f5cb0cf1a5
Samples render slower than before, but hopefully this is made up for with reduced noise in most cases. The main slowdown comes from samples that would previously be wasted and turn out black, which are now continued. GGX sampling is about the same speed as before, while for Beckmann it is slower still. Perhaps optimizations are still possible there, but didn't find anything easy. Code from this paper, which comes with sample code: Importance Sampling Microfacet-Based BSDFs using the Distribution of Visible Normals. E. Heitz and E. d'Eon, EGSR 2014 Differential Revision: https://developer.blender.org/D572
868 lines
25 KiB
C
868 lines
25 KiB
C
/*
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* Adapted from Open Shading Language with this license:
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*
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* Copyright (c) 2009-2010 Sony Pictures Imageworks Inc., et al.
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* All Rights Reserved.
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*
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* Modifications Copyright 2011, Blender Foundation.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are
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* met:
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* * Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* * Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* * Neither the name of Sony Pictures Imageworks nor the names of its
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* contributors may be used to endorse or promote products derived from
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* this software without specific prior written permission.
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#ifndef __BSDF_MICROFACET_H__
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#define __BSDF_MICROFACET_H__
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CCL_NAMESPACE_BEGIN
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/* Approximate erf and erfinv implementations
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*
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* Adapted from code (C) Copyright John Maddock 2006.
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* Use, modification and distribution are subject to the
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* Boost Software License, Version 1.0. (See accompanying file
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* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) */
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ccl_device float approx_erff_impl(float z)
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{
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float result;
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if(z < 0.5f) {
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if(z < 1e-10f) {
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if(z == 0) {
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result = 0;
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}
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else {
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float c = 0.0033791670f;
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result = z * 1.125f + z * c;
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}
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}
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else {
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float Y = 1.044948577f;
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float zz = z * z;
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float num = (((-0.007727583f * zz) + -0.050999073f)*zz + -0.338165134f)*zz + 0.083430589f;
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float denom = (((0.000370900f * zz) + 0.008585719f)*zz + 0.087522260f)*zz + 0.455004033f;
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result = z * (Y + num / denom);
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}
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}
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else if(z < 2.5f) {
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if(z < 1.5f) {
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float Y = 0.4059357643f;
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float fz = z - 0.5f;
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float num = (((0.088890036f * fz) + 0.191003695f)*fz + 0.178114665f)*fz + -0.098090592f;
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float denom = (((0.123850974f * fz) + 0.578052804f)*fz + 1.426280048f)*fz + 1.847590709f;
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result = Y + num / denom;
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result *= expf(-z * z) / z;
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}
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else {
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float Y = 0.506728172f;
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float fz = z - 1.5f;
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float num = (((0.017567943f * fz) + 0.043948189f)*fz + 0.038654037f)*fz + -0.024350047f;
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float denom = (((0.325732924f * fz) + 0.982403709f)*fz + 1.539914949f)*fz + 1;
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result = Y + num / denom;
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result *= expf(-z * z) / z;
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}
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result = 1 - result;
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}
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else {
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result = 1;
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}
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return result;
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}
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ccl_device float approx_erff(float z)
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{
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float s = 1.0f;
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if(z < 0.0f) {
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s = -1.0f;
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z = -z;
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}
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return s * approx_erff_impl(z);
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}
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ccl_device float approx_erfinvf_impl(float p, float q)
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{
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float result = 0;
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if(p <= 0.5f) {
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float Y = 0.089131474f;
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float g = p * (p + 10);
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float num = (((-0.012692614f * p) + 0.033480662f)*p + -0.008368748f)*p + -0.000508781f;
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float denom = (((1.562215583f * p) + -1.565745582f)*p + -0.970005043f)*p + 1.0f;
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float r = num / denom;
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result = g * Y + g * r;
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}
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else if(q >= 0.25f) {
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float Y = 2.249481201f;
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float g = sqrtf(-2 * logf(q));
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float xs = q - 0.25f;
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float num = (((17.644729840f * xs) + 8.370503283f)*xs + 0.105264680f)*xs + -0.202433508f;
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float denom = (((-28.660818049f * xs) + 3.971343795f)*xs + 6.242641248f)*xs + 1.0f;
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float r = num / denom;
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result = g / (Y + r);
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}
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else {
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float x = sqrtf(-logf(q));
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if(x < 3) {
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float Y = 0.807220458f;
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float xs = x - 1.125f;
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float num = (((0.387079738f * xs) + 0.117030156f)*xs + -0.163794047f)*xs + -0.131102781f;
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float denom = (((4.778465929f * xs) + 5.381683457f)*xs + 3.466254072f)*xs + 1.0f;
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float R = num / denom;
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result = Y * x + R * x;
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}
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else {
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float Y = 0.939955711f;
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float xs = x - 3;
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float num = (((0.009508047f * xs) + 0.018557330f)*xs + -0.002224265f)*xs + -0.035035378f;
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float denom = (((0.220091105f * xs) + 0.762059164f)*xs + 1.365334981f)*xs + 1.0f;
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float R = num / denom;
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result = Y * x + R * x;
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}
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}
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return result;
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}
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ccl_device float approx_erfinvf(float z)
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{
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float p, q, s;
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if(z < 0) {
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p = -z;
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q = 1 - p;
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s = -1;
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}
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else {
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p = z;
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q = 1 - z;
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s = 1;
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}
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return s * approx_erfinvf_impl(p, q);
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}
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/* Beckmann and GGX microfacet importance sampling from:
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*
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* Importance Sampling Microfacet-Based BSDFs using the Distribution of Visible Normals.
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* E. Heitz and E. d'Eon, EGSR 2014 */
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ccl_device_inline void microfacet_beckmann_sample_slopes(
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const float cos_theta_i, const float sin_theta_i,
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const float alpha_x, const float alpha_y,
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float randu, float randv, float *slope_x, float *slope_y,
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float *G1i)
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{
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/* special case (normal incidence) */
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if(cos_theta_i >= 0.99999f) {
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const float r = sqrtf(-logf(randu));
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const float phi = M_2PI_F * randv;
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*slope_x = r * cosf(phi);
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*slope_y = r * sinf(phi);
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*G1i = 1.0f;
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return;
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}
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/* precomputations */
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const float tan_theta_i = sin_theta_i/cos_theta_i;
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const float inv_a = tan_theta_i;
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const float a = 1.0f/inv_a;
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const float erf_a = approx_erff(a);
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const float exp_a2 = expf(-a*a);
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const float SQRT_PI_INV = 0.56418958354f;
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const float Lambda = 0.5f*(erf_a - 1.0f) + (0.5f*SQRT_PI_INV)*(exp_a2*inv_a);
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const float G1 = 1.0f/(1.0f + Lambda); /* masking */
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const float C = 1.0f - G1 * erf_a;
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*G1i = G1;
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/* sample slope X */
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if(randu < C) {
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/* rescale randu */
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randu = randu / C;
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const float w_1 = 0.5f * SQRT_PI_INV * sin_theta_i * exp_a2;
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const float w_2 = cos_theta_i * (0.5f - 0.5f*erf_a);
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const float p = w_1 / (w_1 + w_2);
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if(randu < p) {
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randu = randu / p;
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*slope_x = -sqrtf(-logf(randu*exp_a2));
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}
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else {
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randu = (randu - p) / (1.0f - p);
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*slope_x = approx_erfinvf(randu - 1.0f - randu*erf_a);
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}
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}
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else {
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/* rescale randu */
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randu = (randu - C) / (1.0f - C);
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*slope_x = approx_erfinvf((-1.0f + 2.0f*randu)*erf_a);
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const float p = (-(*slope_x)*sin_theta_i + cos_theta_i) / (2.0f*cos_theta_i);
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if(randv > p) {
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*slope_x = -(*slope_x);
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randv = (randv - p) / (1.0f - p);
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}
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else
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randv = randv / p;
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}
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/* sample slope Y */
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*slope_y = approx_erfinvf(2.0f*randv - 1.0f);
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}
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ccl_device_inline void microfacet_ggx_sample_slopes(
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const float cos_theta_i, const float sin_theta_i,
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const float alpha_x, const float alpha_y,
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float randu, float randv, float *slope_x, float *slope_y,
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float *G1i)
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{
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/* special case (normal incidence) */
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if(cos_theta_i >= 0.99999f) {
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const float r = sqrtf(randu/(1.0f - randu));
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const float phi = M_2PI_F * randv;
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*slope_x = r * cosf(phi);
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*slope_y = r * sinf(phi);
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*G1i = 1.0f;
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return;
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}
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/* precomputations */
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const float tan_theta_i = sin_theta_i/cos_theta_i;
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const float G1_inv = 0.5f * (1.0f + safe_sqrtf(1.0f + tan_theta_i*tan_theta_i));
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*G1i = 1.0f/G1_inv;
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/* sample slope_x */
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const float A = 2.0f*randu*G1_inv - 1.0f;
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const float AA = A*A;
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const float tmp = 1.0f/(AA - 1.0f);
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const float B = tan_theta_i;
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const float BB = B*B;
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const float D = safe_sqrtf(BB*(tmp*tmp) - (AA - BB)*tmp);
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const float slope_x_1 = B*tmp - D;
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const float slope_x_2 = B*tmp + D;
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*slope_x = (A < 0.0f || slope_x_2*tan_theta_i > 1.0f)? slope_x_1: slope_x_2;
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/* sample slope_y */
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float S;
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if(randv > 0.5f) {
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S = 1.0f;
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randv = 2.0f*(randv - 0.5f);
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}
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else {
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S = -1.0f;
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randv = 2.0f*(0.5f - randv);
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}
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const float z = (randv*(randv*(randv*0.27385f - 0.73369f) + 0.46341f)) / (randv*(randv*(randv*0.093073f + 0.309420f) - 1.000000f) + 0.597999f);
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*slope_y = S * z * safe_sqrtf(1.0f + (*slope_x)*(*slope_x));
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}
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ccl_device_inline float3 microfacet_sample_stretched(const float3 omega_i,
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const float alpha_x, const float alpha_y,
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const float randu, const float randv,
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bool beckmann, float *G1i)
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{
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/* 1. stretch omega_i */
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float3 omega_i_ = make_float3(alpha_x * omega_i.x, alpha_y * omega_i.y, omega_i.z);
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omega_i_ = normalize(omega_i_);
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/* get polar coordinates of omega_i_ */
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float costheta_ = 1.0f;
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float sintheta_ = 0.0f;
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float cosphi_ = 1.0f;
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float sinphi_ = 0.0f;
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if(omega_i_.z < 0.99999f) {
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costheta_ = omega_i_.z;
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sintheta_ = safe_sqrtf(1.0f - costheta_*costheta_);
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float invlen = 1.0f/sintheta_;
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cosphi_ = omega_i_.x * invlen;
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sinphi_ = omega_i_.y * invlen;
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}
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/* 2. sample P22_{omega_i}(x_slope, y_slope, 1, 1) */
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float slope_x, slope_y;
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if(beckmann)
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microfacet_beckmann_sample_slopes(costheta_, sintheta_,
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alpha_x, alpha_y, randu, randv, &slope_x, &slope_y, G1i);
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else
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microfacet_ggx_sample_slopes(costheta_, sintheta_,
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alpha_x, alpha_y, randu, randv, &slope_x, &slope_y, G1i);
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/* 3. rotate */
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float tmp = cosphi_*slope_x - sinphi_*slope_y;
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slope_y = sinphi_*slope_x + cosphi_*slope_y;
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slope_x = tmp;
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/* 4. unstretch */
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slope_x = alpha_x * slope_x;
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slope_y = alpha_y * slope_y;
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/* 5. compute normal */
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return normalize(make_float3(-slope_x, -slope_y, 1.0f));
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}
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/* GGX microfacet with Smith shadow-masking from:
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*
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* Microfacet Models for Refraction through Rough Surfaces
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* B. Walter, S. R. Marschner, H. Li, K. E. Torrance, EGSR 2007 */
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ccl_device int bsdf_microfacet_ggx_setup(ShaderClosure *sc)
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{
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sc->data0 = clamp(sc->data0, 0.0f, 1.0f); /* m_ag */
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sc->type = CLOSURE_BSDF_MICROFACET_GGX_ID;
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return SD_BSDF|SD_BSDF_HAS_EVAL|SD_BSDF_GLOSSY;
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}
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ccl_device int bsdf_microfacet_ggx_refraction_setup(ShaderClosure *sc)
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{
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sc->data0 = clamp(sc->data0, 0.0f, 1.0f); /* m_ag */
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sc->type = CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
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return SD_BSDF|SD_BSDF_HAS_EVAL|SD_BSDF_GLOSSY;
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}
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ccl_device void bsdf_microfacet_ggx_blur(ShaderClosure *sc, float roughness)
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{
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sc->data0 = fmaxf(roughness, sc->data0); /* m_ag */
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}
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ccl_device float3 bsdf_microfacet_ggx_eval_reflect(const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf)
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{
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float m_ag = max(sc->data0, 1e-4f);
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int m_refractive = sc->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
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float3 N = sc->N;
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if(m_refractive || m_ag <= 1e-4f)
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return make_float3(0, 0, 0);
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float cosNO = dot(N, I);
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float cosNI = dot(N, omega_in);
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if(cosNI > 0 && cosNO > 0) {
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/* get half vector */
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float3 m = normalize(omega_in + I);
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/* eq. 20: (F*G*D)/(4*in*on)
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* eq. 33: first we calculate D(m) */
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float alpha2 = m_ag * m_ag;
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float cosThetaM = dot(N, m);
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float cosThetaM2 = cosThetaM * cosThetaM;
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float tanThetaM2 = (1 - cosThetaM2) / cosThetaM2;
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float cosThetaM4 = cosThetaM2 * cosThetaM2;
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float D = alpha2 / (M_PI_F * cosThetaM4 * (alpha2 + tanThetaM2) * (alpha2 + tanThetaM2));
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/* eq. 34: now calculate G1(i,m) and G1(o,m) */
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float G1o = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNO * cosNO) / (cosNO * cosNO)));
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float G1i = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNI * cosNI) / (cosNI * cosNI)));
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float G = G1o * G1i;
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/* eq. 20 */
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float common = D * 0.25f / cosNO;
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float out = G * common;
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/* eq. 2 in distribution of visible normals sampling
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* pm = Dw = G1o * dot(m, I) * D / dot(N, I); */
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/* eq. 38 - but see also:
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* eq. 17 in http://www.graphics.cornell.edu/~bjw/wardnotes.pdf
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* pdf = pm * 0.25 / dot(m, I); */
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*pdf = G1o * common;
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return make_float3(out, out, out);
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}
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return make_float3(0, 0, 0);
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}
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ccl_device float3 bsdf_microfacet_ggx_eval_transmit(const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf)
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{
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float m_ag = max(sc->data0, 1e-4f);
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float m_eta = sc->data1;
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int m_refractive = sc->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
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float3 N = sc->N;
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if(!m_refractive || m_ag <= 1e-4f)
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return make_float3(0, 0, 0);
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float cosNO = dot(N, I);
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float cosNI = dot(N, omega_in);
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if(cosNO <= 0 || cosNI >= 0)
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return make_float3(0, 0, 0); /* vectors on same side -- not possible */
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/* compute half-vector of the refraction (eq. 16) */
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float3 ht = -(m_eta * omega_in + I);
|
|
float3 Ht = normalize(ht);
|
|
float cosHO = dot(Ht, I);
|
|
float cosHI = dot(Ht, omega_in);
|
|
|
|
/* eq. 33: first we calculate D(m) with m=Ht: */
|
|
float alpha2 = m_ag * m_ag;
|
|
float cosThetaM = dot(N, Ht);
|
|
float cosThetaM2 = cosThetaM * cosThetaM;
|
|
float tanThetaM2 = (1 - cosThetaM2) / cosThetaM2;
|
|
float cosThetaM4 = cosThetaM2 * cosThetaM2;
|
|
float D = alpha2 / (M_PI_F * cosThetaM4 * (alpha2 + tanThetaM2) * (alpha2 + tanThetaM2));
|
|
|
|
/* eq. 34: now calculate G1(i,m) and G1(o,m) */
|
|
float G1o = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNO * cosNO) / (cosNO * cosNO)));
|
|
float 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 * cosHO * fabsf(cosHI) * common;
|
|
|
|
return make_float3(out, out, out);
|
|
}
|
|
|
|
ccl_device int bsdf_microfacet_ggx_sample(const ShaderClosure *sc, float3 Ng, float3 I, float3 dIdx, float3 dIdy, float randu, float randv, float3 *eval, float3 *omega_in, float3 *domega_in_dx, float3 *domega_in_dy, float *pdf)
|
|
{
|
|
float m_ag = sc->data0;
|
|
int m_refractive = sc->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
|
|
float3 N = sc->N;
|
|
|
|
float cosNO = dot(N, I);
|
|
if(cosNO > 0) {
|
|
float3 X, Y, Z = N;
|
|
make_orthonormals(Z, &X, &Y);
|
|
|
|
/* importance sampling with distribution of visible normals. vectors are
|
|
* transformed to local space before and after */
|
|
float3 local_I;
|
|
|
|
local_I.x = dot(X, I);
|
|
local_I.y = dot(Y, I);
|
|
local_I.z = cosNO;
|
|
|
|
float3 local_m;
|
|
float G1o;
|
|
|
|
local_m = microfacet_sample_stretched(local_I, m_ag, m_ag,
|
|
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);
|
|
|
|
if(cosMO > 0) {
|
|
/* eq. 39 - compute actual reflected direction */
|
|
*omega_in = 2 * cosMO * m - I;
|
|
|
|
if(dot(Ng, *omega_in) > 0) {
|
|
if(m_ag <= 1e-4f) {
|
|
/* some high number for MIS */
|
|
*pdf = 1e6f;
|
|
*eval = make_float3(1e6f, 1e6f, 1e6f);
|
|
}
|
|
else {
|
|
/* microfacet normal is visible to this ray */
|
|
/* eq. 33 */
|
|
float alpha2 = m_ag * m_ag;
|
|
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)));
|
|
|
|
/* see eval function for derivation */
|
|
float common = (G1o * D) * 0.25f / cosNO;
|
|
float out = G1i * common;
|
|
*pdf = common;
|
|
|
|
*eval = make_float3(out, out, out);
|
|
}
|
|
|
|
#ifdef __RAY_DIFFERENTIALS__
|
|
*domega_in_dx = (2 * dot(m, dIdx)) * m - dIdx;
|
|
*domega_in_dy = (2 * dot(m, dIdy)) * m - dIdy;
|
|
#endif
|
|
}
|
|
}
|
|
}
|
|
else {
|
|
/* 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 = sc->data1;
|
|
bool inside;
|
|
|
|
fresnel_dielectric(m_eta, m, I, &R, &T,
|
|
#ifdef __RAY_DIFFERENTIALS__
|
|
dIdx, dIdy, &dRdx, &dRdy, &dTdx, &dTdy,
|
|
#endif
|
|
&inside);
|
|
|
|
if(!inside) {
|
|
|
|
*omega_in = T;
|
|
#ifdef __RAY_DIFFERENTIALS__
|
|
*domega_in_dx = dTdx;
|
|
*domega_in_dy = dTdy;
|
|
#endif
|
|
|
|
if(m_ag <= 1e-4f || fabsf(m_eta - 1.0f) < 1e-4f) {
|
|
/* some high number for MIS */
|
|
*pdf = 1e6f;
|
|
*eval = make_float3(1e6f, 1e6f, 1e6f);
|
|
}
|
|
else {
|
|
/* eq. 33 */
|
|
float alpha2 = m_ag * m_ag;
|
|
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_float3(out, out, out);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return (m_refractive) ? LABEL_TRANSMIT|LABEL_GLOSSY : LABEL_REFLECT|LABEL_GLOSSY;
|
|
}
|
|
|
|
/* 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(ShaderClosure *sc)
|
|
{
|
|
sc->data0 = clamp(sc->data0, 0.0f, 1.0f); /* m_ab */
|
|
|
|
sc->type = CLOSURE_BSDF_MICROFACET_BECKMANN_ID;
|
|
return SD_BSDF|SD_BSDF_HAS_EVAL|SD_BSDF_GLOSSY;
|
|
}
|
|
|
|
ccl_device int bsdf_microfacet_beckmann_refraction_setup(ShaderClosure *sc)
|
|
{
|
|
sc->data0 = clamp(sc->data0, 0.0f, 1.0f); /* m_ab */
|
|
|
|
sc->type = CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID;
|
|
return SD_BSDF|SD_BSDF_HAS_EVAL|SD_BSDF_GLOSSY;
|
|
}
|
|
|
|
ccl_device void bsdf_microfacet_beckmann_blur(ShaderClosure *sc, float roughness)
|
|
{
|
|
sc->data0 = fmaxf(roughness, sc->data0); /* m_ab */
|
|
}
|
|
|
|
ccl_device float3 bsdf_microfacet_beckmann_eval_reflect(const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf)
|
|
{
|
|
float m_ab = max(sc->data0, 1e-4f);
|
|
int m_refractive = sc->type == CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID;
|
|
float3 N = sc->N;
|
|
|
|
if(m_refractive || m_ab <= 1e-4f)
|
|
return make_float3(0, 0, 0);
|
|
|
|
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);
|
|
|
|
/* eq. 20: (F*G*D)/(4*in*on)
|
|
* eq. 25: first we calculate D(m) */
|
|
float alpha2 = m_ab * m_ab;
|
|
float cosThetaM = dot(N, m);
|
|
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 ao = 1 / (m_ab * safe_sqrtf((1 - cosNO * cosNO) / (cosNO * cosNO)));
|
|
float ai = 1 / (m_ab * safe_sqrtf((1 - cosNI * cosNI) / (cosNI * cosNI)));
|
|
float G1o = ao < 1.6f ? (3.535f * ao + 2.181f * ao * ao) / (1 + 2.276f * ao + 2.577f * ao * ao) : 1.0f;
|
|
float G1i = ai < 1.6f ? (3.535f * ai + 2.181f * ai * ai) / (1 + 2.276f * ai + 2.577f * ai * ai) : 1.0f;
|
|
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_float3(out, out, out);
|
|
}
|
|
|
|
return make_float3(0, 0, 0);
|
|
}
|
|
|
|
ccl_device float3 bsdf_microfacet_beckmann_eval_transmit(const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf)
|
|
{
|
|
float m_ab = max(sc->data0, 1e-4f);
|
|
float m_eta = sc->data1;
|
|
int m_refractive = sc->type == CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID;
|
|
float3 N = sc->N;
|
|
|
|
if(!m_refractive || m_ab <= 1e-4f)
|
|
return make_float3(0, 0, 0);
|
|
|
|
float cosNO = dot(N, I);
|
|
float cosNI = dot(N, omega_in);
|
|
|
|
if(cosNO <= 0 || cosNI >= 0)
|
|
return make_float3(0, 0, 0);
|
|
|
|
/* 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. 33: first we calculate D(m) with m=Ht: */
|
|
float alpha2 = m_ab * m_ab;
|
|
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 ao = 1 / (m_ab * safe_sqrtf((1 - cosNO * cosNO) / (cosNO * cosNO)));
|
|
float ai = 1 / (m_ab * safe_sqrtf((1 - cosNI * cosNI) / (cosNI * cosNI)));
|
|
float G1o = ao < 1.6f ? (3.535f * ao + 2.181f * ao * ao) / (1 + 2.276f * ao + 2.577f * ao * ao) : 1.0f;
|
|
float G1i = ai < 1.6f ? (3.535f * ai + 2.181f * ai * ai) / (1 + 2.276f * ai + 2.577f * ai * ai) : 1.0f;
|
|
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 * cosHO * fabsf(cosHI) * common;
|
|
|
|
return make_float3(out, out, out);
|
|
}
|
|
|
|
ccl_device int bsdf_microfacet_beckmann_sample(const ShaderClosure *sc, float3 Ng, float3 I, float3 dIdx, float3 dIdy, float randu, float randv, float3 *eval, float3 *omega_in, float3 *domega_in_dx, float3 *domega_in_dy, float *pdf)
|
|
{
|
|
float m_ab = sc->data0;
|
|
int m_refractive = sc->type == CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID;
|
|
float3 N = sc->N;
|
|
|
|
float cosNO = dot(N, I);
|
|
if(cosNO > 0) {
|
|
float3 X, Y, Z = N;
|
|
make_orthonormals(Z, &X, &Y);
|
|
|
|
/* importance sampling with distribution of visible normals. vectors are
|
|
* transformed to local space before and after */
|
|
float3 local_I;
|
|
|
|
local_I.x = dot(X, I);
|
|
local_I.y = dot(Y, I);
|
|
local_I.z = cosNO;
|
|
|
|
float3 local_m;
|
|
float G1o;
|
|
|
|
local_m = microfacet_sample_stretched(local_I, m_ab, m_ab,
|
|
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) {
|
|
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(m_ab <= 1e-4f) {
|
|
/* some high number for MIS */
|
|
*pdf = 1e6f;
|
|
*eval = make_float3(1e6f, 1e6f, 1e6f);
|
|
}
|
|
else {
|
|
/* microfacet normal is visible to this ray
|
|
* eq. 25 */
|
|
float alpha2 = m_ab * m_ab;
|
|
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 ai = 1 / (m_ab * safe_sqrtf((1 - cosNI * cosNI) / (cosNI * cosNI)));
|
|
float G1i = ai < 1.6f ? (3.535f * ai + 2.181f * ai * ai) / (1 + 2.276f * ai + 2.577f * ai * ai) : 1.0f;
|
|
float G = G1o * G1i;
|
|
|
|
/* see eval function for derivation */
|
|
float common = D * 0.25f / cosNO;
|
|
float out = G * common;
|
|
*pdf = G1o * common;
|
|
|
|
*eval = make_float3(out, out, out);
|
|
}
|
|
|
|
#ifdef __RAY_DIFFERENTIALS__
|
|
*domega_in_dx = (2 * dot(m, dIdx)) * m - dIdx;
|
|
*domega_in_dy = (2 * dot(m, dIdy)) * m - dIdy;
|
|
#endif
|
|
}
|
|
}
|
|
}
|
|
else {
|
|
/* 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 = sc->data1;
|
|
bool inside;
|
|
|
|
fresnel_dielectric(m_eta, m, I, &R, &T,
|
|
#ifdef __RAY_DIFFERENTIALS__
|
|
dIdx, dIdy, &dRdx, &dRdy, &dTdx, &dTdy,
|
|
#endif
|
|
&inside);
|
|
|
|
if(!inside) {
|
|
*omega_in = T;
|
|
|
|
#ifdef __RAY_DIFFERENTIALS__
|
|
*domega_in_dx = dTdx;
|
|
*domega_in_dy = dTdy;
|
|
#endif
|
|
|
|
if(m_ab <= 1e-4f || fabsf(m_eta - 1.0f) < 1e-4f) {
|
|
/* some high number for MIS */
|
|
*pdf = 1e6f;
|
|
*eval = make_float3(1e6f, 1e6f, 1e6f);
|
|
}
|
|
else {
|
|
/* eq. 33 */
|
|
float alpha2 = m_ab * m_ab;
|
|
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 ai = 1 / (m_ab * safe_sqrtf((1 - cosNI * cosNI) / (cosNI * cosNI)));
|
|
float G1i = ai < 1.6f ? (3.535f * ai + 2.181f * ai * ai) / (1 + 2.276f * ai + 2.577f * ai * ai) : 1.0f;
|
|
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);
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float out = G * fabsf(cosHI * cosHO) * common;
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|
*pdf = G1o * cosHO * fabsf(cosHI) * common;
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|
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*eval = make_float3(out, out, out);
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}
|
|
}
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|
}
|
|
}
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return (m_refractive) ? LABEL_TRANSMIT|LABEL_GLOSSY : LABEL_REFLECT|LABEL_GLOSSY;
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|
}
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CCL_NAMESPACE_END
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#endif /* __BSDF_MICROFACET_H__ */
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