ScriptableRenderPipeline/com.unity.render-pipelines.high-definition/HDRP/Lighting/SphericalHarmonics.cs

using System;
using UnityEngine;
using UnityEngine.Rendering;

public struct ZonalHarmonicsL2
{
    public float[] coeffs; // Must have the size of 3

    public static ZonalHarmonicsL2 GetHenyeyGreensteinPhaseFunction(float anisotropy)
    {
        float g = anisotropy;

        var zh    = new ZonalHarmonicsL2();
        zh.coeffs = new float[3];

        zh.coeffs[0] = 0.5f * Mathf.Sqrt(1.0f / Mathf.PI);
        zh.coeffs[1] = 0.5f * Mathf.Sqrt(3.0f / Mathf.PI) * g;
        zh.coeffs[2] = 0.5f * Mathf.Sqrt(5.0f / Mathf.PI) * g * g;

        return zh;
    }

    public static ZonalHarmonicsL2 GetCornetteShanksPhaseFunction(float anisotropy)
    {
        float g = anisotropy;

        var zh    = new ZonalHarmonicsL2();
        zh.coeffs = new float[3];

        zh.coeffs[0] = 0.282095f;
        zh.coeffs[1] = 0.293162f * g * (4.0f + (g * g)) / (2.0f + (g * g));
        zh.coeffs[2] = (0.126157f + 1.44179f * (g * g) + 0.324403f * (g * g) * (g * g)) / (2.0f + (g * g));

        return zh;
    }
}

public class SphericalHarmonicMath
{
    // Ref: "Stupid Spherical Harmonics Tricks", p. 6.
    public static SphericalHarmonicsL2 Convolve(SphericalHarmonicsL2 sh, ZonalHarmonicsL2 zh)
    {
        for (int l = 0; l <= 2; l++)
        {
            float n = Mathf.Sqrt((4.0f * Mathf.PI) / (2 * l + 1));
            float k = zh.coeffs[l];
            float p = n * k;

            for (int m = -l; m <= l; m++)
            {
                int i = l * (l + 1) + m;

                for (int c = 0; c < 3; c++)
                {
                    sh[c, i] *= p;
                }
            }
        }

        return sh;
    }

    // Undoes coefficient rescaling due to the convolution with the clamped cosine kernel
    // to obtain the canonical values of SH.
    public static SphericalHarmonicsL2 UndoCosineRescaling(SphericalHarmonicsL2 sh)
    {
        const float c0 = 0.28209479177387814347f; // 1/2  * sqrt(1/Pi)
        const float c1 = 0.32573500793527994772f; // 1/3  * sqrt(3/Pi)
        const float c2 = 0.27313710764801976764f; // 1/8  * sqrt(15/Pi)
        const float c3 = 0.07884789131313000151f; // 1/16 * sqrt(5/Pi)
        const float c4 = 0.13656855382400988382f; // 1/16 * sqrt(15/Pi)

        // Compute the inverse of SphericalHarmonicsL2::kNormalizationConstants.
        // See SetSHEMapConstants() in "Stupid Spherical Harmonics Tricks".
        float[] invNormConsts = { 1 / c0, -1 / c1, 1 / c1, -1 / c1, 1 / c2, -1 / c2, 1 / c3, -1 / c2, 1 / c4 };

        for (int c = 0; c < 3; c++)
        {
            for (int i = 0; i < 9; i++)
            {
                sh[c, i] *= invNormConsts[i];
            }
        }

        return sh;
    }

    // Premultiplies the SH with the polynomial coefficients of SH basis functions,
    // which avoids using any constants during SH evaluation.
    // The resulting evaluation takes the form:
    // (c_0 - c_6) + c_1 y + c_2 z + c_3 x + c_4 x y + c_5 y z + c_6 (3 z^2) + c_7 x z + c_8 (x^2 - y^2)
    public static SphericalHarmonicsL2 PremultiplyCoefficients(SphericalHarmonicsL2 sh)
    {
        const float k0 = 0.28209479177387814347f; // {0, 0} : 1/2 * sqrt(1/Pi)
        const float k1 = 0.48860251190291992159f; // {1, 0} : 1/2 * sqrt(3/Pi)
        const float k2 = 1.09254843059207907054f; // {2,-2} : 1/2 * sqrt(15/Pi)
        const float k3 = 0.31539156525252000603f; // {2, 0} : 1/4 * sqrt(5/Pi)
        const float k4 = 0.54627421529603953527f; // {2, 2} : 1/4 * sqrt(15/Pi)

        float[] ks = { k0, -k1, k1, -k1, k2, -k2, k3, -k2, k4 };

        for (int c = 0; c < 3; c++)
        {
            for (int i = 0; i < 9; i++)
            {
                sh[c, i] *= ks[i];
            }
        }

        return sh;
    }

    // Packs coefficients so that we can use Peter-Pike Sloan's shader code.
    // Does not perform premultiplication with coefficients of SH basis functions.
    // See SetSHEMapConstants() in "Stupid Spherical Harmonics Tricks".
    public static Vector4[] PackCoefficients(SphericalHarmonicsL2 sh)
    {
        Vector4[] coeffs = new Vector4[7];

        // Constant + linear
        for (int c = 0; c < 3; c++)
        {
            coeffs[c].x = sh[c, 3];
            coeffs[c].y = sh[c, 1];
            coeffs[c].z = sh[c, 2];
            coeffs[c].w = sh[c, 0] - sh[c, 6];
        }

        // Quadratic (4/5)
        for (int c = 0; c < 3; c++)
        {
            coeffs[3 + c].x = sh[c, 4];
            coeffs[3 + c].y = sh[c, 5];
            coeffs[3 + c].z = sh[c, 6] * 3.0f;
            coeffs[3 + c].w = sh[c, 7];
        }

        // Quadratic (5)
        coeffs[6].x = sh[0, 8];
        coeffs[6].y = sh[1, 8];
        coeffs[6].z = sh[2, 8];
        coeffs[6].w = 1.0f;

        return coeffs;
    }
}