Aetheria/Assets/Scripts/ServerShared/GravityShader.cs

using System.Globalization;
using System.Linq;

/// <summary>
/// The single author of Assets/Shaders/Gravity.cginc, the GPU lowering of the zone's potential. The law is
/// GravityField's (its constants and smoothstep coefficients are read here, not respelled) and the height is
/// Zone.GetHeight: each term's potential minus its reference, summed over the terms whose edge the point is inside,
/// divided by the exaggeration. Unity does not run C# when it imports a shader, so the committed cginc is this output;
/// GravityShaderTests fails unless it equals Source() exactly.
/// To change the shader, change this file and regenerate: AETHERIA_REGENERATE_GRAVITY_CGINC=1 dotnet test --filter GravityShaderTests.
/// </summary>
public static class GravityShader
{
    public const string Path = "Assets/Shaders/Gravity.cginc";

    /// <summary>The whole file, with LF line ends.</summary>
    public static string Source() => Template
        .Replace("@ORDER@", GravityField.Order.ToString(CultureInfo.InvariantCulture))
        .Replace("@N@", GravityField.S.Length.ToString(CultureInfo.InvariantCulture))
        .Replace("@Q@", (GravityField.S.Length - 1).ToString(CultureInfo.InvariantCulture))
        .Replace("@QLAST@", (GravityField.S.Length - 2).ToString(CultureInfo.InvariantCulture))
        .Replace("@SERIESFROM@", GravityField.SeriesFrom.ToString("R", CultureInfo.InvariantCulture))
        .Replace("@SERIES@", GravityField.SeriesTerms.ToString(CultureInfo.InvariantCulture))
        .Replace("@ONEMINUSS@", Coefficients(GravityField.OneMinusS))
        .Replace("@S@", Coefficients(GravityField.S))
        .Replace("\r\n", "\n");

    private static string Coefficients(float[] c) =>
        string.Join(", ", c.Select(x => x.ToString("R", CultureInfo.InvariantCulture)));

    private const string Template = @"#ifndef AETHERIA_GRAVITY_INCLUDED
#define AETHERIA_GRAVITY_INCLUDED

// GENERATED by ServerShared/GravityShader.cs from GravityField; do not edit (GravityShaderTests fails on any difference).
// The lowering of the zone's potential (aetheria-gravity, cut grid-lowering). The law is ServerShared's GravityField
// and the height is Zone.GetHeight; this file decides nothing. GravityLowering.Lower fills the buffer and the globals
// from the zone's WellTree (positions from the nodes' rails at the drawn time) each frame.
// GravityFieldParityVerify renders it and compares every texel with -Zone.GetHeight.

struct GravityTerm
{
    float2 position;
    float strength;
    float softening;
    float inner;
    float outer;
    float reference;
};

StructuredBuffer<GravityTerm> _GravityWells;
int _GravityWellCount;
float _HeightExaggeration;

// GravityField.OneMinusS and GravityField.S: the band profile B(t) = 1 - S(t) and the order-@ORDER@ smoothstep, lowest first.
static const float GravityOneMinusS[@N@] = { @ONEMINUSS@ };
static const float GravityS[@N@] = { @S@ };

// GravityField.BandClosed: the band's potential at t for tau <= @SERIESFROM@, per unit strength.
float gravityBandClosed(float tau, float t)
{
    float q[@Q@];
    q[@QLAST@] = GravityOneMinusS[@Q@];
    [unroll] for (int i = @QLAST@; i > 0; i--) q[i - 1] = GravityOneMinusS[i] - tau * q[i];
    float remainder = GravityOneMinusS[0] - tau * q[0];
    float whole = 0;
    float part = 0;
    [unroll] for (int j = @QLAST@; j >= 0; j--)
    {
        whole = whole + q[j] / (j + 1);
        part = (part + q[j] / (j + 1)) * t;
    }
    return 0.5 * (remainder * log((t + tau) / (1 + tau)) - (whole - part));
}

// GravityField.BandSeries: the band's potential at t for tau > @SERIESFROM@, a series in (1 - t) / (1 + tau).
float gravityBandSeries(float tau, float t)
{
    float y = 1 - t;
    float yj[@N@];
    yj[0] = 1;
    [unroll] for (int j = 1; j < @N@; j++) yj[j] = yj[j - 1] * y;
    float w = 1 / (1 + tau);
    float wk = w;
    float yk = y;
    float acc = 0;
    for (int k = 0; k < @SERIES@; k++)
    {
        float inner = 0;
        [unroll] for (int m = @ORDER@; m < @N@; m++) inner += GravityS[m] * yj[m] / (m + k + 1);
        acc += wk * yk * inner;
        wk *= w;
        yk *= y;
    }
    return -0.5 * acc;
}

// GravityField.Potential: one band term, per unit strength; the global term when b is infinite.
float gravityTermPotential(float softening, float a, float b, float r)
{
    float s = r * r;
    float e2 = softening * softening;
    if (isinf(b)) return 0.5 * log(s + e2);
    float a2 = a * a;
    float b2 = b * b;
    if (s >= b2) return 0;
    float tau = (a2 + e2) / (b2 - a2);
    if (s <= a2) return 0.5 * log((s + e2) / (a2 + e2)) + (tau <= @SERIESFROM@ ? gravityBandClosed(tau, 0) : gravityBandSeries(tau, 0));
    float t = (s - a2) / (b2 - a2);
    return tau <= @SERIESFROM@ ? gravityBandClosed(tau, t) : gravityBandSeries(tau, t);
}

// Zone.GetHeight at world xz: each term's potential minus its own reference, summed, divided by the exaggeration.
float gravityHeight(float2 p)
{
    float result = 0;
    for (int i = 0; i < _GravityWellCount; i++)
    {
        GravityTerm term = _GravityWells[i];
        float r = length(p - term.position);
        if (r < term.outer)
            result += term.strength * gravityTermPotential(term.softening, term.inner, term.outer, r) - term.reference;
    }
    return result / _HeightExaggeration;
}

#endif
";
}