using System; namespace UnityEngine.Experimental.Rendering.HDPipeline { [GenerateHLSL] public class DiffusionProfileConstants { public const int DIFFUSION_PROFILE_COUNT = 16; // Max. number of profiles, including the slot taken by the neutral profile public const int DIFFUSION_PROFILE_NEUTRAL_ID = 0; // Does not result in blurring public const int SSS_N_SAMPLES_NEAR_FIELD = 55; // Used for extreme close ups; must be a Fibonacci number public const int SSS_N_SAMPLES_FAR_FIELD = 21; // Used at a regular distance; must be a Fibonacci number public const int SSS_LOD_THRESHOLD = 4; // The LoD threshold of the near-field kernel (in pixels) // Old SSS Model >>> public const int SSS_BASIC_N_SAMPLES = 11; // Must be an odd number public const int SSS_BASIC_DISTANCE_SCALE = 3; // SSS distance units per centimeter // <<< Old SSS Model } [Serializable] public sealed class DiffusionProfile { public enum TexturingMode : uint { PreAndPostScatter = 0, PostScatter = 1 } public enum TransmissionMode : uint { Regular = 0, ThinObject = 1 } public string name; [ColorUsage(false, true)] public Color scatteringDistance; // Per color channel (no meaningful units) [ColorUsage(false)] public Color transmissionTint; // Color, 0 to 1 public TexturingMode texturingMode; public TransmissionMode transmissionMode; public Vector2 thicknessRemap; // X = min, Y = max (in millimeters) public float worldScale; // Size of the world unit in meters public float ior; // 1.4 for skin (mean ~0.028) // Old SSS Model >>> [ColorUsage(false, true)] public Color scatterDistance1; [ColorUsage(false, true)] public Color scatterDistance2; [Range(0f, 1f)] public float lerpWeight; // <<< Old SSS Model public Vector3 shapeParam { get; private set; } // RGB = shape parameter: S = 1 / D public float maxRadius { get; private set; } // In millimeters public Vector2[] filterKernelNearField { get; private set; } // X = radius, Y = reciprocal of the PDF public Vector2[] filterKernelFarField { get; private set; } // X = radius, Y = reciprocal of the PDF public Vector4 halfRcpWeightedVariances { get; private set; } public Vector4[] filterKernelBasic { get; private set; } public DiffusionProfile(string name) { this.name = name; scatteringDistance = Color.grey; transmissionTint = Color.white; texturingMode = TexturingMode.PreAndPostScatter; transmissionMode = TransmissionMode.ThinObject; thicknessRemap = new Vector2(0f, 5f); worldScale = 1f; ior = 1.4f; // TYpical value for skin specular reflectance // Old SSS Model >>> scatterDistance1 = new Color(0.3f, 0.3f, 0.3f, 0f); scatterDistance2 = new Color(0.5f, 0.5f, 0.5f, 0f); lerpWeight = 1f; // <<< Old SSS Model } public void Validate() { thicknessRemap.y = Mathf.Max(thicknessRemap.y, 0f); thicknessRemap.x = Mathf.Clamp(thicknessRemap.x, 0f, thicknessRemap.y); worldScale = Mathf.Max(worldScale, 0.001f); ior = Mathf.Clamp(ior, 1.0f, 2.0f); // Old SSS Model >>> scatterDistance1 = new Color { r = Mathf.Max(0.05f, scatterDistance1.r), g = Mathf.Max(0.05f, scatterDistance1.g), b = Mathf.Max(0.05f, scatterDistance1.b), a = 0.0f }; scatterDistance2 = new Color { r = Mathf.Max(0.05f, scatterDistance2.r), g = Mathf.Max(0.05f, scatterDistance2.g), b = Mathf.Max(0.05f, scatterDistance2.b), a = 0f }; // <<< Old SSS Model UpdateKernel(); } // Ref: Approximate Reflectance Profiles for Efficient Subsurface Scattering by Pixar. public void UpdateKernel() { if (filterKernelNearField == null || filterKernelNearField.Length != DiffusionProfileConstants.SSS_N_SAMPLES_NEAR_FIELD) filterKernelNearField = new Vector2[DiffusionProfileConstants.SSS_N_SAMPLES_NEAR_FIELD]; if (filterKernelFarField == null || filterKernelFarField.Length != DiffusionProfileConstants.SSS_N_SAMPLES_FAR_FIELD) filterKernelFarField = new Vector2[DiffusionProfileConstants.SSS_N_SAMPLES_FAR_FIELD]; // Clamp to avoid artifacts. shapeParam = new Vector3( 1f / Mathf.Max(0.001f, scatteringDistance.r), 1f / Mathf.Max(0.001f, scatteringDistance.g), 1f / Mathf.Max(0.001f, scatteringDistance.b) ); // We importance sample the color channel with the widest scattering distance. float s = Mathf.Min(shapeParam.x, shapeParam.y, shapeParam.z); // Importance sample the normalized diffuse reflectance profile for the computed value of 's'. // ------------------------------------------------------------------------------------ // R[r, phi, s] = s * (Exp[-r * s] + Exp[-r * s / 3]) / (8 * Pi * r) // PDF[r, phi, s] = r * R[r, phi, s] // CDF[r, s] = 1 - 1/4 * Exp[-r * s] - 3/4 * Exp[-r * s / 3] // ------------------------------------------------------------------------------------ // Importance sample the near field kernel. for (int i = 0, n = DiffusionProfileConstants.SSS_N_SAMPLES_NEAR_FIELD; i < n; i++) { float p = (i + 0.5f) * (1f / n); float r = DisneyProfileCdfInverse(p, s); // N.b.: computation of normalized weights, and multiplication by the surface albedo // of the actual geometry is performed at runtime (in the shader). filterKernelNearField[i].x = r; filterKernelNearField[i].y = 1f / DisneyProfilePdf(r, s); } // Importance sample the far field kernel. for (int i = 0, n = DiffusionProfileConstants.SSS_N_SAMPLES_FAR_FIELD; i < n; i++) { float p = (i + 0.5f) * (1f / n); float r = DisneyProfileCdfInverse(p, s); // N.b.: computation of normalized weights, and multiplication by the surface albedo // of the actual geometry is performed at runtime (in the shader). filterKernelFarField[i].x = r; filterKernelFarField[i].y = 1f / DisneyProfilePdf(r, s); } maxRadius = filterKernelFarField[DiffusionProfileConstants.SSS_N_SAMPLES_FAR_FIELD - 1].x; // Old SSS Model >>> UpdateKernelAndVarianceData(); // <<< Old SSS Model } // Old SSS Model >>> public void UpdateKernelAndVarianceData() { const int kNumSamples = DiffusionProfileConstants.SSS_BASIC_N_SAMPLES; const int kDistanceScale = DiffusionProfileConstants.SSS_BASIC_DISTANCE_SCALE; if (filterKernelBasic == null || filterKernelBasic.Length != kNumSamples) filterKernelBasic = new Vector4[kNumSamples]; // Apply the three-sigma rule, and rescale. var stdDev1 = ((1f / 3f) * kDistanceScale) * scatterDistance1; var stdDev2 = ((1f / 3f) * kDistanceScale) * scatterDistance2; // Our goal is to blur the image using a filter which is represented // as a product of a linear combination of two normalized 1D Gaussians // as suggested by Jimenez et al. in "Separable Subsurface Scattering". // A normalized (i.e. energy-preserving) 1D Gaussian with the mean of 0 // is defined as follows: G1(x, v) = exp(-x * x / (2 * v)) / sqrt(2 * Pi * v), // where 'v' is variance and 'x' is the radial distance from the origin. // Using the weight 'w', our 1D and the resulting 2D filters are given as: // A1(v1, v2, w, x) = G1(x, v1) * (1 - w) + G1(r, v2) * w, // A2(v1, v2, w, x, y) = A1(v1, v2, w, x) * A1(v1, v2, w, y). // The resulting filter function is a non-Gaussian PDF. // It is separable by design, but generally not radially symmetric. // N.b.: our scattering distance is rather limited. Therefore, in order to allow // for a greater range of standard deviation values for flatter profiles, // we rescale the world using 'distanceScale', effectively reducing the SSS // distance units from centimeters to (1 / distanceScale). // Find the widest Gaussian across 3 color channels. float maxStdDev1 = Mathf.Max(stdDev1.r, stdDev1.g, stdDev1.b); float maxStdDev2 = Mathf.Max(stdDev2.r, stdDev2.g, stdDev2.b); var weightSum = Vector3.zero; float step = 1f / (kNumSamples - 1); // Importance sample the linear combination of two Gaussians. for (int i = 0; i < kNumSamples; i++) { // Generate 'u' on (0, 0.5] and (0.5, 1). float u = (i <= kNumSamples / 2) ? 0.5f - i * step // The center and to the left : i * step; // From the center to the right u = Mathf.Clamp(u, 0.001f, 0.999f); float pos = GaussianCombinationCdfInverse(u, maxStdDev1, maxStdDev2, lerpWeight); float pdf = GaussianCombination(pos, maxStdDev1, maxStdDev2, lerpWeight); Vector3 val; val.x = GaussianCombination(pos, stdDev1.r, stdDev2.r, lerpWeight); val.y = GaussianCombination(pos, stdDev1.g, stdDev2.g, lerpWeight); val.z = GaussianCombination(pos, stdDev1.b, stdDev2.b, lerpWeight); // We do not divide by 'numSamples' since we will renormalize, anyway. filterKernelBasic[i].x = val.x * (1 / pdf); filterKernelBasic[i].y = val.y * (1 / pdf); filterKernelBasic[i].z = val.z * (1 / pdf); filterKernelBasic[i].w = pos; weightSum.x += filterKernelBasic[i].x; weightSum.y += filterKernelBasic[i].y; weightSum.z += filterKernelBasic[i].z; } // Renormalize the weights to conserve energy. for (int i = 0; i < kNumSamples; i++) { filterKernelBasic[i].x *= 1 / weightSum.x; filterKernelBasic[i].y *= 1 / weightSum.y; filterKernelBasic[i].z *= 1 / weightSum.z; } Vector4 weightedStdDev; weightedStdDev.x = Mathf.Lerp(stdDev1.r, stdDev2.r, lerpWeight); weightedStdDev.y = Mathf.Lerp(stdDev1.g, stdDev2.g, lerpWeight); weightedStdDev.z = Mathf.Lerp(stdDev1.b, stdDev2.b, lerpWeight); weightedStdDev.w = Mathf.Lerp(maxStdDev1, maxStdDev2, lerpWeight); // Store (1 / (2 * WeightedVariance)) per color channel. // Warning: do not use halfRcpWeightedVariances.Set(). It will not work. halfRcpWeightedVariances = new Vector4(0.5f / (weightedStdDev.x * weightedStdDev.x), 0.5f / (weightedStdDev.y * weightedStdDev.y), 0.5f / (weightedStdDev.z * weightedStdDev.z), 0.5f / (weightedStdDev.w * weightedStdDev.w)); } // <<< Old SSS Model static float DisneyProfile(float r, float s) { return s * (Mathf.Exp(-r * s) + Mathf.Exp(-r * s * (1.0f / 3.0f))) / (8.0f * Mathf.PI * r); } static float DisneyProfilePdf(float r, float s) { return r * DisneyProfile(r, s); } static float DisneyProfileCdf(float r, float s) { return 1.0f - 0.25f * Mathf.Exp(-r * s) - 0.75f * Mathf.Exp(-r * s * (1.0f / 3.0f)); } static float DisneyProfileCdfDerivative1(float r, float s) { return 0.25f * s * Mathf.Exp(-r * s) * (1.0f + Mathf.Exp(r * s * (2.0f / 3.0f))); } static float DisneyProfileCdfDerivative2(float r, float s) { return (-1.0f / 12.0f) * s * s * Mathf.Exp(-r * s) * (3.0f + Mathf.Exp(r * s * (2.0f / 3.0f))); } // The CDF is not analytically invertible, so we use Halley's Method of root finding. // { f(r, s, p) = CDF(r, s) - p = 0 } with the initial guess { r = (10^p - 1) / s }. static float DisneyProfileCdfInverse(float p, float s) { // Supply the initial guess. float r = (Mathf.Pow(10f, p) - 1f) / s; float t = float.MaxValue; while (true) { float f0 = DisneyProfileCdf(r, s) - p; float f1 = DisneyProfileCdfDerivative1(r, s); float f2 = DisneyProfileCdfDerivative2(r, s); float dr = f0 / (f1 * (1f - f0 * f2 / (2f * f1 * f1))); if (Mathf.Abs(dr) < t) { r = r - dr; t = Mathf.Abs(dr); } else { // Converged to the best result. break; } } return r; } // Old SSS Model >>> static float Gaussian(float x, float stdDev) { float variance = stdDev * stdDev; return Mathf.Exp(-x * x / (2 * variance)) / Mathf.Sqrt(2 * Mathf.PI * variance); } static float GaussianCombination(float x, float stdDev1, float stdDev2, float lerpWeight) { return Mathf.Lerp(Gaussian(x, stdDev1), Gaussian(x, stdDev2), lerpWeight); } static float RationalApproximation(float t) { // Abramowitz and Stegun formula 26.2.23. // The absolute value of the error should be less than 4.5 e-4. float[] c = { 2.515517f, 0.802853f, 0.010328f }; float[] d = { 1.432788f, 0.189269f, 0.001308f }; return t - ((c[2] * t + c[1]) * t + c[0]) / (((d[2] * t + d[1]) * t + d[0]) * t + 1.0f); } // Ref: https://www.johndcook.com/blog/csharp_phi_inverse/ static float NormalCdfInverse(float p, float stdDev) { float x; if (p < 0.5) { // F^-1(p) = - G^-1(p) x = -RationalApproximation(Mathf.Sqrt(-2f * Mathf.Log(p))); } else { // F^-1(p) = G^-1(1-p) x = RationalApproximation(Mathf.Sqrt(-2f * Mathf.Log(1f - p))); } return x * stdDev; } static float GaussianCombinationCdfInverse(float p, float stdDev1, float stdDev2, float lerpWeight) { return Mathf.Lerp(NormalCdfInverse(p, stdDev1), NormalCdfInverse(p, stdDev2), lerpWeight); } // <<< Old SSS Model } public sealed class DiffusionProfileSettings : ScriptableObject { public DiffusionProfile[] profiles; [NonSerialized] public uint texturingModeFlags; // 1 bit/profile; 0 = PreAndPostScatter, 1 = PostScatter [NonSerialized] public uint transmissionFlags; // 2 bit/profile; 0 = inf. thick, 1 = thin, 2 = regular [NonSerialized] public Vector4[] thicknessRemaps; // Remap: 0 = start, 1 = end - start [NonSerialized] public Vector4[] worldScales; // X = meters per world unit; Y = world units per meter [NonSerialized] public Vector4[] shapeParams; // RGB = S = 1 / D, A = filter radius [NonSerialized] public Vector4[] transmissionTintsAndFresnel0; // RGB = color, A = fresnel0 [NonSerialized] public Vector4[] disabledTransmissionTintsAndFresnel0; // RGB = black, A = fresnel0 - For debug to remove the transmission [NonSerialized] public Vector4[] filterKernels; // XY = near field, ZW = far field; 0 = radius, 1 = reciprocal of the PDF // Old SSS Model >>> [NonSerialized] public Vector4[] halfRcpWeightedVariances; [NonSerialized] public Vector4[] halfRcpVariancesAndWeights; [NonSerialized] public Vector4[] filterKernelsBasic; // <<< Old SSS Model public DiffusionProfile this[int index] { get { if (index >= DiffusionProfileConstants.DIFFUSION_PROFILE_COUNT - 1) throw new IndexOutOfRangeException("index"); return profiles[index]; } } void OnEnable() { // The neutral profile is not a part of the array. int profileArraySize = DiffusionProfileConstants.DIFFUSION_PROFILE_COUNT - 1; if (profiles != null && profiles.Length != profileArraySize) Array.Resize(ref profiles, profileArraySize); if (profiles == null) profiles = new DiffusionProfile[profileArraySize]; for (int i = 0; i < profileArraySize; i++) { if (profiles[i] == null) profiles[i] = new DiffusionProfile("Profile " + (i + 1)); profiles[i].Validate(); } ValidateArray(ref thicknessRemaps, DiffusionProfileConstants.DIFFUSION_PROFILE_COUNT); ValidateArray(ref worldScales, DiffusionProfileConstants.DIFFUSION_PROFILE_COUNT); ValidateArray(ref shapeParams, DiffusionProfileConstants.DIFFUSION_PROFILE_COUNT); ValidateArray(ref transmissionTintsAndFresnel0, DiffusionProfileConstants.DIFFUSION_PROFILE_COUNT); ValidateArray(ref disabledTransmissionTintsAndFresnel0, DiffusionProfileConstants.DIFFUSION_PROFILE_COUNT); ValidateArray(ref filterKernels, DiffusionProfileConstants.DIFFUSION_PROFILE_COUNT * DiffusionProfileConstants.SSS_N_SAMPLES_NEAR_FIELD); // Old SSS Model >>> ValidateArray(ref halfRcpWeightedVariances, DiffusionProfileConstants.DIFFUSION_PROFILE_COUNT); ValidateArray(ref halfRcpVariancesAndWeights, DiffusionProfileConstants.DIFFUSION_PROFILE_COUNT * 2); ValidateArray(ref filterKernelsBasic, DiffusionProfileConstants.DIFFUSION_PROFILE_COUNT * DiffusionProfileConstants.SSS_BASIC_N_SAMPLES); Debug.Assert(DiffusionProfileConstants.DIFFUSION_PROFILE_NEUTRAL_ID <= 32, "Transmission and Texture flags (32-bit integer) cannot support more than 32 profiles."); UpdateCache(); } static void ValidateArray(ref T[] array, int len) { if (array == null || array.Length != len) array = new T[len]; } public void UpdateCache() { for (int i = 0; i < DiffusionProfileConstants.DIFFUSION_PROFILE_COUNT - 1; i++) { UpdateCache(i); } // Fill the neutral profile. int neutralId = DiffusionProfileConstants.DIFFUSION_PROFILE_NEUTRAL_ID; worldScales[neutralId] = Vector4.one; shapeParams[neutralId] = Vector4.zero; for (int j = 0, n = DiffusionProfileConstants.SSS_N_SAMPLES_NEAR_FIELD; j < n; j++) { filterKernels[n * neutralId + j].x = 0f; filterKernels[n * neutralId + j].y = 1f; filterKernels[n * neutralId + j].z = 0f; filterKernels[n * neutralId + j].w = 1f; } // Old SSS Model >>> halfRcpWeightedVariances[neutralId] = Vector4.one; for (int j = 0, n = DiffusionProfileConstants.SSS_BASIC_N_SAMPLES; j < n; j++) { filterKernelsBasic[n * neutralId + j] = Vector4.one; filterKernelsBasic[n * neutralId + j].w = 0f; } // <<< Old SSS Model } public void UpdateCache(int p) { // 'p' is the profile array index. 'i' is the index in the shader (accounting for the neutral profile). int i = p + 1; // Erase previous value (This need to be done here individually as in the SSS editor we edit individual component) uint mask = 1u << i; texturingModeFlags &= ~mask; mask = 1u << i; transmissionFlags &= ~mask; texturingModeFlags |= (uint)profiles[p].texturingMode << i; transmissionFlags |= (uint)profiles[p].transmissionMode << i; thicknessRemaps[i] = new Vector4(profiles[p].thicknessRemap.x, profiles[p].thicknessRemap.y - profiles[p].thicknessRemap.x, 0f, 0f); worldScales[i] = new Vector4(profiles[p].worldScale, 1.0f / profiles[p].worldScale, 0f, 0f); shapeParams[i] = profiles[p].shapeParam; shapeParams[i].w = profiles[p].maxRadius; // Convert ior to fresnel0 float fresnel0 = (profiles[p].ior - 1.0f) / (profiles[p].ior + 1.0f); fresnel0 *= fresnel0; // square transmissionTintsAndFresnel0[i] = new Vector4(profiles[p].transmissionTint.r * 0.25f, profiles[p].transmissionTint.g * 0.25f, profiles[p].transmissionTint.b * 0.25f, fresnel0); // Premultiplied disabledTransmissionTintsAndFresnel0[i] = new Vector4(0.0f, 0.0f, 0.0f, fresnel0); for (int j = 0, n = DiffusionProfileConstants.SSS_N_SAMPLES_NEAR_FIELD; j < n; j++) { filterKernels[n * i + j].x = profiles[p].filterKernelNearField[j].x; filterKernels[n * i + j].y = profiles[p].filterKernelNearField[j].y; if (j < DiffusionProfileConstants.SSS_N_SAMPLES_FAR_FIELD) { filterKernels[n * i + j].z = profiles[p].filterKernelFarField[j].x; filterKernels[n * i + j].w = profiles[p].filterKernelFarField[j].y; } } // Old SSS Model >>> halfRcpWeightedVariances[i] = profiles[p].halfRcpWeightedVariances; var stdDev1 = ((1f / 3f) * DiffusionProfileConstants.SSS_BASIC_DISTANCE_SCALE) * (Vector4)profiles[p].scatterDistance1; var stdDev2 = ((1f / 3f) * DiffusionProfileConstants.SSS_BASIC_DISTANCE_SCALE) * (Vector4)profiles[p].scatterDistance2; // Multiply by 0.1 to convert from millimeters to centimeters. Apply the distance scale. // Rescale by 4 to counter rescaling of transmission tints. float a = 0.1f * DiffusionProfileConstants.SSS_BASIC_DISTANCE_SCALE; halfRcpVariancesAndWeights[2 * i + 0] = new Vector4(a * a * 0.5f / (stdDev1.x * stdDev1.x), a * a * 0.5f / (stdDev1.y * stdDev1.y), a * a * 0.5f / (stdDev1.z * stdDev1.z), 4f * (1f - profiles[p].lerpWeight)); halfRcpVariancesAndWeights[2 * i + 1] = new Vector4(a * a * 0.5f / (stdDev2.x * stdDev2.x), a * a * 0.5f / (stdDev2.y * stdDev2.y), a * a * 0.5f / (stdDev2.z * stdDev2.z), 4f * profiles[p].lerpWeight); for (int j = 0, n = DiffusionProfileConstants.SSS_BASIC_N_SAMPLES; j < n; j++) { filterKernelsBasic[n * i + j] = profiles[p].filterKernelBasic[j]; } // <<< Old SSS Model } } }