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cultmath: span fold test for the acceleration term alone

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SpanFoldCoversAccelerationAlone draws spans with zero midpoint velocity and an acceleration along the gradient
that carries n across zero, so the fold's acceleration term and its gradient bound are the only thing holding
the branch departure under fold; two hand mutants survived without it.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
This commit is contained in:
Meta Vens 2026-10-14 21:03:52 +02:00
commit f722f7c177
1 changed files with 47 additions and 0 deletions
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47
packages/cultmath/tests/CultMath.Tests/SpanStageTests.cs
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@ -453,4 +453,51 @@ public sealed class SpanStageTests
Assert.True(found >= 5, $"only {found} calm midpoints found");
}
/// <summary>
/// The fold's acceleration term, alone: the midpoint velocity is zero and the acceleration points along
/// the gradient, against the sign of n, so n reaches zero and crosses it on the way to the span's ends
/// by acceleration only. Without the acceleration term (or with the gradient bound under the gradient
/// the path reaches) the departure from the midpoint branch exceeds fold.
/// </summary>
[Fact]
public void SpanFoldCoversAccelerationAlone()
{
var random = new System.Random(0xACCE1);
var identity = new Stage(1.0f, 1.0f, new float3(0.0f, 0.0f, 0.0f), new float3(0.0f, 0.0f, 0.0f), new float3(0.0f, 0.0f, 0.0f), new float3(0.0f, 0.0f, 0.0f), 1, 2.0f, 0.5f);
var still = new float3(0.0f, 0.0f, 0.0f);
var cases = 0;
var crossings = 0;
var tightest = double.MaxValue;
for (var trial = 0; trial < 200_000 && cases < 150; trial++)
{
var q = Vector(random, -60.0f, 60.0f);
var n = snoise_grad(q);
var gradient = new float3(n.x, n.y, n.z);
var halfLength = Uniform(random, 0.05f, 0.15f);
var acceleration = Uniform(random, 4.0f, 12.0f);
// n at the midpoint close enough to zero that the acceleration alone carries it across.
if (length(gradient) < 1.5f || abs(n.w) > 0.4f * length(gradient) * acceleration * halfLength * halfLength * 0.5f)
continue;
var c = -(float)Math.Sign(n.w) * acceleration * normalize(gradient);
var span = new Span(q, still, c, acceleration * halfLength, acceleration, halfLength);
var fold = identity.Ridged(q, still, span.Speed, acceleration, halfLength).fold;
var departure = 0.0;
for (var s = 0; s < 64; s++)
{
var value = (double)snoise(span.At(halfLength * (2.0f * s / 63 - 1.0f)));
departure = Math.Max(departure, Math.Abs(Math.Sign(n.w) * value - Math.Abs(value)));
}
if (departure > 0.0)
crossings++;
Assert.True(departure <= fold * (1.0 + 1.0e-3), $"q {q}, acceleration {acceleration:R}, half-length {halfLength:R}: the branch departure is {departure:R}, above fold {fold:R}");
if (departure > 0.0)
tightest = Math.Min(tightest, departure / fold);
cases++;
}
Assert.True(crossings >= 100, $"only {crossings} of {cases} paths crossed zero by acceleration alone");
output.WriteLine($"IV-REPORT span fold, acceleration only: {crossings} of {cases} paths cross zero, tightest departure / fold {tightest:R}");
}
}