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// Copyright 2009 Intel Corporation
// SPDX-License-Identifier: Apache-2.0
#pragma once
#include "MicrofacetDistribution.ih"
OSPRAY_BEGIN_ISPC_NAMESPACE
// GGX (Trowbridge-Reitz) microfacet distribution
// [Walter et al., 2007, "Microfacet Models for Refraction through Rough
// Surfaces"] [Heitz, 2014, "Understanding the Masking-Shadowing Function in
// Microfacet-Based BRDFs"] [Heitz and d'Eon, 2014, "Importance Sampling
// Microfacet-Based BSDFs using the Distribution of Visible Normals"] [Heitz,
// 2017, "A Simpler and Exact Sampling Routine for the GGX Distribution of
// Visible Normals"]
struct GGXDistribution
{
vec2f alpha;
};
inline GGXDistribution make_GGXDistribution(const vec2f &alpha)
{
GGXDistribution self;
self.alpha = alpha;
return self;
}
// D(\omega_m) = \frac{1}{\pi \alpha_x \alpha_y \cos^4\theta_m \left(1 +
// \tan^2\theta_m \left(\frac{\cos^2\phi_m}{\alpha_x^2} +
// \frac{\sin^2\phi_m}{\alpha_y^2}\right)\right)^2}
inline float eval(const GGXDistribution &self, const vec3f &wh)
{
float cosTheta = wh.z;
float cosTheta2 = sqr(cosTheta);
float e = (sqr(wh.x / self.alpha.x) + sqr(wh.y / self.alpha.y)) / cosTheta2;
return rcp(
(float)pi * self.alpha.x * self.alpha.y * sqr(cosTheta2 * (1.f + e)));
}
// p(\omega_m) = D(\omega_m) \cos\theta_m
inline float eval(const GGXDistribution &self, const vec3f &wh, float &pdf)
{
float cosTheta = wh.z;
float D = eval(self, wh);
pdf = D * abs(cosTheta);
return D;
}
// \theta_m = \arctan \left( \frac{\alpha\sqrt{\xi_1}}{\sqrt{1-\xi_1}} \right)
// \phi_m = 2\pi \xi_2
// p(\omega_m) = D(\omega_m) \cos\theta_m
inline vec3f sample(const GGXDistribution &self, float &pdf, const vec2f &s)
{
float phi;
if (self.alpha.x == self.alpha.y) {
phi = 2.f * (float)pi * s.y;
} else {
phi =
atan(self.alpha.y / self.alpha.x * tan((float)pi * (2.f * s.y + 0.5f)));
if (s.y > 0.5f)
phi += (float)pi;
}
float sinPhi, cosPhi;
sincos(phi, &sinPhi, &cosPhi);
float alpha2;
if (self.alpha.x == self.alpha.y)
alpha2 = sqr(self.alpha.x);
else
alpha2 = rcp(sqr(cosPhi / self.alpha.x) + sqr(sinPhi / self.alpha.y));
float tanTheta2 = alpha2 * s.x / (1.f - s.x);
float cosTheta = rsqrt(1.f + tanTheta2);
float cosTheta3 = sqr(cosTheta) * cosTheta;
float sinTheta = cos2sin(cosTheta);
float e = tanTheta2 / alpha2;
pdf = rcp((float)pi * self.alpha.x * self.alpha.y * cosTheta3 * sqr(1.f + e));
float x = cosPhi * sinTheta;
float y = sinPhi * sinTheta;
float z = cosTheta;
return make_vec3f(x, y, z);
}
// Smith Lambda function [Heitz, 2014]
// \Lambda(\omega_o) = \frac{-1 + \sqrt{1+\frac{1}{a^2}}}{2}
// a = \frac{1}{\alpha_o \tan\theta_o}
// \alpha_o = \sqrt{cos^2\phi_o \alpha_x^2 + sin^2\phi_o \alpha_y^2}
inline float evalLambda(const GGXDistribution &self, const vec3f &wo)
{
float cosThetaO = wo.z;
float cosThetaO2 = sqr(cosThetaO);
float invA2 =
(sqr(wo.x * self.alpha.x) + sqr(wo.y * self.alpha.y)) / cosThetaO2;
return 0.5f * (-1.f + sqrt(1.f + invA2));
}
inline float evalG1(
const GGXDistribution &self, const vec3f &wo, float cosThetaOH)
{
float cosThetaO = wo.z;
if (cosThetaO * cosThetaOH <= 0.f)
return 0.f;
return rcp(1.f + evalLambda(self, wo));
}
// Smith's height-correlated masking-shadowing function
// [Heitz, 2014, "Understanding the Masking-Shadowing Function in
// Microfacet-Based BRDFs"]
inline float evalG2(const GGXDistribution &self,
const vec3f &wo,
const vec3f &wi,
float cosThetaOH,
float cosThetaIH)
{
float cosThetaO = wo.z;
float cosThetaI = wi.z;
if (cosThetaO * cosThetaOH <= 0.f || cosThetaI * cosThetaIH <= 0.f)
return 0.f;
return rcp(1.f + evalLambda(self, wo) + evalLambda(self, wi));
}
inline float evalVisible(const GGXDistribution &self,
const vec3f &wh,
const vec3f &wo,
float cosThetaOH,
float &pdf)
{
float cosThetaO = wo.z;
float D = eval(self, wh);
pdf = evalG1(self, wo, cosThetaOH) * abs(cosThetaOH) * D / abs(cosThetaO);
return D;
}
// Fast visible normal sampling (wo must be in the upper hemisphere)
// [Heitz, 2017, "A Simpler and Exact Sampling Routine for the GGX Distribution
// of Visible Normals"]
inline vec3f sampleVisible(
const GGXDistribution &self, const vec3f &wo, float &pdf, const vec2f &s)
{
// Stretch wo
vec3f V =
normalize(make_vec3f(self.alpha.x * wo.x, self.alpha.y * wo.y, wo.z));
// Orthonormal basis
vec3f T1 = (V.z < 0.9999f) ? normalize(cross(V, make_vec3f(0, 0, 1)))
: make_vec3f(1, 0, 0);
vec3f T2 = cross(T1, V);
// Sample point with polar coordinates (r, phi)
float a = 1.f / (1.f + V.z);
float r = sqrt(s.x);
float phi = (s.y < a) ? s.y / a * (float)pi
: (float)pi + (s.y - a) / (1.f - a) * (float)pi;
float sinPhi, cosPhi;
sincos(phi, &sinPhi, &cosPhi);
float P1 = r * cosPhi;
float P2 = r * sinPhi * ((s.y < a) ? 1.f : V.z);
// Compute normal
vec3f wh = P1 * T1 + P2 * T2 + sqrt(max(0.f, 1.f - P1 * P1 - P2 * P2)) * V;
// Unstretch
wh = normalize(
make_vec3f(self.alpha.x * wh.x, self.alpha.y * wh.y, max(0.f, wh.z)));
// Compute pdf
float cosThetaO = wo.z;
pdf = evalG1(self, wo, dot(wo, wh)) * abs(dot(wo, wh)) * eval(self, wh)
/ abs(cosThetaO);
return wh;
}
OSPRAY_END_ISPC_NAMESPACE
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