stage.Matrix();
var referenceValue = 0.0;
var referenceGradient = new double[3];
for (var o = 0; o < stage.Octaves; o++)
{
var n = snoise_grad(stage.Point(q, o));
var sign = ridged ? -Math.Sign(n.w) : 1.0;
referenceValue += stage.Amplitude(o) * (ridged ? 1.0 - Math.Abs(n.w) : n.w);
var g = new double[] { n.x, n.y, n.z };
for (var i = 0; i < 3; i++)
for (var j = 0; j < 3; j++)
referenceGradient[i] += sign * stage.Amplitude(o) * stage.Scale(o) * matrix[i, j] * g[j];
}
var weight = 0.0;
for (var o = 0; o < stage.Octaves; o++)
weight += stage.Amplitude(o) * stage.Scale(o) * stage.Norm();
Assert.True(Math.Abs(referenceValue - centre.field.w) <= 5.0e-4 * (1.0 + weight), $"stage {stage}: the value is {centre.field.w:R}, an independent octave sum gives {referenceValue:R}");
for (var i = 0; i < 3; i++)
Assert.True(Math.Abs(referenceGradient[i] - centre.field[i]) <= 5.0e-3 * (1.0 + weight), $"stage {stage}: gradient {"xyz"[i]} is {centre.field[i]:R}, an independent octave sum gives {referenceGradient[i]:R}");
// A step of 0.02 in the noise space of the fastest octave.
var fastest = stage.Norm() * Math.Pow(stage.Lacunarity, stage.Octaves - 1);
var h = (float)(0.02 / fastest);