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d832d993c5b47b0de7ca24914ad9c064607830c7
blender/intern/cycles/kernel/closure/bsdf_microfacet.h
Andrii Symkin d832d993c5 Cycles: add new Spectrum and PackedSpectrum types 
These replace float3 and packed_float3 in various places in the kernel where a
spectral color representation will be used in the future. That representation
will require more than 3 channels and conversion to from/RGB. The kernel code
was refactored to remove the assumption that Spectrum and RGB colors are the
same thing.

There are no functional changes, Spectrum is still a float3 and the conversion
functions are no-ops.

Differential Revision: https://developer.blender.org/D15535
2022-08-09 16:49:34 +02:00

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/* SPDX-License-Identifier: BSD-3-Clause
*
* Adapted from Open Shading Language
* Copyright (c) 2009-2010 Sony Pictures Imageworks Inc., et al.
* All Rights Reserved.
*
* Modifications Copyright 2011-2022 Blender Foundation. */
#pragma once
#include "kernel/closure/bsdf_util.h"
#include "kernel/sample/pattern.h"
#include "kernel/util/lookup_table.h"
CCL_NAMESPACE_BEGIN
typedef struct MicrofacetExtra {
Spectrum color, cspec0;
Spectrum fresnel_color;
float clearcoat;
} MicrofacetExtra;
typedef struct MicrofacetBsdf {
SHADER_CLOSURE_BASE;
float alpha_x, alpha_y, ior;
ccl_private MicrofacetExtra *extra;
float3 T;
} MicrofacetBsdf;
static_assert(sizeof(ShaderClosure) >= sizeof(MicrofacetBsdf), "MicrofacetBsdf is too large!");
/* Beckmann and GGX microfacet importance sampling. */
ccl_device_inline void microfacet_beckmann_sample_slopes(KernelGlobals kg,
const float cos_theta_i,
const float sin_theta_i,
float randu,
float randv,
ccl_private float *slope_x,
ccl_private float *slope_y,
ccl_private float *G1i)
{
/* special case (normal incidence) */
if (cos_theta_i >= 0.99999f) {
const float r = sqrtf(-logf(randu));
const float phi = M_2PI_F * randv;
*slope_x = r * cosf(phi);
*slope_y = r * sinf(phi);
*G1i = 1.0f;
return;
}
/* precomputations */
const float tan_theta_i = sin_theta_i / cos_theta_i;
const float inv_a = tan_theta_i;
const float cot_theta_i = 1.0f / tan_theta_i;
const float erf_a = fast_erff(cot_theta_i);
const float exp_a2 = expf(-cot_theta_i * cot_theta_i);
const float SQRT_PI_INV = 0.56418958354f;
const float Lambda = 0.5f * (erf_a - 1.0f) + (0.5f * SQRT_PI_INV) * (exp_a2 * inv_a);
const float G1 = 1.0f / (1.0f + Lambda); /* masking */
*G1i = G1;
#if defined(__KERNEL_GPU__)
/* Based on paper from Wenzel Jakob
* An Improved Visible Normal Sampling Routine for the Beckmann Distribution
*
* http://www.mitsuba-renderer.org/~wenzel/files/visnormal.pdf
*
* Reformulation from OpenShadingLanguage which avoids using inverse
* trigonometric functions.
*/
/* Sample slope X.
*
* Compute a coarse approximation using the approximation:
* exp(-ierf(x)^2) ~= 1 - x * x
* solve y = 1 + b + K * (1 - b * b)
*/
float K = tan_theta_i * SQRT_PI_INV;
float y_approx = randu * (1.0f + erf_a + K * (1 - erf_a * erf_a));
float y_exact = randu * (1.0f + erf_a + K * exp_a2);
float b = K > 0 ? (0.5f - sqrtf(K * (K - y_approx + 1.0f) + 0.25f)) / K : y_approx - 1.0f;
/* Perform newton step to refine toward the true root. */
float inv_erf = fast_ierff(b);
float value = 1.0f + b + K * expf(-inv_erf * inv_erf) - y_exact;
/* Check if we are close enough already,
* this also avoids NaNs as we get close to the root.
*/
if (fabsf(value) > 1e-6f) {
b -= value / (1.0f - inv_erf * tan_theta_i); /* newton step 1. */
inv_erf = fast_ierff(b);
value = 1.0f + b + K * expf(-inv_erf * inv_erf) - y_exact;
b -= value / (1.0f - inv_erf * tan_theta_i); /* newton step 2. */
/* Compute the slope from the refined value. */
*slope_x = fast_ierff(b);
}
else {
/* We are close enough already. */
*slope_x = inv_erf;
}
*slope_y = fast_ierff(2.0f * randv - 1.0f);
#else
/* Use precomputed table on CPU, it gives better performance. */
int beckmann_table_offset = kernel_data.tables.beckmann_offset;
*slope_x = lookup_table_read_2D(
kg, randu, cos_theta_i, beckmann_table_offset, BECKMANN_TABLE_SIZE, BECKMANN_TABLE_SIZE);
*slope_y = fast_ierff(2.0f * randv - 1.0f);
#endif
}
/* GGX microfacet importance sampling from:
*
* Importance Sampling Microfacet-Based BSDFs using the Distribution of Visible Normals.
* E. Heitz and E. d'Eon, EGSR 2014
*/
ccl_device_inline void microfacet_ggx_sample_slopes(const float cos_theta_i,
const float sin_theta_i,
float randu,
float randv,
ccl_private float *slope_x,
ccl_private float *slope_y,
ccl_private float *G1i)
{
/* special case (normal incidence) */
if (cos_theta_i >= 0.99999f) {
const float r = sqrtf(randu / (1.0f - randu));
const float phi = M_2PI_F * randv;
*slope_x = r * cosf(phi);
*slope_y = r * sinf(phi);
*G1i = 1.0f;
return;
}
/* precomputations */
const float tan_theta_i = sin_theta_i / cos_theta_i;
const float G1_inv = 0.5f * (1.0f + safe_sqrtf(1.0f + tan_theta_i * tan_theta_i));
*G1i = 1.0f / G1_inv;
/* sample slope_x */
const float A = 2.0f * randu * G1_inv - 1.0f;
const float AA = A * A;
const float tmp = 1.0f / (AA - 1.0f);
const float B = tan_theta_i;
const float BB = B * B;
const float D = safe_sqrtf(BB * (tmp * tmp) - (AA - BB) * tmp);
const float slope_x_1 = B * tmp - D;
const float slope_x_2 = B * tmp + D;
*slope_x = (A < 0.0f || slope_x_2 * tan_theta_i > 1.0f) ? slope_x_1 : slope_x_2;
/* sample slope_y */
float S;
if (randv > 0.5f) {
S = 1.0f;
randv = 2.0f * (randv - 0.5f);
}
else {
S = -1.0f;
randv = 2.0f * (0.5f - randv);
}
const float z = (randv * (randv * (randv * 0.27385f - 0.73369f) + 0.46341f)) /
(randv * (randv * (randv * 0.093073f + 0.309420f) - 1.000000f) + 0.597999f);
*slope_y = S * z * safe_sqrtf(1.0f + (*slope_x) * (*slope_x));
}
ccl_device_forceinline float3 microfacet_sample_stretched(KernelGlobals kg,
const float3 omega_i,
const float alpha_x,
const float alpha_y,
const float randu,
const float randv,
bool beckmann,
ccl_private float *G1i)
{
/* 1. stretch omega_i */
float3 omega_i_ = make_float3(alpha_x * omega_i.x, alpha_y * omega_i.y, omega_i.z);
omega_i_ = normalize(omega_i_);
/* get polar coordinates of omega_i_ */
float costheta_ = 1.0f;
float sintheta_ = 0.0f;
float cosphi_ = 1.0f;
float sinphi_ = 0.0f;
if (omega_i_.z < 0.99999f) {
costheta_ = omega_i_.z;
sintheta_ = safe_sqrtf(1.0f - costheta_ * costheta_);
float invlen = 1.0f / sintheta_;
cosphi_ = omega_i_.x * invlen;
sinphi_ = omega_i_.y * invlen;
}
/* 2. sample P22_{omega_i}(x_slope, y_slope, 1, 1) */
float slope_x, slope_y;
if (beckmann) {
microfacet_beckmann_sample_slopes(
kg, costheta_, sintheta_, randu, randv, &slope_x, &slope_y, G1i);
}
else {
microfacet_ggx_sample_slopes(costheta_, sintheta_, randu, randv, &slope_x, &slope_y, G1i);
}
/* 3. rotate */
float tmp = cosphi_ * slope_x - sinphi_ * slope_y;
slope_y = sinphi_ * slope_x + cosphi_ * slope_y;
slope_x = tmp;
/* 4. unstretch */
slope_x = alpha_x * slope_x;
slope_y = alpha_y * slope_y;
/* 5. compute normal */
return normalize(make_float3(-slope_x, -slope_y, 1.0f));
}
/* Calculate the reflection color
*
* If fresnel is used, the color is an interpolation of the F0 color and white
* with respect to the fresnel
*
* Else it is simply white
*/
ccl_device_forceinline Spectrum reflection_color(ccl_private const MicrofacetBsdf *bsdf,
float3 L,
float3 H)
{
Spectrum F = one_spectrum();
bool use_fresnel = (bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_FRESNEL_ID ||
bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID);
if (use_fresnel) {
float F0 = fresnel_dielectric_cos(1.0f, bsdf->ior);
F = interpolate_fresnel_color(L, H, bsdf->ior, F0, bsdf->extra->cspec0);
}
return F;
}
ccl_device_forceinline float D_GTR1(float NdotH, float alpha)
{
if (alpha >= 1.0f)
return M_1_PI_F;
float alpha2 = alpha * alpha;
float t = 1.0f + (alpha2 - 1.0f) * NdotH * NdotH;
return (alpha2 - 1.0f) / (M_PI_F * logf(alpha2) * t);
}
ccl_device_forceinline void bsdf_microfacet_fresnel_color(ccl_private const ShaderData *sd,
ccl_private MicrofacetBsdf *bsdf)
{
kernel_assert(CLOSURE_IS_BSDF_MICROFACET_FRESNEL(bsdf->type));
float F0 = fresnel_dielectric_cos(1.0f, bsdf->ior);
bsdf->extra->fresnel_color = interpolate_fresnel_color(
sd->I, bsdf->N, bsdf->ior, F0, bsdf->extra->cspec0);
if (bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID) {
bsdf->extra->fresnel_color *= 0.25f * bsdf->extra->clearcoat;
}
bsdf->sample_weight *= average(bsdf->extra->fresnel_color);
}
/* GGX microfacet with Smith shadow-masking from:
*
* Microfacet Models for Refraction through Rough Surfaces
* B. Walter, S. R. Marschner, H. Li, K. E. Torrance, EGSR 2007
*
* Anisotropic from:
*
* Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs
* E. Heitz, Research Report 2014
*
* Anisotropy is only supported for reflection currently, but adding it for
* transmission is just a matter of copying code from reflection if needed. */
ccl_device int bsdf_microfacet_ggx_setup(ccl_private MicrofacetBsdf *bsdf)
{
bsdf->extra = NULL;
bsdf->alpha_x = saturatef(bsdf->alpha_x);
bsdf->alpha_y = saturatef(bsdf->alpha_y);
bsdf->type = CLOSURE_BSDF_MICROFACET_GGX_ID;
return SD_BSDF | SD_BSDF_HAS_EVAL;
}
/* Required to maintain OSL interface. */
ccl_device int bsdf_microfacet_ggx_isotropic_setup(ccl_private MicrofacetBsdf *bsdf)
{
bsdf->alpha_y = bsdf->alpha_x;
return bsdf_microfacet_ggx_setup(bsdf);
}
ccl_device int bsdf_microfacet_ggx_fresnel_setup(ccl_private MicrofacetBsdf *bsdf,
ccl_private const ShaderData *sd)
{
bsdf->extra->cspec0 = saturate(bsdf->extra->cspec0);
bsdf->alpha_x = saturatef(bsdf->alpha_x);
bsdf->alpha_y = saturatef(bsdf->alpha_y);
bsdf->type = CLOSURE_BSDF_MICROFACET_GGX_FRESNEL_ID;
bsdf_microfacet_fresnel_color(sd, bsdf);
return SD_BSDF | SD_BSDF_HAS_EVAL;
}
ccl_device int bsdf_microfacet_ggx_clearcoat_setup(ccl_private MicrofacetBsdf *bsdf,
ccl_private const ShaderData *sd)
{
bsdf->extra->cspec0 = saturate(bsdf->extra->cspec0);
bsdf->alpha_x = saturatef(bsdf->alpha_x);
bsdf->alpha_y = bsdf->alpha_x;
bsdf->type = CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID;
bsdf_microfacet_fresnel_color(sd, bsdf);
return SD_BSDF | SD_BSDF_HAS_EVAL;
}
ccl_device int bsdf_microfacet_ggx_refraction_setup(ccl_private MicrofacetBsdf *bsdf)
{
bsdf->extra = NULL;
bsdf->alpha_x = saturatef(bsdf->alpha_x);
bsdf->alpha_y = bsdf->alpha_x;
bsdf->type = CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
return SD_BSDF | SD_BSDF_HAS_EVAL;
}
ccl_device void bsdf_microfacet_ggx_blur(ccl_private ShaderClosure *sc, float roughness)
{
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)sc;
bsdf->alpha_x = fmaxf(roughness, bsdf->alpha_x);
bsdf->alpha_y = fmaxf(roughness, bsdf->alpha_y);
}
ccl_device Spectrum bsdf_microfacet_ggx_eval_reflect(ccl_private const ShaderClosure *sc,
const float3 I,
const float3 omega_in,
ccl_private float *pdf)
{
ccl_private const MicrofacetBsdf *bsdf = (ccl_private const MicrofacetBsdf *)sc;
float alpha_x = bsdf->alpha_x;
float alpha_y = bsdf->alpha_y;
bool m_refractive = bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
float3 N = bsdf->N;
if (m_refractive || alpha_x * alpha_y <= 1e-7f) {
*pdf = 0.0f;
return zero_spectrum();
}
float cosNO = dot(N, I);
float cosNI = dot(N, omega_in);
if (cosNI > 0 && cosNO > 0) {
/* get half vector */
float3 m = normalize(omega_in + I);
float alpha2 = alpha_x * alpha_y;
float D, G1o, G1i;
if (alpha_x == alpha_y) {
/* isotropic
* eq. 20: (F*G*D)/(4*in*on)
* eq. 33: first we calculate D(m) */
float cosThetaM = dot(N, m);
float cosThetaM2 = cosThetaM * cosThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
float tanThetaM2 = (1 - cosThetaM2) / cosThetaM2;
if (bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID) {
/* use GTR1 for clearcoat */
D = D_GTR1(cosThetaM, bsdf->alpha_x);
/* the alpha value for clearcoat is a fixed 0.25 => alpha2 = 0.25 * 0.25 */
alpha2 = 0.0625f;
}
else {
/* use GTR2 otherwise */
D = alpha2 / (M_PI_F * cosThetaM4 * (alpha2 + tanThetaM2) * (alpha2 + tanThetaM2));
}
/* eq. 34: now calculate G1(i,m) and G1(o,m) */
G1o = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNO * cosNO) / (cosNO * cosNO)));
G1i = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNI * cosNI) / (cosNI * cosNI)));
}
else {
/* anisotropic */
float3 X, Y, Z = N;
make_orthonormals_tangent(Z, bsdf->T, &X, &Y);
/* distribution */
float3 local_m = make_float3(dot(X, m), dot(Y, m), dot(Z, m));
float slope_x = -local_m.x / (local_m.z * alpha_x);
float slope_y = -local_m.y / (local_m.z * alpha_y);
float slope_len = 1 + slope_x * slope_x + slope_y * slope_y;
float cosThetaM = local_m.z;
float cosThetaM2 = cosThetaM * cosThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
D = 1 / ((slope_len * slope_len) * M_PI_F * alpha2 * cosThetaM4);
/* G1(i,m) and G1(o,m) */
float tanThetaO2 = (1 - cosNO * cosNO) / (cosNO * cosNO);
float cosPhiO = dot(I, X);
float sinPhiO = dot(I, Y);
float alphaO2 = (cosPhiO * cosPhiO) * (alpha_x * alpha_x) +
(sinPhiO * sinPhiO) * (alpha_y * alpha_y);
alphaO2 /= cosPhiO * cosPhiO + sinPhiO * sinPhiO;
G1o = 2 / (1 + safe_sqrtf(1 + alphaO2 * tanThetaO2));
float tanThetaI2 = (1 - cosNI * cosNI) / (cosNI * cosNI);
float cosPhiI = dot(omega_in, X);
float sinPhiI = dot(omega_in, Y);
float alphaI2 = (cosPhiI * cosPhiI) * (alpha_x * alpha_x) +
(sinPhiI * sinPhiI) * (alpha_y * alpha_y);
alphaI2 /= cosPhiI * cosPhiI + sinPhiI * sinPhiI;
G1i = 2 / (1 + safe_sqrtf(1 + alphaI2 * tanThetaI2));
}
float G = G1o * G1i;
/* eq. 20 */
float common = D * 0.25f / cosNO;
Spectrum F = reflection_color(bsdf, omega_in, m);
if (bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID) {
F *= 0.25f * bsdf->extra->clearcoat;
}
Spectrum out = F * G * common;
/* eq. 2 in distribution of visible normals sampling
* `pm = Dw = G1o * dot(m, I) * D / dot(N, I);` */
/* eq. 38 - but see also:
* eq. 17 in http://www.graphics.cornell.edu/~bjw/wardnotes.pdf
* `pdf = pm * 0.25 / dot(m, I);` */
*pdf = G1o * common;
return out;
}
return zero_spectrum();
}
ccl_device Spectrum bsdf_microfacet_ggx_eval_transmit(ccl_private const ShaderClosure *sc,
const float3 I,
const float3 omega_in,
ccl_private float *pdf)
{
ccl_private const MicrofacetBsdf *bsdf = (ccl_private const MicrofacetBsdf *)sc;
float alpha_x = bsdf->alpha_x;
float alpha_y = bsdf->alpha_y;
float m_eta = bsdf->ior;
bool m_refractive = bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
float3 N = bsdf->N;
if (!m_refractive || alpha_x * alpha_y <= 1e-7f) {
*pdf = 0.0f;
return zero_spectrum();
}
float cosNO = dot(N, I);
float cosNI = dot(N, omega_in);
if (cosNO <= 0 || cosNI >= 0) {
*pdf = 0.0f;
return zero_spectrum(); /* vectors on same side -- not possible */
}
/* compute half-vector of the refraction (eq. 16) */
float3 ht = -(m_eta * omega_in + I);
float3 Ht = normalize(ht);
float cosHO = dot(Ht, I);
float cosHI = dot(Ht, omega_in);
float D, G1o, G1i;
/* eq. 33: first we calculate D(m) with m=Ht: */
float alpha2 = alpha_x * alpha_y;
float cosThetaM = dot(N, Ht);
float cosThetaM2 = cosThetaM * cosThetaM;
float tanThetaM2 = (1 - cosThetaM2) / cosThetaM2;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
D = alpha2 / (M_PI_F * cosThetaM4 * (alpha2 + tanThetaM2) * (alpha2 + tanThetaM2));
/* eq. 34: now calculate G1(i,m) and G1(o,m) */
G1o = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNO * cosNO) / (cosNO * cosNO)));
G1i = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNI * cosNI) / (cosNI * cosNI)));
float G = G1o * G1i;
/* probability */
float Ht2 = dot(ht, ht);
/* eq. 2 in distribution of visible normals sampling
* pm = Dw = G1o * dot(m, I) * D / dot(N, I); */
/* out = fabsf(cosHI * cosHO) * (m_eta * m_eta) * G * D / (cosNO * Ht2)
* pdf = pm * (m_eta * m_eta) * fabsf(cosHI) / Ht2 */
float common = D * (m_eta * m_eta) / (cosNO * Ht2);
float out = G * fabsf(cosHI * cosHO) * common;
*pdf = G1o * fabsf(cosHO * cosHI) * common;
return make_spectrum(out);
}
ccl_device int bsdf_microfacet_ggx_sample(KernelGlobals kg,
ccl_private const ShaderClosure *sc,
float3 Ng,
float3 I,
float3 dIdx,
float3 dIdy,
float randu,
float randv,
ccl_private Spectrum *eval,
ccl_private float3 *omega_in,
ccl_private float3 *domega_in_dx,
ccl_private float3 *domega_in_dy,
ccl_private float *pdf)
{
ccl_private const MicrofacetBsdf *bsdf = (ccl_private const MicrofacetBsdf *)sc;
float alpha_x = bsdf->alpha_x;
float alpha_y = bsdf->alpha_y;
bool m_refractive = bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
float3 N = bsdf->N;
int label;
float cosNO = dot(N, I);
if (cosNO > 0) {
float3 X, Y, Z = N;
if (alpha_x == alpha_y)
make_orthonormals(Z, &X, &Y);
else
make_orthonormals_tangent(Z, bsdf->T, &X, &Y);
/* importance sampling with distribution of visible normals. vectors are
* transformed to local space before and after */
float3 local_I = make_float3(dot(X, I), dot(Y, I), cosNO);
float3 local_m;
float G1o;
local_m = microfacet_sample_stretched(
kg, local_I, alpha_x, alpha_y, randu, randv, false, &G1o);
float3 m = X * local_m.x + Y * local_m.y + Z * local_m.z;
float cosThetaM = local_m.z;
/* reflection or refraction? */
if (!m_refractive) {
float cosMO = dot(m, I);
label = LABEL_REFLECT | LABEL_GLOSSY;
if (cosMO > 0) {
/* eq. 39 - compute actual reflected direction */
*omega_in = 2 * cosMO * m - I;
if (dot(Ng, *omega_in) > 0) {
if (alpha_x * alpha_y <= 1e-7f) {
/* some high number for MIS */
*pdf = 1e6f;
*eval = make_spectrum(1e6f);
bool use_fresnel = (bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_FRESNEL_ID ||
bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID);
/* if fresnel is used, calculate the color with reflection_color(...) */
if (use_fresnel) {
*eval *= reflection_color(bsdf, *omega_in, m);
}
label = LABEL_REFLECT | LABEL_SINGULAR;
}
else {
/* microfacet normal is visible to this ray */
/* eq. 33 */
float alpha2 = alpha_x * alpha_y;
float D, G1i;
if (alpha_x == alpha_y) {
/* isotropic */
float cosThetaM2 = cosThetaM * cosThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
float tanThetaM2 = 1 / (cosThetaM2)-1;
/* eval BRDF*cosNI */
float cosNI = dot(N, *omega_in);
if (bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID) {
/* use GTR1 for clearcoat */
D = D_GTR1(cosThetaM, bsdf->alpha_x);
/* the alpha value for clearcoat is a fixed 0.25 => alpha2 = 0.25 * 0.25 */
alpha2 = 0.0625f;
/* recalculate G1o */
G1o = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNO * cosNO) / (cosNO * cosNO)));
}
else {
/* use GTR2 otherwise */
D = alpha2 / (M_PI_F * cosThetaM4 * (alpha2 + tanThetaM2) * (alpha2 + tanThetaM2));
}
/* eq. 34: now calculate G1(i,m) */
G1i = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNI * cosNI) / (cosNI * cosNI)));
}
else {
/* anisotropic distribution */
float3 local_m = make_float3(dot(X, m), dot(Y, m), dot(Z, m));
float slope_x = -local_m.x / (local_m.z * alpha_x);
float slope_y = -local_m.y / (local_m.z * alpha_y);
float slope_len = 1 + slope_x * slope_x + slope_y * slope_y;
float cosThetaM = local_m.z;
float cosThetaM2 = cosThetaM * cosThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
D = 1 / ((slope_len * slope_len) * M_PI_F * alpha2 * cosThetaM4);
/* calculate G1(i,m) */
float cosNI = dot(N, *omega_in);
float tanThetaI2 = (1 - cosNI * cosNI) / (cosNI * cosNI);
float cosPhiI = dot(*omega_in, X);
float sinPhiI = dot(*omega_in, Y);
float alphaI2 = (cosPhiI * cosPhiI) * (alpha_x * alpha_x) +
(sinPhiI * sinPhiI) * (alpha_y * alpha_y);
alphaI2 /= cosPhiI * cosPhiI + sinPhiI * sinPhiI;
G1i = 2 / (1 + safe_sqrtf(1 + alphaI2 * tanThetaI2));
}
/* see eval function for derivation */
float common = (G1o * D) * 0.25f / cosNO;
*pdf = common;
Spectrum F = reflection_color(bsdf, *omega_in, m);
*eval = G1i * common * F;
}
if (bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID) {
*eval *= 0.25f * bsdf->extra->clearcoat;
}
#ifdef __RAY_DIFFERENTIALS__
*domega_in_dx = (2 * dot(m, dIdx)) * m - dIdx;
*domega_in_dy = (2 * dot(m, dIdy)) * m - dIdy;
#endif
}
else {
*eval = zero_spectrum();
*pdf = 0.0f;
}
}
}
else {
label = LABEL_TRANSMIT | LABEL_GLOSSY;
/* CAUTION: the i and o variables are inverted relative to the paper
* eq. 39 - compute actual refractive direction */
float3 R, T;
#ifdef __RAY_DIFFERENTIALS__
float3 dRdx, dRdy, dTdx, dTdy;
#endif
float m_eta = bsdf->ior, fresnel;
bool inside;
fresnel = fresnel_dielectric(m_eta,
m,
I,
&R,
&T,
#ifdef __RAY_DIFFERENTIALS__
dIdx,
dIdy,
&dRdx,
&dRdy,
&dTdx,
&dTdy,
#endif
&inside);
if (!inside && fresnel != 1.0f) {
*omega_in = T;
#ifdef __RAY_DIFFERENTIALS__
*domega_in_dx = dTdx;
*domega_in_dy = dTdy;
#endif
if (alpha_x * alpha_y <= 1e-7f || fabsf(m_eta - 1.0f) < 1e-4f) {
/* some high number for MIS */
*pdf = 1e6f;
*eval = make_spectrum(1e6f);
label = LABEL_TRANSMIT | LABEL_SINGULAR;
}
else {
/* eq. 33 */
float alpha2 = alpha_x * alpha_y;
float cosThetaM2 = cosThetaM * cosThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
float tanThetaM2 = 1 / (cosThetaM2)-1;
float D = alpha2 / (M_PI_F * cosThetaM4 * (alpha2 + tanThetaM2) * (alpha2 + tanThetaM2));
/* eval BRDF*cosNI */
float cosNI = dot(N, *omega_in);
/* eq. 34: now calculate G1(i,m) */
float G1i = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNI * cosNI) / (cosNI * cosNI)));
/* eq. 21 */
float cosHI = dot(m, *omega_in);
float cosHO = dot(m, I);
float Ht2 = m_eta * cosHI + cosHO;
Ht2 *= Ht2;
/* see eval function for derivation */
float common = (G1o * D) * (m_eta * m_eta) / (cosNO * Ht2);
float out = G1i * fabsf(cosHI * cosHO) * common;
*pdf = cosHO * fabsf(cosHI) * common;
*eval = make_spectrum(out);
}
}
else {
*eval = zero_spectrum();
*pdf = 0.0f;
}
}
}
else {
label = (m_refractive) ? LABEL_TRANSMIT | LABEL_GLOSSY : LABEL_REFLECT | LABEL_GLOSSY;
}
return label;
}
/* Beckmann microfacet with Smith shadow-masking from:
*
* Microfacet Models for Refraction through Rough Surfaces
* B. Walter, S. R. Marschner, H. Li, K. E. Torrance, EGSR 2007 */
ccl_device int bsdf_microfacet_beckmann_setup(ccl_private MicrofacetBsdf *bsdf)
{
bsdf->alpha_x = saturatef(bsdf->alpha_x);
bsdf->alpha_y = saturatef(bsdf->alpha_y);
bsdf->type = CLOSURE_BSDF_MICROFACET_BECKMANN_ID;
return SD_BSDF | SD_BSDF_HAS_EVAL;
}
/* Required to maintain OSL interface. */
ccl_device int bsdf_microfacet_beckmann_isotropic_setup(ccl_private MicrofacetBsdf *bsdf)
{
bsdf->alpha_y = bsdf->alpha_x;
return bsdf_microfacet_beckmann_setup(bsdf);
}
ccl_device int bsdf_microfacet_beckmann_refraction_setup(ccl_private MicrofacetBsdf *bsdf)
{
bsdf->alpha_x = saturatef(bsdf->alpha_x);
bsdf->alpha_y = bsdf->alpha_x;
bsdf->type = CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID;
return SD_BSDF | SD_BSDF_HAS_EVAL;
}
ccl_device void bsdf_microfacet_beckmann_blur(ccl_private ShaderClosure *sc, float roughness)
{
ccl_private MicrofacetBsdf *bsdf = (ccl_private MicrofacetBsdf *)sc;
bsdf->alpha_x = fmaxf(roughness, bsdf->alpha_x);
bsdf->alpha_y = fmaxf(roughness, bsdf->alpha_y);
}
ccl_device_inline float bsdf_beckmann_G1(float alpha, float cos_n)
{
cos_n *= cos_n;
float invA = alpha * safe_sqrtf((1.0f - cos_n) / cos_n);
if (invA < 0.625f) {
return 1.0f;
}
float a = 1.0f / invA;
return ((2.181f * a + 3.535f) * a) / ((2.577f * a + 2.276f) * a + 1.0f);
}
ccl_device_inline float bsdf_beckmann_aniso_G1(
float alpha_x, float alpha_y, float cos_n, float cos_phi, float sin_phi)
{
cos_n *= cos_n;
sin_phi *= sin_phi;
cos_phi *= cos_phi;
alpha_x *= alpha_x;
alpha_y *= alpha_y;
float alphaO2 = (cos_phi * alpha_x + sin_phi * alpha_y) / (cos_phi + sin_phi);
float invA = safe_sqrtf(alphaO2 * (1 - cos_n) / cos_n);
if (invA < 0.625f) {
return 1.0f;
}
float a = 1.0f / invA;
return ((2.181f * a + 3.535f) * a) / ((2.577f * a + 2.276f) * a + 1.0f);
}
ccl_device Spectrum bsdf_microfacet_beckmann_eval_reflect(ccl_private const ShaderClosure *sc,
const float3 I,
const float3 omega_in,
ccl_private float *pdf)
{
ccl_private const MicrofacetBsdf *bsdf = (ccl_private const MicrofacetBsdf *)sc;
float alpha_x = bsdf->alpha_x;
float alpha_y = bsdf->alpha_y;
bool m_refractive = bsdf->type == CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID;
float3 N = bsdf->N;
if (m_refractive || alpha_x * alpha_y <= 1e-7f) {
*pdf = 0.0f;
return zero_spectrum();
}
float cosNO = dot(N, I);
float cosNI = dot(N, omega_in);
if (cosNO > 0 && cosNI > 0) {
/* get half vector */
float3 m = normalize(omega_in + I);
float alpha2 = alpha_x * alpha_y;
float D, G1o, G1i;
if (alpha_x == alpha_y) {
/* isotropic
* eq. 20: (F*G*D)/(4*in*on)
* eq. 25: first we calculate D(m) */
float cosThetaM = dot(N, m);
float cosThetaM2 = cosThetaM * cosThetaM;
float tanThetaM2 = (1 - cosThetaM2) / cosThetaM2;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
D = expf(-tanThetaM2 / alpha2) / (M_PI_F * alpha2 * cosThetaM4);
/* eq. 26, 27: now calculate G1(i,m) and G1(o,m) */
G1o = bsdf_beckmann_G1(alpha_x, cosNO);
G1i = bsdf_beckmann_G1(alpha_x, cosNI);
}
else {
/* anisotropic */
float3 X, Y, Z = N;
make_orthonormals_tangent(Z, bsdf->T, &X, &Y);
/* distribution */
float3 local_m = make_float3(dot(X, m), dot(Y, m), dot(Z, m));
float slope_x = -local_m.x / (local_m.z * alpha_x);
float slope_y = -local_m.y / (local_m.z * alpha_y);
float cosThetaM = local_m.z;
float cosThetaM2 = cosThetaM * cosThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
D = expf(-slope_x * slope_x - slope_y * slope_y) / (M_PI_F * alpha2 * cosThetaM4);
/* G1(i,m) and G1(o,m) */
G1o = bsdf_beckmann_aniso_G1(alpha_x, alpha_y, cosNO, dot(I, X), dot(I, Y));
G1i = bsdf_beckmann_aniso_G1(alpha_x, alpha_y, cosNI, dot(omega_in, X), dot(omega_in, Y));
}
float G = G1o * G1i;
/* eq. 20 */
float common = D * 0.25f / cosNO;
float out = G * common;
/* eq. 2 in distribution of visible normals sampling
* pm = Dw = G1o * dot(m, I) * D / dot(N, I); */
/* eq. 38 - but see also:
* eq. 17 in http://www.graphics.cornell.edu/~bjw/wardnotes.pdf
* pdf = pm * 0.25 / dot(m, I); */
*pdf = G1o * common;
return make_spectrum(out);
}
return zero_spectrum();
}
ccl_device Spectrum bsdf_microfacet_beckmann_eval_transmit(ccl_private const ShaderClosure *sc,
const float3 I,
const float3 omega_in,
ccl_private float *pdf)
{
ccl_private const MicrofacetBsdf *bsdf = (ccl_private const MicrofacetBsdf *)sc;
float alpha_x = bsdf->alpha_x;
float alpha_y = bsdf->alpha_y;
float m_eta = bsdf->ior;
bool m_refractive = bsdf->type == CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID;
float3 N = bsdf->N;
if (!m_refractive || alpha_x * alpha_y <= 1e-7f) {
*pdf = 0.0f;
return zero_spectrum();
}
float cosNO = dot(N, I);
float cosNI = dot(N, omega_in);
if (cosNO <= 0 || cosNI >= 0) {
*pdf = 0.0f;
return zero_spectrum();
}
/* compute half-vector of the refraction (eq. 16) */
float3 ht = -(m_eta * omega_in + I);
float3 Ht = normalize(ht);
float cosHO = dot(Ht, I);
float cosHI = dot(Ht, omega_in);
/* eq. 25: first we calculate D(m) with m=Ht: */
float alpha2 = alpha_x * alpha_y;
float cosThetaM = min(dot(N, Ht), 1.0f);
float cosThetaM2 = cosThetaM * cosThetaM;
float tanThetaM2 = (1 - cosThetaM2) / cosThetaM2;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
float D = expf(-tanThetaM2 / alpha2) / (M_PI_F * alpha2 * cosThetaM4);
/* eq. 26, 27: now calculate G1(i,m) and G1(o,m) */
float G1o = bsdf_beckmann_G1(alpha_x, cosNO);
float G1i = bsdf_beckmann_G1(alpha_x, cosNI);
float G = G1o * G1i;
/* probability */
float Ht2 = dot(ht, ht);
/* eq. 2 in distribution of visible normals sampling
* pm = Dw = G1o * dot(m, I) * D / dot(N, I); */
/* out = fabsf(cosHI * cosHO) * (m_eta * m_eta) * G * D / (cosNO * Ht2)
* pdf = pm * (m_eta * m_eta) * fabsf(cosHI) / Ht2 */
float common = D * (m_eta * m_eta) / (cosNO * Ht2);
float out = G * fabsf(cosHI * cosHO) * common;
*pdf = G1o * fabsf(cosHO * cosHI) * common;
return make_spectrum(out);
}
ccl_device int bsdf_microfacet_beckmann_sample(KernelGlobals kg,
ccl_private const ShaderClosure *sc,
float3 Ng,
float3 I,
float3 dIdx,
float3 dIdy,
float randu,
float randv,
ccl_private Spectrum *eval,
ccl_private float3 *omega_in,
ccl_private float3 *domega_in_dx,
ccl_private float3 *domega_in_dy,
ccl_private float *pdf)
{
ccl_private const MicrofacetBsdf *bsdf = (ccl_private const MicrofacetBsdf *)sc;
float alpha_x = bsdf->alpha_x;
float alpha_y = bsdf->alpha_y;
bool m_refractive = bsdf->type == CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID;
float3 N = bsdf->N;
int label;
float cosNO = dot(N, I);
if (cosNO > 0) {
float3 X, Y, Z = N;
if (alpha_x == alpha_y)
make_orthonormals(Z, &X, &Y);
else
make_orthonormals_tangent(Z, bsdf->T, &X, &Y);
/* importance sampling with distribution of visible normals. vectors are
* transformed to local space before and after */
float3 local_I = make_float3(dot(X, I), dot(Y, I), cosNO);
float3 local_m;
float G1o;
local_m = microfacet_sample_stretched(kg, local_I, alpha_x, alpha_x, randu, randv, true, &G1o);
float3 m = X * local_m.x + Y * local_m.y + Z * local_m.z;
float cosThetaM = local_m.z;
/* reflection or refraction? */
if (!m_refractive) {
label = LABEL_REFLECT | LABEL_GLOSSY;
float cosMO = dot(m, I);
if (cosMO > 0) {
/* eq. 39 - compute actual reflected direction */
*omega_in = 2 * cosMO * m - I;
if (dot(Ng, *omega_in) > 0) {
if (alpha_x * alpha_y <= 1e-7f) {
/* some high number for MIS */
*pdf = 1e6f;
*eval = make_spectrum(1e6f);
label = LABEL_REFLECT | LABEL_SINGULAR;
}
else {
/* microfacet normal is visible to this ray
* eq. 25 */
float alpha2 = alpha_x * alpha_y;
float D, G1i;
if (alpha_x == alpha_y) {
/* Isotropic distribution. */
float cosThetaM2 = cosThetaM * cosThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
float tanThetaM2 = 1 / (cosThetaM2)-1;
D = expf(-tanThetaM2 / alpha2) / (M_PI_F * alpha2 * cosThetaM4);
/* eval BRDF*cosNI */
float cosNI = dot(N, *omega_in);
/* eq. 26, 27: now calculate G1(i,m) */
G1i = bsdf_beckmann_G1(alpha_x, cosNI);
}
else {
/* anisotropic distribution */
float3 local_m = make_float3(dot(X, m), dot(Y, m), dot(Z, m));
float slope_x = -local_m.x / (local_m.z * alpha_x);
float slope_y = -local_m.y / (local_m.z * alpha_y);
float cosThetaM = local_m.z;
float cosThetaM2 = cosThetaM * cosThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
D = expf(-slope_x * slope_x - slope_y * slope_y) / (M_PI_F * alpha2 * cosThetaM4);
/* G1(i,m) */
G1i = bsdf_beckmann_aniso_G1(
alpha_x, alpha_y, dot(*omega_in, N), dot(*omega_in, X), dot(*omega_in, Y));
}
float G = G1o * G1i;
/* see eval function for derivation */
float common = D * 0.25f / cosNO;
float out = G * common;
*pdf = G1o * common;
*eval = make_spectrum(out);
}
#ifdef __RAY_DIFFERENTIALS__
*domega_in_dx = (2 * dot(m, dIdx)) * m - dIdx;
*domega_in_dy = (2 * dot(m, dIdy)) * m - dIdy;
#endif
}
else {
*eval = zero_spectrum();
*pdf = 0.0f;
}
}
}
else {
label = LABEL_TRANSMIT | LABEL_GLOSSY;
/* CAUTION: the i and o variables are inverted relative to the paper
* eq. 39 - compute actual refractive direction */
float3 R, T;
#ifdef __RAY_DIFFERENTIALS__
float3 dRdx, dRdy, dTdx, dTdy;
#endif
float m_eta = bsdf->ior, fresnel;
bool inside;
fresnel = fresnel_dielectric(m_eta,
m,
I,
&R,
&T,
#ifdef __RAY_DIFFERENTIALS__
dIdx,
dIdy,
&dRdx,
&dRdy,
&dTdx,
&dTdy,
#endif
&inside);
if (!inside && fresnel != 1.0f) {
*omega_in = T;
#ifdef __RAY_DIFFERENTIALS__
*domega_in_dx = dTdx;
*domega_in_dy = dTdy;
#endif
if (alpha_x * alpha_y <= 1e-7f || fabsf(m_eta - 1.0f) < 1e-4f) {
/* some high number for MIS */
*pdf = 1e6f;
*eval = make_spectrum(1e6f);
label = LABEL_TRANSMIT | LABEL_SINGULAR;
}
else {
/* eq. 33 */
float alpha2 = alpha_x * alpha_y;
float cosThetaM2 = cosThetaM * cosThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
float tanThetaM2 = 1 / (cosThetaM2)-1;
float D = expf(-tanThetaM2 / alpha2) / (M_PI_F * alpha2 * cosThetaM4);
/* eval BRDF*cosNI */
float cosNI = dot(N, *omega_in);
/* eq. 26, 27: now calculate G1(i,m) */
float G1i = bsdf_beckmann_G1(alpha_x, cosNI);
float G = G1o * G1i;
/* eq. 21 */
float cosHI = dot(m, *omega_in);
float cosHO = dot(m, I);
float Ht2 = m_eta * cosHI + cosHO;
Ht2 *= Ht2;
/* see eval function for derivation */
float common = D * (m_eta * m_eta) / (cosNO * Ht2);
float out = G * fabsf(cosHI * cosHO) * common;
*pdf = G1o * cosHO * fabsf(cosHI) * common;
*eval = make_spectrum(out);
}
}
else {
*eval = zero_spectrum();
*pdf = 0.0f;
}
}
}
else {
label = (m_refractive) ? LABEL_TRANSMIT | LABEL_GLOSSY : LABEL_REFLECT | LABEL_GLOSSY;
}
return label;
}
CCL_NAMESPACE_END
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