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/*
* Copyright 2011-2016 Blender Foundation
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/* Evaluate the BSDF from wi to wo.
* Evaluation is split into the analytical single-scattering BSDF and the multi-scattering BSDF,
* which is evaluated stochastically through a random walk. At each bounce (except for the first one),
* the amount of reflection from here towards wo is evaluated before bouncing again.
*
* Because of the random walk, the evaluation is not deterministic, but its expected value is equal to
* the correct BSDF, which is enough for Monte-Carlo rendering. The PDF also can't be determined
* analytically, so the single-scattering PDF plus a diffuse term to account for the multi-scattered
* energy is used. In combination with MIS, that is enough to produce an unbiased result, although
* the balance heuristic isn't necessarily optimal anymore.
*/
ccl_device_forceinline float3 MF_FUNCTION_FULL_NAME(mf_eval)(
float3 wi,
float3 wo,
const bool wo_outside,
const float3 color,
const float alpha_x,
const float alpha_y,
ccl_addr_space uint *lcg_state
#ifdef MF_MULTI_GLASS
, const float eta
#elif defined(MF_MULTI_GLOSSY)
, float3 *n, float3 *k
#endif
)
{
/* Evaluating for a shallower incoming direction produces less noise, and the properties of the BSDF guarantee reciprocity. */
bool swapped = false;
#ifdef MF_MULTI_GLASS
if(wi.z*wo.z < 0.0f) {
/* Glass transmission is a special case and requires the directions to change hemisphere. */
if(-wo.z < wi.z) {
swapped = true;
float3 tmp = -wo;
wo = -wi;
wi = tmp;
}
}
else
#endif
if(wo.z < wi.z) {
swapped = true;
float3 tmp = wo;
wo = wi;
wi = tmp;
}
if(wi.z < 1e-5f || (wo.z < 1e-5f && wo_outside) || (wo.z > -1e-5f && !wo_outside))
return make_float3(0.0f, 0.0f, 0.0f);
const float2 alpha = make_float2(alpha_x, alpha_y);
float lambda_r = mf_lambda(-wi, alpha);
float shadowing_lambda = mf_lambda(wo_outside? wo: -wo, alpha);
/* Analytically compute single scattering for lower noise. */
float3 eval;
#ifdef MF_MULTI_GLASS
eval = mf_eval_phase_glass(-wi, lambda_r, wo, wo_outside, alpha, eta);
if(wo_outside)
eval *= -lambda_r / (shadowing_lambda - lambda_r);
else
eval *= -lambda_r * beta(-lambda_r, shadowing_lambda+1.0f);
#elif defined(MF_MULTI_DIFFUSE)
/* Diffuse has no special closed form for the single scattering bounce */
eval = make_float3(0.0f, 0.0f, 0.0f);
#else /* MF_MULTI_GLOSSY */
const float3 wh = normalize(wi+wo);
const float G2 = 1.0f / (1.0f - (lambda_r + 1.0f) + shadowing_lambda);
float val = G2 * 0.25f / wi.z;
if(alpha.x == alpha.y)
val *= D_ggx(wh, alpha.x);
else
val *= D_ggx_aniso(wh, alpha);
if(n && k) {
eval = fresnel_conductor(dot(wh, wi), *n, *k) * val;
}
else {
eval = make_float3(val, val, val);
}
#endif
float3 wr = -wi;
float hr = 1.0f;
float C1_r = 1.0f;
float G1_r = 0.0f;
bool outside = true;
float3 throughput = make_float3(1.0f, 1.0f, 1.0f);
for(int order = 0; order < 10; order++) {
/* Sample microfacet height and normal */
if(!mf_sample_height(wr, &hr, &C1_r, &G1_r, &lambda_r, lcg_step_float_addrspace(lcg_state)))
break;
float3 wm = mf_sample_vndf(-wr, alpha, make_float2(lcg_step_float_addrspace(lcg_state),
lcg_step_float_addrspace(lcg_state)));
#ifdef MF_MULTI_DIFFUSE
if(order == 0) {
/* Compute single-scattering for diffuse. */
const float G2_G1 = -lambda_r / (shadowing_lambda - lambda_r);
eval += throughput * G2_G1 * mf_eval_phase_diffuse(wo, wm);
}
#endif
if(order > 0) {
/* Evaluate amount of scattering towards wo on this microfacet. */
float3 phase;
#ifdef MF_MULTI_GLASS
if(outside)
phase = mf_eval_phase_glass(wr, lambda_r, wo, wo_outside, alpha, eta);
else
phase = mf_eval_phase_glass(wr, lambda_r, -wo, !wo_outside, alpha, 1.0f/eta);
#elif defined(MF_MULTI_DIFFUSE)
phase = mf_eval_phase_diffuse(wo, wm);
#else /* MF_MULTI_GLOSSY */
phase = mf_eval_phase_glossy(wr, lambda_r, wo, alpha, n, k) * throughput;
#endif
eval += throughput * phase * mf_G1(wo_outside? wo: -wo, mf_C1((outside == wo_outside)? hr: -hr), shadowing_lambda);
}
if(order+1 < 10) {
/* Bounce from the microfacet. */
#ifdef MF_MULTI_GLASS
bool next_outside;
wr = mf_sample_phase_glass(-wr, outside? eta: 1.0f/eta, wm, lcg_step_float_addrspace(lcg_state), &next_outside);
if(!next_outside) {
outside = !outside;
wr = -wr;
hr = -hr;
}
#elif defined(MF_MULTI_DIFFUSE)
wr = mf_sample_phase_diffuse(wm,
lcg_step_float_addrspace(lcg_state),
lcg_step_float_addrspace(lcg_state));
#else /* MF_MULTI_GLOSSY */
wr = mf_sample_phase_glossy(-wr, n, k, &throughput, wm);
#endif
lambda_r = mf_lambda(wr, alpha);
throughput *= color;
C1_r = mf_C1(hr);
G1_r = mf_G1(wr, C1_r, lambda_r);
}
}
if(swapped)
eval *= fabsf(wi.z / wo.z);
return eval;
}
/* Perform a random walk on the microsurface starting from wi, returning the direction in which the walk
* escaped the surface in wo. The function returns the throughput between wi and wo.
* Without reflection losses due to coloring or fresnel absorption in conductors, the sampling is optimal.
*/
ccl_device_forceinline float3 MF_FUNCTION_FULL_NAME(mf_sample)(float3 wi, float3 *wo, const float3 color, const float alpha_x, const float alpha_y, ccl_addr_space uint *lcg_state
#ifdef MF_MULTI_GLASS
, const float eta
#elif defined(MF_MULTI_GLOSSY)
, float3 *n, float3 *k
#endif
)
{
const float2 alpha = make_float2(alpha_x, alpha_y);
float3 throughput = make_float3(1.0f, 1.0f, 1.0f);
float3 wr = -wi;
float lambda_r = mf_lambda(wr, alpha);
float hr = 1.0f;
float C1_r = 1.0f;
float G1_r = 0.0f;
bool outside = true;
int order;
for(order = 0; order < 10; order++) {
/* Sample microfacet height. */
if(!mf_sample_height(wr, &hr, &C1_r, &G1_r, &lambda_r, lcg_step_float_addrspace(lcg_state))) {
/* The random walk has left the surface. */
*wo = outside? wr: -wr;
return throughput;
}
/* Sample microfacet normal. */
float3 wm = mf_sample_vndf(-wr, alpha, make_float2(lcg_step_float_addrspace(lcg_state),
lcg_step_float_addrspace(lcg_state)));
/* First-bounce color is already accounted for in mix weight. */
if(order > 0)
throughput *= color;
/* Bounce from the microfacet. */
#ifdef MF_MULTI_GLASS
bool next_outside;
wr = mf_sample_phase_glass(-wr, outside? eta: 1.0f/eta, wm, lcg_step_float_addrspace(lcg_state), &next_outside);
if(!next_outside) {
hr = -hr;
wr = -wr;
outside = !outside;
}
#elif defined(MF_MULTI_DIFFUSE)
wr = mf_sample_phase_diffuse(wm,
lcg_step_float_addrspace(lcg_state),
lcg_step_float_addrspace(lcg_state));
#else /* MF_MULTI_GLOSSY */
wr = mf_sample_phase_glossy(-wr, n, k, &throughput, wm);
#endif
/* Update random walk parameters. */
lambda_r = mf_lambda(wr, alpha);
G1_r = mf_G1(wr, C1_r, lambda_r);
}
*wo = make_float3(0.0f, 0.0f, 1.0f);
return make_float3(0.0f, 0.0f, 0.0f);
}
#undef MF_MULTI_GLASS
#undef MF_MULTI_DIFFUSE
#undef MF_MULTI_GLOSSY
#undef MF_PHASE_FUNCTION
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