Eevee: SSS: Add Christensen-Burley diffusion profile.
This seems to be a correct implementation of the same diffusion profile as Cycles uses by default. There are a few bias though: - We consider _A_ the albedo to be 1 when evaluating _s_. - We use a factor of 0.6 when computing _d_ to match more or less cycles results. Note that doing per pixel jittering does bias the result even further (loss of energy).
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@ -235,7 +235,7 @@ void GPU_material_enable_alpha(GPUMaterial *material);
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GPUBuiltin GPU_get_material_builtins(GPUMaterial *material);
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GPUBlendMode GPU_material_alpha_blend(GPUMaterial *material, float obcol[4]);
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void GPU_material_sss_profile_create(GPUMaterial *material, float *radii);
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void GPU_material_sss_profile_create(GPUMaterial *material, float *radii, int *falloff_type);
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struct GPUUniformBuffer *GPU_material_sss_profile_get(GPUMaterial *material, int sample_ct);
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/* High level functions to create and use GPU materials */
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@ -145,6 +145,7 @@ struct GPUMaterial {
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GPUUniformBuffer *sss_profile; /* UBO containing SSS profile. */
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float *sss_radii; /* UBO containing SSS profile. */
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int sss_samples;
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int *sss_falloff;
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bool sss_dirty;
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};
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@ -505,17 +506,6 @@ static void sss_calculate_offsets(GPUSssKernelData *kd, int count)
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}
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}
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#if 0 /* Maybe used for other distributions */
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static void sss_calculate_areas(GPUSssKernelData *kd, float areas[SSS_SAMPLES])
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{
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for (int i = 0; i < SSS_SAMPLES; i++) {
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float w0 = (i > 0) ? fabsf(kd->kernel[i][3] - kd->kernel[i-1][3]) : 0.0f;
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float w1 = (i < SSS_SAMPLES - 1) ? fabsf(kd->kernel[i][3] - kd->kernel[i+1][3]) : 0.0f;
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areas[i] = (w0 + w1) / 2.0f;
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}
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}
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#endif
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static float error_function(float x) {
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/* Approximation of the error function by Abramowitz and Stegun
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* https://en.wikipedia.org/wiki/Error_function#Approximation_with_elementary_functions */
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@ -541,29 +531,67 @@ static float gaussian_primitive(float x) {
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}
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static float gaussian_integral(float x0, float x1) {
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return gaussian_primitive(x0) - gaussian_primitive(x1);
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return gaussian_primitive(x1) - gaussian_primitive(x0);
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}
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static void compute_sss_kernel(GPUSssKernelData *kd, float *radii, int sample_ct)
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/* Resolution for each sample of the precomputed kernel profile */
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#define INTEGRAL_RESOLUTION 32
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#define BURLEY_TRUNCATE 16.0f
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static float burley_profile(float r, float d)
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{
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float exp_r_3_d = expf(-r / (3.0f * d));
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float exp_r_d = exp_r_3_d * exp_r_3_d * exp_r_3_d;
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return (exp_r_d + exp_r_3_d) / (4.0f * d);
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}
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static float burley_integral(float x0, float x1, float d)
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{
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const float range = x1 - x0;
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const float step = range / INTEGRAL_RESOLUTION;
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float integral = 0.0f;
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for(int i = 0; i < INTEGRAL_RESOLUTION; ++i) {
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float x = x0 + range * ((float)i + 0.5f) / (float)INTEGRAL_RESOLUTION;
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float y = burley_profile(fabsf(x), d);
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integral += y * step;
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}
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return integral;
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}
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static void compute_sss_kernel(GPUSssKernelData *kd, float *radii, int sample_ct, int falloff_type)
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{
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for (int i = 0; i < 3; ++i) {
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/* Minimum radius */
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kd->radii_n[i] = MAX2(radii[i], 1e-15f);
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}
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/* Christensen-Burley fitting */
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float l[3], d[3];
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if (falloff_type == SHD_SUBSURFACE_BURLEY) {
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mul_v3_v3fl(l, kd->radii_n, 0.25f * M_1_PI);
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const float A = 1.0f;
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const float s = 1.9f - A + 3.5f * (A - 0.8f) * (A - 0.8f);
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/* XXX 0.6f Out of nowhere to match cycles! Empirical! Can be tweak better. */
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mul_v3_v3fl(d, l, 0.6f / s);
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mul_v3_v3fl(kd->radii_n, d, BURLEY_TRUNCATE);
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}
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/* Normalize size */
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copy_v3_v3(kd->radii_n, radii);
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kd->max_radius = MAX3(kd->radii_n[0], kd->radii_n[1], kd->radii_n[2]);
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mul_v3_fl(kd->radii_n, 1.0f / kd->max_radius);
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kd->radii_n[0] /= kd->max_radius;
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kd->radii_n[1] /= kd->max_radius;
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kd->radii_n[2] /= kd->max_radius;
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/* Compute samples locations on the 1d kernel */
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/* Compute samples locations on the 1d kernel [-1..1] */
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sss_calculate_offsets(kd, sample_ct);
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#if 0 /* Maybe used for other distributions */
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/* Calculate areas (using importance-sampling) */
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float areas[SSS_SAMPLES];
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sss_calculate_areas(&kd, areas);
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#endif
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/* Weights sum for normalization */
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float sum[3] = {0.0f, 0.0f, 0.0f};
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/* Compute interpolated weights */
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/* Compute integral of each sample footprint */
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for (int i = 0; i < sample_ct; i++) {
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float x0, x1;
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@ -581,20 +609,35 @@ static void compute_sss_kernel(GPUSssKernelData *kd, float *radii, int sample_ct
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x1 = (kd->kernel[i][3] + kd->kernel[i + 1][3]) / 2.0f;
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}
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kd->kernel[i][0] = gaussian_integral(x0 / kd->radii_n[0], x1 / kd->radii_n[0]);
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kd->kernel[i][1] = gaussian_integral(x0 / kd->radii_n[1], x1 / kd->radii_n[1]);
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kd->kernel[i][2] = gaussian_integral(x0 / kd->radii_n[2], x1 / kd->radii_n[2]);
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if (falloff_type == SHD_SUBSURFACE_BURLEY) {
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x0 *= kd->max_radius;
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x1 *= kd->max_radius;
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kd->kernel[i][0] = burley_integral(x0, x1, d[0]);
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kd->kernel[i][1] = burley_integral(x0, x1, d[1]);
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kd->kernel[i][2] = burley_integral(x0, x1, d[2]);
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}
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else {
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kd->kernel[i][0] = gaussian_integral(x0 / kd->radii_n[0], x1 / kd->radii_n[0]);
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kd->kernel[i][1] = gaussian_integral(x0 / kd->radii_n[1], x1 / kd->radii_n[1]);
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kd->kernel[i][2] = gaussian_integral(x0 / kd->radii_n[2], x1 / kd->radii_n[2]);
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}
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sum[0] += kd->kernel[i][0];
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sum[1] += kd->kernel[i][1];
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sum[2] += kd->kernel[i][2];
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}
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/* Normalize */
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for (int i = 0; i < sample_ct; i++) {
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kd->kernel[i][0] /= sum[0];
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kd->kernel[i][1] /= sum[1];
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kd->kernel[i][2] /= sum[2];
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for (int i = 0; i < 3; ++i) {
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if (sum[i] > 0.0f) {
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/* Normalize */
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for (int j = 0; j < sample_ct; j++) {
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kd->kernel[j][i] /= sum[i];
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}
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}
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else {
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/* Avoid 0 kernel sum. */
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kd->kernel[sample_ct / 2][i] = 1.0f;
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}
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}
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/* Put center sample at the start of the array (to sample first) */
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@ -606,9 +649,10 @@ static void compute_sss_kernel(GPUSssKernelData *kd, float *radii, int sample_ct
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copy_v4_v4(kd->kernel[0], tmpv);
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}
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void GPU_material_sss_profile_create(GPUMaterial *material, float *radii)
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void GPU_material_sss_profile_create(GPUMaterial *material, float *radii, int *falloff_type)
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{
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material->sss_radii = radii;
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material->sss_falloff = falloff_type;
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material->sss_dirty = true;
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/* Update / Create UBO */
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@ -628,7 +672,7 @@ struct GPUUniformBuffer *GPU_material_sss_profile_get(GPUMaterial *material, int
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if (material->sss_dirty || (material->sss_samples != sample_ct)) {
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GPUSssKernelData kd;
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compute_sss_kernel(&kd, material->sss_radii, sample_ct);
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compute_sss_kernel(&kd, material->sss_radii, sample_ct, *material->sss_falloff);
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/* Update / Create UBO */
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GPU_uniformbuffer_update(material->sss_profile, &kd);
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@ -58,7 +58,7 @@ static int node_shader_gpu_subsurface_scattering(GPUMaterial *mat, bNode *node,
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bNodeSocket *socket = BLI_findlink(&node->original->inputs, 2);
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bNodeSocketValueRGBA *socket_data = socket->default_value;
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/* For some reason it seems that the socket value is in ARGB format. */
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GPU_material_sss_profile_create(mat, &socket_data->value[1]);
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GPU_material_sss_profile_create(mat, &socket_data->value[1], &node->original->custom1);
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}
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return GPU_stack_link(mat, node, "node_subsurface_scattering", in, out, GPU_uniform(&node->sss_id));
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