Cycles: Add multi-scattering, energy-conserving GGX as an option to the Glossy, Anisotropic and Glass BSDFs

This commit adds a new distribution to the Glossy, Anisotropic and Glass BSDFs that implements the
multiple-scattering microfacet model described in the paper "Multiple-Scattering Microfacet BSDFs with the Smith Model".

Essentially, the improvement is that unlike classical GGX, which only models single scattering and assumes
the contribution of multiple bounces to be zero, this new model performs a random walk on the microsurface until
the ray leaves it again, which ensures perfect energy conservation.

In practise, this means that the "darkening problem" - GGX materials becoming darker with increasing
roughness - is solved in a physically correct and efficient way.

The downside of this model is that it has no (known) analytic expression for evalation. However, it can be
evaluated stochastically, and although the correct PDF isn't known either, the properties of MIS and the
balance heuristic guarantee an unbiased result at the cost of slightly higher noise.

Reviewers: dingto, #cycles, brecht

Reviewed By: dingto, #cycles, brecht

Subscribers: bliblubli, ace_dragon, gregzaal, brecht, harvester, dingto, marcog, swerner, jtheninja, Blendify, nutel

Differential Revision: https://developer.blender.org/D2002

1 files changed, 14 insertions, 0 deletions

diff --git a/intern/cycles/util/util_math.h b/intern/cycles/util/util_math.h
index 53944ec1cc4..cfe6fa65143 100644
--- a/intern/cycles/util/util_math.h
+++ b/intern/cycles/util/util_math.h
@@ -545,6 +545,11 @@ ccl_device_inline float3 normalize(const float3 a)
 
 #endif
 
+ccl_device_inline float3 saturate3(float3 a)
+{
+	return make_float3(saturate(a.x), saturate(a.y), saturate(a.z));
+}
+
 ccl_device_inline float3 normalize_len(const float3 a, float *t)
 {
 	*t = len(a);
@@ -1329,6 +1334,15 @@ ccl_device float safe_modulo(float a, float b)
 	return (b != 0.0f)? fmodf(a, b): 0.0f;
 }
 
+ccl_device_inline float beta(float x, float y)
+{
+#ifndef __KERNEL_OPENCL__
+	return expf(lgammaf(x) + lgammaf(y) - lgammaf(x+y));
+#else
+	return expf(lgamma(x) + lgamma(y) - lgamma(x+y));
+#endif
+}
+
 /* Ray Intersection */
 
 ccl_device bool ray_sphere_intersect(