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test2/intern/cycles/kernel/closure/bsdf_microfacet.h

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/* SPDX-FileCopyrightText: 2009-2010 Sony Pictures Imageworks Inc., et al. All Rights Reserved.
* SPDX-FileCopyrightText: 2011-2022 Blender Foundation
*
* SPDX-License-Identifier: BSD-3-Clause
*
* Adapted code from Open Shading Language. */
#pragma once
#include "kernel/closure/bsdf_util.h"
#include "kernel/sample/mapping.h"
#include "kernel/util/lookup_table.h"
#include "util/math_fast.h"
CCL_NAMESPACE_BEGIN
enum MicrofacetType {
BECKMANN,
GGX,
};
enum MicrofacetFresnel {
NONE = 0,
DIELECTRIC,
DIELECTRIC_TINT, /* used by the OSL MaterialX closures */
CONDUCTOR,
GENERALIZED_SCHLICK,
F82_TINT,
};
struct FresnelThinFilm {
float thickness;
float ior;
};
struct FresnelDielectricTint {
FresnelThinFilm thin_film;
Spectrum reflection_tint;
Spectrum transmission_tint;
};
struct FresnelConductor {
Spectrum n, k;
};
struct FresnelGeneralizedSchlick {
FresnelThinFilm thin_film;
Spectrum reflection_tint;
Spectrum transmission_tint;
/* Reflectivity at perpendicular (F0) and glancing (F90) angles. */
Spectrum f0, f90;
/* Negative exponent signals a special case where the real Fresnel is remapped to F0...F90. */
float exponent;
};
struct FresnelF82Tint {
/* Perpendicular reflectivity. */
Spectrum f0;
/* Precomputed (1-cos)^6 factor for edge tint. */
Spectrum b;
};
struct MicrofacetBsdf {
SHADER_CLOSURE_BASE;
float alpha_x, alpha_y, ior;
/* Used to account for missing energy due to the single-scattering microfacet model.
* This could be included in bsdf->weight as well, but there it would mess up the color
* channels.
* Note that this is currently only used by GGX. */
float energy_scale;
/* Fresnel model to apply, as well as the extra data for it.
* For NONE and DIELECTRIC, no extra storage is needed, so the pointer is nullptr for them. */
int fresnel_type;
ccl_private void *fresnel;
float3 T;
};
static_assert(sizeof(ShaderClosure) >= sizeof(MicrofacetBsdf), "MicrofacetBsdf is too large!");
/* Beckmann VNDF importance sampling algorithm from:
* Importance Sampling Microfacet-Based BSDFs using the Distribution of Visible Normals.
* Eric Heitz and Eugene d'Eon, EGSR 2014.
* https://hal.inria.fr/hal-00996995v2/document */
ccl_device_forceinline float3 microfacet_beckmann_sample_vndf(const float3 wi,
const float alpha_x,
const float alpha_y,
const float2 rand)
{
/* 1. stretch wi */
float3 wi_ = make_float3(alpha_x * wi.x, alpha_y * wi.y, wi.z);
wi_ = normalize(wi_);
/* 2. sample P22_{wi}(x_slope, y_slope, 1, 1) */
float2 slope;
float cos_phi_i = 1.0f;
float sin_phi_i = 0.0f;
if (wi_.z >= 0.99999f) {
/* Special case (normal incidence). */
const float r = sqrtf(-logf(rand.x));
const float phi = M_2PI_F * rand.y;
slope = polar_to_cartesian(r, phi);
}
else {
/* Precomputations. */
const float cos_theta_i = wi_.z;
const float sin_theta_i = sin_from_cos(cos_theta_i);
const float tan_theta_i = sin_theta_i / cos_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 invlen = 1.0f / sin_theta_i;
cos_phi_i = wi_.x * invlen;
sin_phi_i = wi_.y * invlen;
/* 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)`
*/
const float K = tan_theta_i * SQRT_PI_INV;
const float y_approx = rand.x * (1.0f + erf_a + K * (1 - erf_a * erf_a));
const float y_exact = rand.x * (1.0f + erf_a + K * exp_a2);
const float b = K > 0 ? (0.5f - sqrtf(K * (K - y_approx + 1.0f) + 0.25f)) / K :
y_approx - 1.0f;
float inv_erf = fast_ierff(b);
float2 begin = make_float2(-1.0f, -y_exact);
float2 end = make_float2(erf_a, 1.0f + erf_a + K * exp_a2 - y_exact);
float2 current = make_float2(b, 1.0f + b + K * expf(-sqr(inv_erf)) - y_exact);
/* Find root in a monotonic interval using newton method, under given precision and maximal
* iterations. Falls back to bisection if newton step produces results outside of the valid
* interval. */
const float precision = 1e-6f;
const int max_iter = 3;
int iter = 0;
while (fabsf(current.y) > precision && iter++ < max_iter) {
if (signf(begin.y) == signf(current.y)) {
begin.x = current.x;
begin.y = current.y;
}
else {
end.x = current.x;
}
const float newton_x = current.x - current.y / (1.0f - inv_erf * tan_theta_i);
current.x = (newton_x >= begin.x && newton_x <= end.x) ? newton_x : 0.5f * (begin.x + end.x);
inv_erf = fast_ierff(current.x);
current.y = 1.0f + current.x + K * expf(-sqr(inv_erf)) - y_exact;
}
slope.x = inv_erf;
slope.y = fast_ierff(2.0f * rand.y - 1.0f);
}
/* 3. rotate */
slope = make_float2(cos_phi_i * slope.x - sin_phi_i * slope.y,
sin_phi_i * slope.x + cos_phi_i * slope.y);
/* 4. unstretch */
slope *= make_float2(alpha_x, alpha_y);
/* 5. compute normal */
return normalize(make_float3(-slope.x, -slope.y, 1.0f));
}
/* GGX VNDF importance sampling algorithm from:
* Sampling the GGX Distribution of Visible Normals.
* Eric Heitz, JCGT Vol. 7, No. 4, 2018.
* https://jcgt.org/published/0007/04/01/ */
ccl_device_forceinline float3 microfacet_ggx_sample_vndf(const float3 wi,
const float alpha_x,
const float alpha_y,
const float2 rand)
{
/* Section 3.2: Transforming the view direction to the hemisphere configuration. */
const float3 wi_ = normalize(make_float3(alpha_x * wi.x, alpha_y * wi.y, wi.z));
/* Section 4.1: Orthonormal basis. */
const float lensq = sqr(wi_.x) + sqr(wi_.y);
float3 T1;
float3 T2;
if (lensq > 1e-7f) {
T1 = make_float3(-wi_.y, wi_.x, 0.0f) * inversesqrtf(lensq);
T2 = cross(wi_, T1);
}
else {
/* Normal incidence, any basis is fine. */
T1 = make_float3(1.0f, 0.0f, 0.0f);
T2 = make_float3(0.0f, 1.0f, 0.0f);
}
/* Section 4.2: Parameterization of the projected area. */
float2 t = sample_uniform_disk(rand);
t.y = mix(safe_sqrtf(1.0f - sqr(t.x)), t.y, 0.5f * (1.0f + wi_.z));
/* Section 4.3: Reprojection onto hemisphere. */
const float3 H_ = to_global(disk_to_hemisphere(t), T1, T2, wi_);
/* Section 3.4: Transforming the normal back to the ellipsoid configuration. */
return normalize(make_float3(alpha_x * H_.x, alpha_y * H_.y, max(0.0f, H_.z)));
}
/* Computes the Fresnel reflectance and transmittance given the Microfacet BSDF and the cosine of
* the incoming angle `cos_theta_i`.
* Also returns the cosine of the angle between the normal and the refracted ray as `r_cos_theta_t`
* if provided. */
ccl_device_forceinline void microfacet_fresnel(KernelGlobals kg,
const ccl_private MicrofacetBsdf *bsdf,
const float cos_theta_i,
ccl_private float *r_cos_theta_t,
ccl_private Spectrum *r_reflectance,
ccl_private Spectrum *r_transmittance)
{
/* Whether the closure has reflective or transmissive lobes. */
const bool has_reflection = !CLOSURE_IS_REFRACTION(bsdf->type);
const bool has_transmission = CLOSURE_IS_GLASS(bsdf->type) || !has_reflection;
if (bsdf->fresnel_type == MicrofacetFresnel::DIELECTRIC) {
const Spectrum F = make_spectrum(fresnel_dielectric(cos_theta_i, bsdf->ior, r_cos_theta_t));
*r_reflectance = F;
*r_transmittance = one_spectrum() - F;
}
else if (bsdf->fresnel_type == MicrofacetFresnel::DIELECTRIC_TINT) {
ccl_private FresnelDielectricTint *fresnel = (ccl_private FresnelDielectricTint *)
bsdf->fresnel;
const float F = fresnel_dielectric(cos_theta_i, bsdf->ior, r_cos_theta_t);
*r_reflectance = F * fresnel->reflection_tint;
*r_transmittance = (1.0f - F) * fresnel->transmission_tint;
}
else if (bsdf->fresnel_type == MicrofacetFresnel::CONDUCTOR) {
ccl_private FresnelConductor *fresnel = (ccl_private FresnelConductor *)bsdf->fresnel;
*r_reflectance = fresnel_conductor(cos_theta_i, fresnel->n, fresnel->k);
*r_transmittance = zero_spectrum();
}
else if (bsdf->fresnel_type == MicrofacetFresnel::F82_TINT) {
/* F82-Tint model, described in "Novel aspects of the Adobe Standard Material" by Kutz et al.
* Essentially, this is the usual Schlick Fresnel with an additional cosI*(1-cosI)^6
* term which modulates the reflectivity around acos(1/7) degrees (ca. 82°). */
ccl_private FresnelF82Tint *fresnel = (ccl_private FresnelF82Tint *)bsdf->fresnel;
const float mu = saturatef(1.0f - cos_theta_i);
const float mu5 = sqr(sqr(mu)) * mu;
const Spectrum F_schlick = mix(fresnel->f0, one_spectrum(), mu5);
*r_reflectance = saturate(F_schlick - fresnel->b * cos_theta_i * mu5 * mu);
*r_transmittance = zero_spectrum();
}
else if (bsdf->fresnel_type == MicrofacetFresnel::GENERALIZED_SCHLICK) {
ccl_private FresnelGeneralizedSchlick *fresnel = (ccl_private FresnelGeneralizedSchlick *)
bsdf->fresnel;
Spectrum F;
if (fresnel->thin_film.thickness > 0.1f) {
/* Iridescence doesn't combine well with the general case. We only expose it through the
* Principled BSDF for now, so it's fine to not support custom exponents and F90. */
kernel_assert(fresnel->exponent < 0.0f);
kernel_assert(fresnel->f90 == one_spectrum());
F = fresnel_iridescence(kg,
1.0f,
fresnel->thin_film.ior,
bsdf->ior,
cos_theta_i,
fresnel->thin_film.thickness,
r_cos_theta_t);
/* Apply F0 scaling (here per-channel, since iridescence produces colored output).
* Note that the usual approach (as used below) cannot be used here, since F may be below
* F0_real. Therefore, use a different approach: Scale the result by (F0 / F0_real), with
* the strength of the scaling depending on how close F is to F0_real.
* There isn't one single "correct" way to do this, it's just for artistic control anyways.
*/
const float F0_real = F0_from_ior(bsdf->ior);
if (F0_real > 1e-5f && !isequal(F, one_spectrum())) {
FOREACH_SPECTRUM_CHANNEL (i) {
const float s = saturatef(inverse_lerp(1.0f, F0_real, GET_SPECTRUM_CHANNEL(F, i)));
const float factor = GET_SPECTRUM_CHANNEL(fresnel->f0, i) / F0_real;
GET_SPECTRUM_CHANNEL(F, i) *= mix(1.0f, factor, s);
}
}
}
else if (fresnel->exponent < 0.0f) {
/* Special case: Use real Fresnel curve to determine the interpolation between F0 and F90.
* Used by Principled BSDF. */
const float F_real = fresnel_dielectric(cos_theta_i, bsdf->ior, r_cos_theta_t);
const float F0_real = F0_from_ior(bsdf->ior);
const float s = saturatef(inverse_lerp(F0_real, 1.0f, F_real));
F = mix(fresnel->f0, fresnel->f90, s);
}
else {
/* Regular case: Generalized Schlick term. */
const float cos_theta_t_sq = 1.0f - (1.0f - sqr(cos_theta_i)) / sqr(bsdf->ior);
if (cos_theta_t_sq <= 0.0f) {
/* Total internal reflection */
*r_reflectance = fresnel->reflection_tint * (float)has_reflection;
*r_transmittance = zero_spectrum();
return;
}
const float cos_theta_t = sqrtf(cos_theta_t_sq);
if (r_cos_theta_t) {
*r_cos_theta_t = cos_theta_t;
}
/* TODO(lukas): Is a special case for exponent==5 worth it? */
/* When going from a higher to a lower IOR, we must use the transmitted angle. */
const float fresnel_angle = ((bsdf->ior < 1.0f) ? cos_theta_t : cos_theta_i);
const float s = powf(1.0f - fresnel_angle, fresnel->exponent);
F = mix(fresnel->f0, fresnel->f90, s);
}
*r_reflectance = F * fresnel->reflection_tint;
*r_transmittance = (one_spectrum() - F) * fresnel->transmission_tint;
}
else {
kernel_assert(bsdf->fresnel_type == MicrofacetFresnel::NONE);
/* No Fresnel used, this is either purely reflective or purely refractive closure. */
*r_reflectance = *r_transmittance = one_spectrum();
/* Exclude total internal reflection. */
if (has_transmission && fresnel_dielectric(cos_theta_i, bsdf->ior, r_cos_theta_t) == 1.0f) {
*r_transmittance = zero_spectrum();
}
}
*r_reflectance *= (float)has_reflection;
*r_transmittance *= (float)has_transmission;
}
ccl_device_inline void microfacet_ggx_preserve_energy(KernelGlobals kg,
ccl_private MicrofacetBsdf *bsdf,
const ccl_private ShaderData *sd,
const Spectrum Fss)
{
const float mu = dot(sd->wi, bsdf->N);
const float rough = sqrtf(sqrtf(bsdf->alpha_x * bsdf->alpha_y));
float E;
float E_avg;
if (bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_ID) {
E = lookup_table_read_2D(kg, rough, mu, kernel_data.tables.ggx_E, 32, 32);
E_avg = lookup_table_read(kg, rough, kernel_data.tables.ggx_Eavg, 32);
}
else if (bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID) {
int ofs = kernel_data.tables.ggx_glass_E;
int avg_ofs = kernel_data.tables.ggx_glass_Eavg;
float ior = bsdf->ior;
if (ior < 1.0f) {
ior = 1.0f / ior;
ofs = kernel_data.tables.ggx_glass_inv_E;
avg_ofs = kernel_data.tables.ggx_glass_inv_Eavg;
}
/* TODO: Bias mu towards more precision for low values. */
const float z = sqrtf(fabsf((ior - 1.0f) / (ior + 1.0f)));
E = lookup_table_read_3D(kg, rough, mu, z, ofs, 16, 16, 16);
E_avg = lookup_table_read_2D(kg, rough, z, avg_ofs, 16, 16);
}
else {
kernel_assert(false);
E = 1.0f;
E_avg = 1.0f;
}
const float missing_factor = ((1.0f - E) / E);
bsdf->energy_scale = 1.0f + missing_factor;
/* Check if we need to account for extra darkening/saturation due to multi-bounce Fresnel. */
if (!isequal(Fss, one_spectrum())) {
/* Fms here is based on the appendix of "Revisiting Physically Based Shading at Imageworks"
* by Christopher Kulla and Alejandro Conty,
* with one Fss cancelled out since this is just a multiplier on top of
* the single-scattering BSDF, which already contains one bounce of Fresnel. */
const Spectrum Fms = Fss * E_avg / (one_spectrum() - Fss * (1.0f - E_avg));
/* Since we already include the energy compensation in bsdf->energy_scale,
* this term is what's needed to make the full BSDF * weight * energy_scale
* computation work out to the correct value. */
const Spectrum darkening = (one_spectrum() + Fms * missing_factor) / bsdf->energy_scale;
bsdf->weight *= darkening;
bsdf->sample_weight *= average(darkening);
}
}
/* This function estimates the albedo of the BSDF (NOT including the bsdf->weight) as caused by
* the applied Fresnel model for the given view direction.
* The base microfacet model is assumed to have an albedo of 1 (we have the energy preservation
* code for that), but e.g. a reflection-only closure with Fresnel applied can end up having
* a very low overall albedo.
* This is used to adjust the sample weight, as well as for the Diff/Gloss/Trans Color pass
* and the Denoising Albedo pass.
*
* TODO: The Schlick LUT seems to assume energy preservation, which is not true for GGX. if
* energy-preserving then transmission should just be `1 - reflection`. For dielectric we could
* probably split the LUT for multiGGX if smooth assumption is not good enough. */
ccl_device Spectrum bsdf_microfacet_estimate_albedo(KernelGlobals kg,
const ccl_private ShaderData *sd,
const ccl_private MicrofacetBsdf *bsdf,
const bool eval_reflection,
const bool eval_transmission)
{
const float cos_NI = dot(sd->wi, bsdf->N);
Spectrum reflectance;
Spectrum transmittance;
microfacet_fresnel(kg, bsdf, cos_NI, nullptr, &reflectance, &transmittance);
reflectance *= (float)eval_reflection;
transmittance *= (float)eval_transmission;
/* Use lookup tables for generalized Schlick reflection, otherwise assume smooth surface. */
if (!is_zero(reflectance) && bsdf->fresnel_type == MicrofacetFresnel::GENERALIZED_SCHLICK) {
ccl_private FresnelGeneralizedSchlick *fresnel = (ccl_private FresnelGeneralizedSchlick *)
bsdf->fresnel;
if (fresnel->thin_film.thickness > 0.1f) {
/* Precomputing LUTs for thin-film iridescence isn't viable, so fall back to the specular
* reflection approximation from the microfacet_fresnel call above in that case. */
}
else {
const float rough = sqrtf(sqrtf(bsdf->alpha_x * bsdf->alpha_y));
float s;
if (fresnel->exponent < 0.0f) {
const float z = sqrtf(fabsf((bsdf->ior - 1.0f) / (bsdf->ior + 1.0f)));
s = lookup_table_read_3D(
kg, rough, cos_NI, z, kernel_data.tables.ggx_gen_schlick_ior_s, 16, 16, 16);
}
else {
const float z = 1.0f / (0.2f * fresnel->exponent + 1.0f);
s = lookup_table_read_3D(
kg, rough, cos_NI, z, kernel_data.tables.ggx_gen_schlick_s, 16, 16, 16);
}
reflectance = mix(fresnel->f0, fresnel->f90, s) * fresnel->reflection_tint;
}
}
else if (bsdf->fresnel_type == MicrofacetFresnel::F82_TINT) {
ccl_private FresnelF82Tint *fresnel = (ccl_private FresnelF82Tint *)bsdf->fresnel;
const float rough = sqrtf(sqrtf(bsdf->alpha_x * bsdf->alpha_y));
const float s = lookup_table_read_3D(
kg, rough, cos_NI, 0.5f, kernel_data.tables.ggx_gen_schlick_s, 16, 16, 16);
/* TODO: Precompute B factor term and account for it here. */
reflectance = mix(fresnel->f0, one_spectrum(), s);
}
return reflectance + transmittance;
}
/* Smith shadowing-masking term, here in the non-separable form.
* For details, see:
* Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs.
* Eric Heitz, JCGT Vol. 3, No. 2, 2014.
* https://jcgt.org/published/0003/02/03/ */
template<MicrofacetType m_type>
ccl_device_inline float bsdf_lambda_from_sqr_alpha_tan_n(const float sqr_alpha_tan_n)
{
if (m_type == MicrofacetType::GGX) {
/* Equation 72. */
return 0.5f * (sqrtf(1.0f + sqr_alpha_tan_n) - 1.0f);
}
kernel_assert(m_type == MicrofacetType::BECKMANN);
/* Approximation from below Equation 69. */
if (sqr_alpha_tan_n < 0.39f) {
/* Equivalent to a >= 1.6f, but also handles sqr_alpha_tan_n == 0.0f cleanly. */
return 0.0f;
}
const float a = inversesqrtf(sqr_alpha_tan_n);
return ((0.396f * a - 1.259f) * a + 1.0f) / ((2.181f * a + 3.535f) * a);
}
template<MicrofacetType m_type>
ccl_device_inline float bsdf_lambda(const float alpha2, const float cos_N)
{
return bsdf_lambda_from_sqr_alpha_tan_n<m_type>(alpha2 * fmaxf(1.0f / sqr(cos_N) - 1.0f, 0.0f));
}
template<MicrofacetType m_type>
ccl_device_inline float bsdf_aniso_lambda(const float alpha_x, const float alpha_y, const float3 V)
{
const float sqr_alpha_tan_n = (sqr(alpha_x * V.x) + sqr(alpha_y * V.y)) / sqr(V.z);
return bsdf_lambda_from_sqr_alpha_tan_n<m_type>(sqr_alpha_tan_n);
}
/* Mono-directional shadowing-masking term. */
template<MicrofacetType m_type>
ccl_device_inline float bsdf_G(const float alpha2, const float cos_N)
{
return 1.0f / (1.0f + bsdf_lambda<m_type>(alpha2, cos_N));
}
/* Combined shadowing-masking term. */
template<MicrofacetType m_type>
ccl_device_inline float bsdf_G(const float alpha2, const float cos_NI, const float cos_NO)
{
return 1.0f / (1.0f + bsdf_lambda<m_type>(alpha2, cos_NI) + bsdf_lambda<m_type>(alpha2, cos_NO));
}
/* Normal distribution function. */
template<MicrofacetType m_type>
ccl_device_inline float bsdf_D(const float alpha2, const float cos_NH)
{
const float cos_NH2 = min(sqr(cos_NH), 1.0f);
const float one_minus_cos_NH2 = 1.0f - cos_NH2;
if (m_type == MicrofacetType::BECKMANN) {
return 1.0f / (expf(one_minus_cos_NH2 / (cos_NH2 * alpha2)) * M_PI_F * alpha2 * sqr(cos_NH2));
}
kernel_assert(m_type == MicrofacetType::GGX);
return alpha2 / (M_PI_F * sqr(one_minus_cos_NH2 + alpha2 * cos_NH2));
}
template<MicrofacetType m_type>
ccl_device_inline float bsdf_aniso_D(const float alpha_x, const float alpha_y, float3 H)
{
H /= make_float3(alpha_x, alpha_y, 1.0f);
const float cos_NH2 = sqr(H.z);
const float alpha2 = alpha_x * alpha_y;
if (m_type == MicrofacetType::BECKMANN) {
return expf(-(sqr(H.x) + sqr(H.y)) / cos_NH2) / (M_PI_F * alpha2 * sqr(cos_NH2));
}
kernel_assert(m_type == MicrofacetType::GGX);
return M_1_PI_F / (alpha2 * sqr(len_squared(H)));
}
/* Do not set `SD_BSDF_HAS_EVAL` flag if the squared roughness is below a certain threshold. */
ccl_device_forceinline int bsdf_microfacet_eval_flag(const ccl_private MicrofacetBsdf *bsdf)
{
return (bsdf->alpha_x * bsdf->alpha_y > BSDF_ROUGHNESS_SQ_THRESH) ? SD_BSDF_HAS_EVAL : 0;
}
template<MicrofacetType m_type>
ccl_device Spectrum bsdf_microfacet_eval(KernelGlobals kg,
const ccl_private ShaderClosure *sc,
const float3 Ng,
const float3 wi,
const float3 wo,
ccl_private float *pdf)
{
const ccl_private MicrofacetBsdf *bsdf = (const ccl_private MicrofacetBsdf *)sc;
/* Whether the closure has reflective or transmissive lobes. */
const bool has_reflection = !CLOSURE_IS_REFRACTION(bsdf->type);
const bool has_transmission = CLOSURE_IS_GLASS(bsdf->type) || !has_reflection;
const float3 N = bsdf->N;
const float cos_NI = dot(N, wi);
const float cos_NO = dot(N, wo);
const float cos_NgO = dot(Ng, wo);
const float alpha_x = bsdf->alpha_x;
const float alpha_y = bsdf->alpha_y;
const bool is_transmission = (cos_NO < 0.0f);
/* Check whether the pair of directions is valid for evaluation:
* - Incoming direction has to be in the upper hemisphere (Cycles convention)
* - Specular cases can't be evaluated, only sampled.
* - The outgoing direction has to be the in the same hemisphere w.r.t. both normals.
* - Purely reflective closures can't have refraction.
* - Purely refractive closures can't have reflection.
*/
if ((cos_NI <= 0) || !bsdf_microfacet_eval_flag(bsdf) || ((cos_NgO < 0.0f) != is_transmission) ||
(is_transmission && !has_transmission) || (!is_transmission && !has_reflection))
{
return zero_spectrum();
}
/* Compute half vector. */
/* TODO: deal with the case when `bsdf->ior` is close to one. */
/* TODO: check if the refraction configuration is valid. See `btdf_ggx()` in
* `eevee_bxdf_lib.glsl`. */
float3 H = is_transmission ? -(bsdf->ior * wo + wi) : (wi + wo);
const float inv_len_H = safe_divide(1.0f, len(H));
H *= inv_len_H;
/* Compute Fresnel coefficients. */
const float cos_HI = dot(H, wi);
Spectrum reflectance;
Spectrum transmittance;
microfacet_fresnel(kg, bsdf, cos_HI, nullptr, &reflectance, &transmittance);
if (is_zero(reflectance) && is_zero(transmittance)) {
return zero_spectrum();
}
const float cos_NH = dot(N, H);
float D;
float lambdaI;
float lambdaO;
/* NOTE: we could add support for anisotropic transmission, although it will make dispersion
* harder to compute. */
if (alpha_x == alpha_y || is_transmission) { /* Isotropic. */
const float alpha2 = alpha_x * alpha_y;
D = bsdf_D<m_type>(alpha2, cos_NH);
lambdaI = bsdf_lambda<m_type>(alpha2, cos_NI);
lambdaO = bsdf_lambda<m_type>(alpha2, cos_NO);
}
else { /* Anisotropic. */
float3 X;
float3 Y;
make_orthonormals_tangent(N, bsdf->T, &X, &Y);
const float3 local_H = make_float3(dot(X, H), dot(Y, H), cos_NH);
const float3 local_I = make_float3(dot(X, wi), dot(Y, wi), cos_NI);
const float3 local_O = make_float3(dot(X, wo), dot(Y, wo), cos_NO);
D = bsdf_aniso_D<m_type>(alpha_x, alpha_y, local_H);
lambdaI = bsdf_aniso_lambda<m_type>(alpha_x, alpha_y, local_I);
lambdaO = bsdf_aniso_lambda<m_type>(alpha_x, alpha_y, local_O);
}
const float common = D / cos_NI *
(is_transmission ? sqr(bsdf->ior * inv_len_H) * fabsf(cos_HI * dot(H, wo)) :
0.25f);
const float pdf_reflect = average(reflectance) / average(reflectance + transmittance);
const float lobe_pdf = is_transmission ? 1.0f - pdf_reflect : pdf_reflect;
*pdf = common * lobe_pdf / (1.0f + lambdaI);
return (is_transmission ? transmittance : reflectance) * common / (1.0f + lambdaO + lambdaI);
}
template<MicrofacetType m_type>
ccl_device int bsdf_microfacet_sample(KernelGlobals kg,
const ccl_private ShaderClosure *sc,
const float3 Ng,
const float3 wi,
const float3 rand,
ccl_private Spectrum *eval,
ccl_private float3 *wo,
ccl_private float *pdf,
ccl_private float2 *sampled_roughness,
ccl_private float *eta)
{
const ccl_private MicrofacetBsdf *bsdf = (const ccl_private MicrofacetBsdf *)sc;
const float3 N = bsdf->N;
const float cos_NI = dot(N, wi);
if (cos_NI <= 0) {
/* Incident angle from the lower hemisphere is invalid. */
return LABEL_NONE;
}
const float m_eta = bsdf->ior;
const float m_inv_eta = 1.0f / bsdf->ior;
const float alpha_x = bsdf->alpha_x;
const float alpha_y = bsdf->alpha_y;
bool m_singular = !bsdf_microfacet_eval_flag(bsdf);
/* Half vector. */
float3 H;
/* Needed for anisotropic microfacets later. */
float3 local_H;
float3 local_I;
if (m_singular) {
H = N;
}
else {
float3 X;
float3 Y;
if (alpha_x == alpha_y) {
make_orthonormals(N, &X, &Y);
}
else {
make_orthonormals_tangent(N, bsdf->T, &X, &Y);
}
/* Importance sampling with distribution of visible normals. Vectors are transformed to local
* space before and after sampling. */
local_I = make_float3(dot(X, wi), dot(Y, wi), cos_NI);
if (m_type == MicrofacetType::GGX) {
local_H = microfacet_ggx_sample_vndf(local_I, alpha_x, alpha_y, make_float2(rand));
}
else {
/* m_type == MicrofacetType::BECKMANN */
local_H = microfacet_beckmann_sample_vndf(local_I, alpha_x, alpha_y, make_float2(rand));
}
H = to_global(local_H, X, Y, N);
}
const float cos_HI = dot(H, wi);
/* The angle between the half vector and the refracted ray. Not used when sampling reflection. */
float cos_HO;
/* Compute Fresnel coefficients. */
Spectrum reflectance;
Spectrum transmittance;
microfacet_fresnel(kg, bsdf, cos_HI, &cos_HO, &reflectance, &transmittance);
if (is_zero(reflectance) && is_zero(transmittance)) {
return LABEL_NONE;
}
/* Decide between refraction and reflection based on the energy. */
const float pdf_reflect = average(reflectance) / average(reflectance + transmittance);
const bool do_refract = (rand.z >= pdf_reflect);
/* Compute actual reflected or refracted direction. */
*wo = do_refract ? refract_angle(wi, H, cos_HO, m_inv_eta) : 2.0f * cos_HI * H - wi;
if ((dot(Ng, *wo) < 0) != do_refract) {
return LABEL_NONE;
}
if (do_refract) {
*eval = transmittance;
*pdf = 1.0f - pdf_reflect;
/* If the IOR is close enough to 1.0, just treat the interaction as specular. */
m_singular = m_singular || (fabsf(m_eta - 1.0f) < 1e-4f);
}
else {
*eval = reflectance;
*pdf = pdf_reflect;
}
if (m_singular) {
/* Some high number for MIS. */
*pdf *= 1e6f;
*eval *= 1e6f;
}
else {
float D;
float lambdaI;
float lambdaO;
/* TODO: add support for anisotropic transmission. */
if (alpha_x == alpha_y || do_refract) { /* Isotropic. */
const float alpha2 = alpha_x * alpha_y;
const float cos_NH = local_H.z;
const float cos_NO = dot(N, *wo);
D = bsdf_D<m_type>(alpha2, cos_NH);
lambdaO = bsdf_lambda<m_type>(alpha2, cos_NO);
lambdaI = bsdf_lambda<m_type>(alpha2, cos_NI);
}
else { /* Anisotropic. */
const float3 local_O = 2.0f * cos_HI * local_H - local_I;
D = bsdf_aniso_D<m_type>(alpha_x, alpha_y, local_H);
lambdaO = bsdf_aniso_lambda<m_type>(alpha_x, alpha_y, local_O);
lambdaI = bsdf_aniso_lambda<m_type>(alpha_x, alpha_y, local_I);
}
const float common = D / cos_NI *
(do_refract ? fabsf(cos_HI * cos_HO) / sqr(cos_HO + cos_HI * m_inv_eta) :
0.25f);
*pdf *= common / (1.0f + lambdaI);
*eval *= common / (1.0f + lambdaI + lambdaO);
}
*sampled_roughness = make_float2(alpha_x, alpha_y);
*eta = do_refract ? m_eta : 1.0f;
return (do_refract ? LABEL_TRANSMIT : LABEL_REFLECT) |
(m_singular ? LABEL_SINGULAR : LABEL_GLOSSY);
}
/* Fresnel term setup functions. These get called after the distribution-specific setup functions
* like bsdf_microfacet_ggx_setup. */
ccl_device void bsdf_microfacet_setup_fresnel_conductor(KernelGlobals kg,
ccl_private MicrofacetBsdf *bsdf,
const ccl_private ShaderData *sd,
ccl_private FresnelConductor *fresnel,
const bool preserve_energy)
{
bsdf->fresnel_type = MicrofacetFresnel::CONDUCTOR;
bsdf->fresnel = fresnel;
bsdf->sample_weight *= average(bsdf_microfacet_estimate_albedo(kg, sd, bsdf, true, true));
if (preserve_energy) {
/* In order to estimate Fss of the conductor, we fit the F82-tint model to it based on the
* value at 0° and ~82° and then use the analytic expression for its Fss. */
const Spectrum F0 = fresnel_conductor(1.0f, fresnel->n, fresnel->k);
const Spectrum F82 = fresnel_conductor(1.0f / 7.0f, fresnel->n, fresnel->k);
/* 0.46266436f is (1 - 1/7)^5, 17.651384f is 1/(1/7 * (1 - 1/7)^6) */
const Spectrum B = (mix(F0, one_spectrum(), 0.46266436f) - F82) * 17.651384f;
const Spectrum Fss = saturate(mix(F0, one_spectrum(), 1.0f / 21.0f) - B * (1.0f / 126.0f));
microfacet_ggx_preserve_energy(kg, bsdf, sd, Fss);
}
}
ccl_device void bsdf_microfacet_setup_fresnel_dielectric_tint(
KernelGlobals kg,
ccl_private MicrofacetBsdf *bsdf,
const ccl_private ShaderData *sd,
ccl_private FresnelDielectricTint *fresnel,
const bool preserve_energy)
{
bsdf->fresnel_type = MicrofacetFresnel::DIELECTRIC_TINT;
bsdf->fresnel = fresnel;
bsdf->sample_weight *= average(bsdf_microfacet_estimate_albedo(kg, sd, bsdf, true, true));
if (preserve_energy) {
/* Assume that the transmissive tint makes up most of the overall color. */
microfacet_ggx_preserve_energy(kg, bsdf, sd, fresnel->transmission_tint);
}
}
ccl_device void bsdf_microfacet_setup_fresnel_generalized_schlick(
KernelGlobals kg,
ccl_private MicrofacetBsdf *bsdf,
const ccl_private ShaderData *sd,
ccl_private FresnelGeneralizedSchlick *fresnel,
const bool preserve_energy)
{
fresnel->f0 = saturate(fresnel->f0);
bsdf->fresnel_type = MicrofacetFresnel::GENERALIZED_SCHLICK;
bsdf->fresnel = fresnel;
bsdf->sample_weight *= average(bsdf_microfacet_estimate_albedo(kg, sd, bsdf, true, true));
if (preserve_energy) {
Spectrum Fss = one_spectrum();
/* Multi-bounce Fresnel is only supported for reflective lobes here. */
if (is_zero(fresnel->transmission_tint)) {
float s;
if (fresnel->exponent < 0.0f) {
const float eta = bsdf->ior;
const float real_F0 = F0_from_ior(bsdf->ior);
/* Numerical fit for the integral of 2*cosI * F(cosI, eta) over 0...1 with F being
* the real dielectric Fresnel. From "Revisiting Physically Based Shading at Imageworks"
* by Christopher Kulla and Alejandro Conty. */
float real_Fss;
if (eta < 1.0f) {
real_Fss = 0.997118f + eta * (0.1014f - eta * (0.965241f + eta * 0.130607f));
}
else {
real_Fss = (eta - 1.0f) / (4.08567f + 1.00071f * eta);
}
s = saturatef(inverse_lerp(real_F0, 1.0f, real_Fss));
}
else {
/* Integral of 2*cosI * (1 - cosI)^exponent over 0...1. */
s = 2.0f / ((fresnel->exponent + 3.0f) * fresnel->exponent + 2.0f);
}
/* Due to the linearity of the generalized model, this ends up working. */
Fss = fresnel->reflection_tint * mix(fresnel->f0, fresnel->f90, s);
}
else {
/* For transmissive BSDFs, assume that the transmissive tint makes up most of the overall
* color. */
Fss = fresnel->transmission_tint;
}
microfacet_ggx_preserve_energy(kg, bsdf, sd, Fss);
}
}
ccl_device void bsdf_microfacet_setup_fresnel_f82_tint(KernelGlobals kg,
ccl_private MicrofacetBsdf *bsdf,
const ccl_private ShaderData *sd,
ccl_private FresnelF82Tint *fresnel,
const Spectrum f82_tint,
const bool preserve_energy)
{
if (isequal(f82_tint, one_spectrum())) {
fresnel->b = zero_spectrum();
}
else {
/* Precompute the F82 term factor for the Fresnel model.
* In the classic F82 model, the F82 input directly determines the value of the Fresnel
* model at ~82°, similar to F0 and F90.
* With F82-Tint, on the other hand, the value at 82° is the value of the classic Schlick
* model multiplied by the tint input.
* Therefore, the factor follows by setting F82Tint(cosI) = FSchlick(cosI) - b*cosI*(1-cosI)^6
* and F82Tint(acos(1/7)) = FSchlick(acos(1/7)) * f82_tint and solving for b. */
const float f = 6.0f / 7.0f;
const float f5 = sqr(sqr(f)) * f;
const Spectrum F_schlick = mix(fresnel->f0, one_spectrum(), f5);
fresnel->b = F_schlick * (7.0f / (f5 * f)) * (one_spectrum() - f82_tint);
}
bsdf->fresnel_type = MicrofacetFresnel::F82_TINT;
bsdf->fresnel = fresnel;
bsdf->sample_weight *= average(bsdf_microfacet_estimate_albedo(kg, sd, bsdf, true, true));
if (preserve_energy) {
const Spectrum Fss = mix(fresnel->f0, one_spectrum(), 1.0f / 21.0f) -
fresnel->b * (1.0f / 126.0f);
microfacet_ggx_preserve_energy(kg, bsdf, sd, Fss);
}
}
ccl_device void bsdf_microfacet_setup_fresnel_constant(KernelGlobals kg,
ccl_private MicrofacetBsdf *bsdf,
const ccl_private ShaderData *sd,
const Spectrum color)
{
/* Constant Fresnel is a special case - the color is already baked into the closure's
* weight, so we just need to perform the energy preservation. */
kernel_assert(bsdf->fresnel_type == MicrofacetFresnel::NONE ||
bsdf->fresnel_type == MicrofacetFresnel::DIELECTRIC);
microfacet_ggx_preserve_energy(kg, bsdf, sd, color);
}
ccl_device void bsdf_microfacet_setup_fresnel_dielectric(KernelGlobals kg,
ccl_private MicrofacetBsdf *bsdf,
const ccl_private ShaderData *sd)
{
bsdf->fresnel_type = MicrofacetFresnel::DIELECTRIC;
bsdf->sample_weight *= average(bsdf_microfacet_estimate_albedo(kg, sd, bsdf, true, true));
}
/* 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->alpha_x = saturatef(bsdf->alpha_x);
bsdf->alpha_y = saturatef(bsdf->alpha_y);
bsdf->fresnel_type = MicrofacetFresnel::NONE;
bsdf->energy_scale = 1.0f;
bsdf->type = CLOSURE_BSDF_MICROFACET_GGX_ID;
return SD_BSDF | bsdf_microfacet_eval_flag(bsdf);
}
ccl_device int bsdf_microfacet_ggx_refraction_setup(ccl_private MicrofacetBsdf *bsdf)
{
bsdf->alpha_x = saturatef(bsdf->alpha_x);
bsdf->alpha_y = bsdf->alpha_x;
bsdf->fresnel_type = MicrofacetFresnel::NONE;
bsdf->energy_scale = 1.0f;
bsdf->type = CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
return SD_BSDF | SD_BSDF_HAS_TRANSMISSION | bsdf_microfacet_eval_flag(bsdf);
}
ccl_device int bsdf_microfacet_ggx_glass_setup(ccl_private MicrofacetBsdf *bsdf)
{
bsdf->alpha_x = saturatef(bsdf->alpha_x);
bsdf->alpha_y = bsdf->alpha_x;
bsdf->fresnel_type = MicrofacetFresnel::DIELECTRIC;
bsdf->energy_scale = 1.0f;
bsdf->type = CLOSURE_BSDF_MICROFACET_GGX_GLASS_ID;
return SD_BSDF | SD_BSDF_HAS_TRANSMISSION | bsdf_microfacet_eval_flag(bsdf);
}
ccl_device void bsdf_microfacet_blur(ccl_private ShaderClosure *sc, const 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(KernelGlobals kg,
const ccl_private ShaderClosure *sc,
const float3 Ng,
const float3 wi,
const float3 wo,
ccl_private float *pdf)
{
const ccl_private MicrofacetBsdf *bsdf = (const ccl_private MicrofacetBsdf *)sc;
return bsdf->energy_scale * bsdf_microfacet_eval<MicrofacetType::GGX>(kg, sc, Ng, wi, wo, pdf);
}
ccl_device int bsdf_microfacet_ggx_sample(KernelGlobals kg,
const ccl_private ShaderClosure *sc,
const float3 Ng,
const float3 wi,
const float3 rand,
ccl_private Spectrum *eval,
ccl_private float3 *wo,
ccl_private float *pdf,
ccl_private float2 *sampled_roughness,
ccl_private float *eta)
{
const int label = bsdf_microfacet_sample<MicrofacetType::GGX>(
kg, sc, Ng, wi, rand, eval, wo, pdf, sampled_roughness, eta);
*eval *= ((const ccl_private MicrofacetBsdf *)sc)->energy_scale;
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->fresnel_type = MicrofacetFresnel::NONE;
bsdf->type = CLOSURE_BSDF_MICROFACET_BECKMANN_ID;
return SD_BSDF | bsdf_microfacet_eval_flag(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->fresnel_type = MicrofacetFresnel::NONE;
bsdf->type = CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID;
return SD_BSDF | SD_BSDF_HAS_TRANSMISSION | bsdf_microfacet_eval_flag(bsdf);
}
ccl_device int bsdf_microfacet_beckmann_glass_setup(ccl_private MicrofacetBsdf *bsdf)
{
bsdf->alpha_x = saturatef(bsdf->alpha_x);
bsdf->alpha_y = bsdf->alpha_x;
bsdf->fresnel_type = MicrofacetFresnel::DIELECTRIC;
bsdf->type = CLOSURE_BSDF_MICROFACET_BECKMANN_GLASS_ID;
return SD_BSDF | SD_BSDF_HAS_TRANSMISSION | bsdf_microfacet_eval_flag(bsdf);
}
ccl_device Spectrum bsdf_microfacet_beckmann_eval(KernelGlobals kg,
const ccl_private ShaderClosure *sc,
const float3 Ng,
const float3 wi,
const float3 wo,
ccl_private float *pdf)
{
return bsdf_microfacet_eval<MicrofacetType::BECKMANN>(kg, sc, Ng, wi, wo, pdf);
}
ccl_device int bsdf_microfacet_beckmann_sample(KernelGlobals kg,
const ccl_private ShaderClosure *sc,
const float3 Ng,
const float3 wi,
const float3 rand,
ccl_private Spectrum *eval,
ccl_private float3 *wo,
ccl_private float *pdf,
ccl_private float2 *sampled_roughness,
ccl_private float *eta)
{
return bsdf_microfacet_sample<MicrofacetType::BECKMANN>(
kg, sc, Ng, wi, rand, eval, wo, pdf, sampled_roughness, eta);
}
CCL_NAMESPACE_END
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