250b61be2c
One zone node at the massive roots' centre of mass owns the only global term (SubzoneReach is the one place the subzone shape is decided: isolated-subzones). WellNode gains Extent and Anchor; a belt orbit's extent is its outermost asteroid. GravityField.SeriesFrom = 0.4 is emitted into the shader template and Gravity.cginc. Tests: the spec's WellLawTests; the old seam test is replaced by TheBandPotentialIsExactInSinglePrecision. GravityFieldParityVerify runs the multi-root fixture (second sun, moon inside the planet's Roche limit, far window): PASS, largest drawn tau 1.228, max error 0.01028 u. The dotnet suite has not been run at this commit. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
96 lines
3.4 KiB
HLSL
96 lines
3.4 KiB
HLSL
#ifndef AETHERIA_GRAVITY_INCLUDED
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#define AETHERIA_GRAVITY_INCLUDED
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// GENERATED by ServerShared/GravityShader.cs from GravityField; do not edit (GravityShaderTests fails on any difference).
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// The lowering of the zone's potential (aetheria-gravity, cut grid-lowering). The law is ServerShared's GravityField
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// and the height is Zone.GetHeight; this file decides nothing. GravityLowering.Lower fills the buffer and the globals
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// from the zone's WellTree (positions from the nodes' rails at the drawn time) each frame.
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// GravityFieldParityVerify renders it and compares every texel with -Zone.GetHeight.
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struct GravityTerm
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{
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float2 position;
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float strength;
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float softening;
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float inner;
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float outer;
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float reference;
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};
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StructuredBuffer<GravityTerm> _GravityWells;
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int _GravityWellCount;
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float _HeightExaggeration;
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// GravityField.OneMinusS and GravityField.S: the band profile B(t) = 1 - S(t) and the order-4 smoothstep, lowest first.
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static const float GravityOneMinusS[8] = { 1, -0, -0, -0, -35, 84, -70, 20 };
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static const float GravityS[8] = { 0, 0, 0, 0, 35, -84, 70, -20 };
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// GravityField.BandClosed: the band's potential at t for tau <= 0.4, per unit strength.
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float gravityBandClosed(float tau, float t)
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{
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float q[7];
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q[6] = GravityOneMinusS[7];
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[unroll] for (int i = 6; i > 0; i--) q[i - 1] = GravityOneMinusS[i] - tau * q[i];
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float remainder = GravityOneMinusS[0] - tau * q[0];
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float whole = 0;
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float part = 0;
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[unroll] for (int j = 6; j >= 0; j--)
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{
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whole = whole + q[j] / (j + 1);
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part = (part + q[j] / (j + 1)) * t;
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}
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return 0.5 * (remainder * log((t + tau) / (1 + tau)) - (whole - part));
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}
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// GravityField.BandSeries: the band's potential at t for tau > 0.4, a series in (1 - t) / (1 + tau).
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float gravityBandSeries(float tau, float t)
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{
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float y = 1 - t;
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float yj[8];
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yj[0] = 1;
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[unroll] for (int j = 1; j < 8; j++) yj[j] = yj[j - 1] * y;
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float w = 1 / (1 + tau);
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float wk = w;
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float yk = y;
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float acc = 0;
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for (int k = 0; k < 40; k++)
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{
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float inner = 0;
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[unroll] for (int m = 4; m < 8; m++) inner += GravityS[m] * yj[m] / (m + k + 1);
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acc += wk * yk * inner;
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wk *= w;
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yk *= y;
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}
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return -0.5 * acc;
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}
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// GravityField.Potential: one band term, per unit strength; the global term when b is infinite.
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float gravityTermPotential(float softening, float a, float b, float r)
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{
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float s = r * r;
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float e2 = softening * softening;
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if (isinf(b)) return 0.5 * log(s + e2);
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float a2 = a * a;
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float b2 = b * b;
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if (s >= b2) return 0;
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float tau = (a2 + e2) / (b2 - a2);
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if (s <= a2) return 0.5 * log((s + e2) / (a2 + e2)) + (tau <= 0.4 ? gravityBandClosed(tau, 0) : gravityBandSeries(tau, 0));
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float t = (s - a2) / (b2 - a2);
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return tau <= 0.4 ? gravityBandClosed(tau, t) : gravityBandSeries(tau, t);
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}
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// Zone.GetHeight at world xz: each term's potential minus its own reference, summed, divided by the exaggeration.
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float gravityHeight(float2 p)
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{
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float result = 0;
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for (int i = 0; i < _GravityWellCount; i++)
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{
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GravityTerm term = _GravityWells[i];
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float r = length(p - term.position);
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if (r < term.outer)
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result += term.strength * gravityTermPotential(term.softening, term.inner, term.outer, r) - term.reference;
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}
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return result / _HeightExaggeration;
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}
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#endif
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