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// Ceres Solver - A fast non-linear least squares minimizer
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// http://ceres-solver.org/
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// Author: darius.rueckert@fau.de (Darius Rueckert)
//
//
#ifndef CERES_INTERNAL_AUTODIFF_BENCHMARK_BRDF_COST_FUNCTION_H_
#define CERES_INTERNAL_AUTODIFF_BENCHMARK_BRDF_COST_FUNCTION_H_
#include <Eigen/Core>
#include <cmath>
namespace ceres {
// The brdf is based on:
// Burley, Brent, and Walt Disney Animation Studios. "Physically-based shading
// at disney." ACM SIGGRAPH. Vol. 2012. 2012.
//
// The implementation is based on:
// https://github.com/wdas/brdf/blob/master/src/brdfs/disney.brdf
struct Brdf {
public:
Brdf() {}
template <typename T>
inline bool operator()(const T* const material,
const T* const c_ptr,
const T* const n_ptr,
const T* const v_ptr,
const T* const l_ptr,
const T* const x_ptr,
const T* const y_ptr,
T* residual) const {
using Vec3 = Eigen::Matrix<T, 3, 1>;
T metallic = material[0];
T subsurface = material[1];
T specular = material[2];
T roughness = material[3];
T specular_tint = material[4];
T anisotropic = material[5];
T sheen = material[6];
T sheen_tint = material[7];
T clearcoat = material[8];
T clearcoat_gloss = material[9];
Eigen::Map<const Vec3> c(c_ptr);
Eigen::Map<const Vec3> n(n_ptr);
Eigen::Map<const Vec3> v(v_ptr);
Eigen::Map<const Vec3> l(l_ptr);
Eigen::Map<const Vec3> x(x_ptr);
Eigen::Map<const Vec3> y(y_ptr);
const T n_dot_l = n.dot(l);
const T n_dot_v = n.dot(v);
const Vec3 l_p_v = l + v;
const Vec3 h = l_p_v / l_p_v.norm();
const T n_dot_h = n.dot(h);
const T l_dot_h = l.dot(h);
const T h_dot_x = h.dot(x);
const T h_dot_y = h.dot(y);
const T c_dlum = T(0.3) * c[0] + T(0.6) * c[1] + T(0.1) * c[2];
const Vec3 c_tint = c / c_dlum;
const Vec3 c_spec0 =
Lerp(specular * T(0.08) *
Lerp(Vec3(T(1), T(1), T(1)), c_tint, specular_tint),
c,
metallic);
const Vec3 c_sheen = Lerp(Vec3(T(1), T(1), T(1)), c_tint, sheen_tint);
// Diffuse fresnel - go from 1 at normal incidence to .5 at grazing
// and mix in diffuse retro-reflection based on roughness
const T fl = SchlickFresnel(n_dot_l);
const T fv = SchlickFresnel(n_dot_v);
const T fd_90 = T(0.5) + T(2) * l_dot_h * l_dot_h * roughness;
const T fd = Lerp(T(1), fd_90, fl) * Lerp(T(1), fd_90, fv);
// Based on Hanrahan-Krueger brdf approximation of isotropic bssrdf
// 1.25 scale is used to (roughly) preserve albedo
// Fss90 used to "flatten" retroreflection based on roughness
const T fss_90 = l_dot_h * l_dot_h * roughness;
const T fss = Lerp(T(1), fss_90, fl) * Lerp(T(1), fss_90, fv);
const T ss =
T(1.25) * (fss * (T(1) / (n_dot_l + n_dot_v) - T(0.5)) + T(0.5));
// specular
const T eps = T(0.001);
const T aspct = Aspect(anisotropic);
const T ax_temp = Square(roughness) / aspct;
const T ay_temp = Square(roughness) * aspct;
const T ax = (ax_temp < eps ? eps : ax_temp);
const T ay = (ay_temp < eps ? eps : ay_temp);
const T ds = GTR2Aniso(n_dot_h, h_dot_x, h_dot_y, ax, ay);
const T fh = SchlickFresnel(l_dot_h);
const Vec3 fs = Lerp(c_spec0, Vec3(T(1), T(1), T(1)), fh);
const T roughg = Square(roughness * T(0.5) + T(0.5));
const T ggxn_dot_l = SmithG_GGX(n_dot_l, roughg);
const T ggxn_dot_v = SmithG_GGX(n_dot_v, roughg);
const T gs = ggxn_dot_l * ggxn_dot_v;
// sheen
const Vec3 f_sheen = fh * sheen * c_sheen;
// clearcoat (ior = 1.5 -> F0 = 0.04)
const T a = Lerp(T(0.1), T(0.001), clearcoat_gloss);
const T dr = GTR1(n_dot_h, a);
const T fr = Lerp(T(0.04), T(1), fh);
const T cggxn_dot_l = SmithG_GGX(n_dot_l, T(0.25));
const T cggxn_dot_v = SmithG_GGX(n_dot_v, T(0.25));
const T gr = cggxn_dot_l * cggxn_dot_v;
const Vec3 result_no_cosine =
(T(1.0 / M_PI) * Lerp(fd, ss, subsurface) * c + f_sheen) *
(T(1) - metallic) +
gs * fs * ds +
Vec3(T(0.25), T(0.25), T(0.25)) * clearcoat * gr * fr * dr;
const Vec3 result = n_dot_l * result_no_cosine;
residual[0] = result(0);
residual[1] = result(1);
residual[2] = result(2);
return true;
}
template <typename T>
inline T SchlickFresnel(const T& u) const {
T m = T(1) - u;
const T m2 = m * m;
return m2 * m2 * m; // (1-u)^5
}
template <typename T>
inline T Aspect(const T& anisotropic) const {
return T(sqrt(T(1) - anisotropic * T(0.9)));
}
template <typename T>
inline T SmithG_GGX(const T& n_dot_v, const T& alpha_g) const {
const T a = alpha_g * alpha_g;
const T b = n_dot_v * n_dot_v;
return T(1) / (n_dot_v + T(sqrt(a + b - a * b)));
}
// Generalized-Trowbridge-Reitz (GTR) Microfacet Distribution
// See paper, Appendix B
template <typename T>
inline T GTR1(const T& n_dot_h, const T& a) const {
T result = T(0);
if (a >= T(1)) {
result = T(1 / M_PI);
} else {
const T a2 = a * a;
const T t = T(1) + (a2 - T(1)) * n_dot_h * n_dot_h;
result = (a2 - T(1)) / (T(M_PI) * T(log(a2) * t));
}
return result;
}
template <typename T>
inline T GTR2Aniso(const T& n_dot_h,
const T& h_dot_x,
const T& h_dot_y,
const T& ax,
const T& ay) const {
return T(1) / (T(M_PI) * ax * ay *
Square(Square(h_dot_x / ax) + Square(h_dot_y / ay) +
n_dot_h * n_dot_h));
}
template <typename T>
inline T Lerp(const T& a, const T& b, const T& u) const {
return a + u * (b - a);
}
template <typename Derived1, typename Derived2>
inline typename Derived1::PlainObject Lerp(
const Eigen::MatrixBase<Derived1>& a,
const Eigen::MatrixBase<Derived2>& b,
typename Derived1::Scalar alpha) const {
return (typename Derived1::Scalar(1) - alpha) * a + alpha * b;
}
template <typename T>
inline T Square(const T& x) const {
return x * x;
}
};
} // namespace ceres
#endif // CERES_INTERNAL_AUTODIFF_BENCHMARK_BRDF_COST_FUNCTION_H_