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, 472 insertions, 0 deletions

diff --git a/intern/cycles/kernel/closure/bsdf_microfacet_multi.h b/intern/cycles/kernel/closure/bsdf_microfacet_multi.h
new file mode 100644
index 00000000000..21fbfa9b025
--- /dev/null
+++ b/intern/cycles/kernel/closure/bsdf_microfacet_multi.h
@@ -0,0 +1,472 @@
+/*
+ * 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.
+ */
+
+CCL_NAMESPACE_BEGIN
+
+/* Most of the code is based on the supplemental implementations from https://eheitzresearch.wordpress.com/240-2/. */
+
+/* === GGX Microfacet distribution functions === */
+
+/* Isotropic GGX microfacet distribution */
+ccl_device_inline float D_ggx(float3 wm, float alpha)
+{
+	wm.z *= wm.z;
+	alpha *= alpha;
+	float tmp = (1.0f - wm.z) + alpha * wm.z;
+	return alpha / max(M_PI_F * tmp*tmp, 1e-7f);
+}
+
+/* Anisotropic GGX microfacet distribution */
+ccl_device_inline float D_ggx_aniso(const float3 wm, const float2 alpha)
+{
+	float slope_x = -wm.x/alpha.x;
+	float slope_y = -wm.y/alpha.y;
+	float tmp = wm.z*wm.z + slope_x*slope_x + slope_y*slope_y;
+
+	return 1.0f / max(M_PI_F * tmp*tmp * alpha.x*alpha.y, 1e-7f);
+}
+
+/* Sample slope distribution (based on page 14 of the supplemental implementation). */
+ccl_device_inline float2 mf_sampleP22_11(const float cosI, const float2 randU)
+{
+	if(cosI > 0.9999f) {
+		const float r = sqrtf(randU.x / (1.0f - randU.x));
+		const float phi = M_2PI_F * randU.y;
+		return make_float2(r*cosf(phi), r*sinf(phi));
+	}
+
+	const float sinI = sqrtf(1.0f - cosI*cosI);
+	const float tanI = sinI/cosI;
+	const float projA = 0.5f * (cosI + 1.0f);
+	if(projA < 0.0001f)
+		return make_float2(0.0f, 0.0f);
+	const float A = 2.0f*randU.x*projA / cosI - 1.0f;
+	float tmp = A*A-1.0f;
+	if(fabsf(tmp) < 1e-7f)
+		return make_float2(0.0f, 0.0f);
+	tmp = 1.0f / tmp;
+	const float D = safe_sqrtf(tanI*tanI*tmp*tmp - (A*A-tanI*tanI)*tmp);
+
+	const float slopeX2 = tanI*tmp + D;
+	const float slopeX = (A < 0.0f || slopeX2 > 1.0f/tanI)? (tanI*tmp - D) : slopeX2;
+
+	float U2;
+	if(randU.y >= 0.5f)
+		U2 = 2.0f*(randU.y - 0.5f);
+	else
+		U2 = 2.0f*(0.5f - randU.y);
+	const float z = (U2*(U2*(U2*0.27385f-0.73369f)+0.46341f)) / (U2*(U2*(U2*0.093073f+0.309420f)-1.0f)+0.597999f);
+	const float slopeY = z * sqrtf(1.0f + slopeX*slopeX);
+
+	if(randU.y >= 0.5f)
+		return make_float2(slopeX, slopeY);
+	else
+		return make_float2(slopeX, -slopeY);
+}
+
+/* Visible normal sampling for the GGX distribution (based on page 7 of the supplemental implementation). */
+ccl_device_inline float3 mf_sample_vndf(const float3 wi, const float2 alpha, const float2 randU)
+{
+	const float3 wi_11 = normalize(make_float3(alpha.x*wi.x, alpha.y*wi.y, wi.z));
+	const float2 slope_11 = mf_sampleP22_11(wi_11.z, randU);
+
+	const float2 cossin_phi = normalize(make_float2(wi_11.x, wi_11.y));
+	const float slope_x = alpha.x*(cossin_phi.x * slope_11.x - cossin_phi.y * slope_11.y);
+	const float slope_y = alpha.y*(cossin_phi.y * slope_11.x + cossin_phi.x * slope_11.y);
+
+	kernel_assert(isfinite(slope_x));
+	return normalize(make_float3(-slope_x, -slope_y, 1.0f));
+}
+
+/* === Phase functions: Glossy, Diffuse and Glass === */
+
+/* Phase function for reflective materials, either without a fresnel term (for compatibility) or with the conductive fresnel term. */
+ccl_device_inline float3 mf_sample_phase_glossy(const float3 wi, float3 *n, float3 *k, float3 *weight, const float3 wm)
+{
+	if(n && k)
+		*weight *= fresnel_conductor(dot(wi, wm), *n, *k);
+
+	return -wi + 2.0f * wm * dot(wi, wm);
+}
+
+ccl_device_inline float3 mf_eval_phase_glossy(const float3 w, const float lambda, const float3 wo, const float2 alpha, float3 *n, float3 *k)
+{
+	if(w.z > 0.9999f)
+		return make_float3(0.0f, 0.0f, 0.0f);
+
+	const float3 wh = normalize(wo - w);
+	if(wh.z < 0.0f)
+		return make_float3(0.0f, 0.0f, 0.0f);
+
+	float pArea = (w.z < -0.9999f)? 1.0f: lambda*w.z;
+
+	const float dotW_WH = dot(-w, wh);
+	if(dotW_WH < 0.0f)
+		return make_float3(0.0f, 0.0f, 0.0f);
+
+	float phase = max(0.0f, dotW_WH) * 0.25f / (pArea * dotW_WH);
+	if(alpha.x == alpha.y)
+		phase *= D_ggx(wh, alpha.x);
+	else
+		phase *= D_ggx_aniso(wh, alpha);
+
+	if(n && k) {
+		/* Apply conductive fresnel term. */
+		return phase * fresnel_conductor(dotW_WH, *n, *k);
+	}
+
+	return make_float3(phase, phase, phase);
+}
+
+/* Phase function for rough lambertian diffuse surfaces. */
+ccl_device_inline float3 mf_sample_phase_diffuse(const float3 wm, const float randu, const float randv)
+{
+	float3 tm, bm;
+	make_orthonormals(wm, &tm, &bm);
+
+	float2 disk = concentric_sample_disk(randu, randv);
+	return disk.x*tm + disk.y*bm + safe_sqrtf(1.0f - disk.x*disk.x - disk.y*disk.y)*wm;
+}
+
+ccl_device_inline float3 mf_eval_phase_diffuse(const float3 w, const float3 wm)
+{
+	const float v = max(0.0f, dot(w, wm)) * M_1_PI_F;
+	return make_float3(v, v, v);
+}
+
+/* Phase function for dielectric transmissive materials, including both reflection and refraction according to the dielectric fresnel term. */
+ccl_device_inline float3 mf_sample_phase_glass(const float3 wi, const float eta, const float3 wm, const float randV, bool *outside)
+{
+	float cosI = dot(wi, wm);
+	float f = fresnel_dielectric_cos(cosI, eta);
+	if(randV < f) {
+		*outside = true;
+		return -wi + 2.0f * wm * cosI;
+	}
+	*outside = false;
+	float inv_eta = 1.0f/eta;
+	float cosT = -safe_sqrtf(1.0f - (1.0f - cosI*cosI) * inv_eta*inv_eta);
+	return normalize(wm*(cosI*inv_eta + cosT) - wi*inv_eta);
+}
+
+ccl_device_inline float3 mf_eval_phase_glass(const float3 w, const float lambda, const float3 wo, const bool wo_outside, const float2 alpha, const float eta)
+{
+	if(w.z > 0.9999f)
+		return make_float3(0.0f, 0.0f, 0.0f);
+
+	float pArea = (w.z < -0.9999f)? 1.0f: lambda*w.z;
+	float v;
+	if(wo_outside) {
+		const float3 wh = normalize(wo - w);
+		if(wh.z < 0.0f)
+			return make_float3(0.0f, 0.0f, 0.0f);
+
+		const float dotW_WH = dot(-w, wh);
+		v = fresnel_dielectric_cos(dotW_WH, eta) * max(0.0f, dotW_WH) * D_ggx(wh, alpha.x) * 0.25f / (pArea * dotW_WH);
+	}
+	else {
+		float3 wh = normalize(wo*eta - w);
+		if(wh.z < 0.0f)
+			wh = -wh;
+		const float dotW_WH = dot(-w, wh), dotWO_WH = dot(wo, wh);
+		if(dotW_WH < 0.0f)
+			return make_float3(0.0f, 0.0f, 0.0f);
+
+		float temp = dotW_WH + eta*dotWO_WH;
+		v = (1.0f - fresnel_dielectric_cos(dotW_WH, eta)) * max(0.0f, dotW_WH) * max(0.0f, -dotWO_WH) * D_ggx(wh, alpha.x) / (pArea * temp * temp);
+	}
+
+	return make_float3(v, v, v);
+}
+
+/* === Utility functions for the random walks === */
+
+/* Smith Lambda function for GGX (based on page 12 of the supplemental implementation). */
+ccl_device_inline float mf_lambda(const float3 w, const float2 alpha)
+{
+	if(w.z > 0.9999f)
+		return 0.0f;
+	else if(w.z < -0.9999f)
+		return -1.0f;
+
+	const float inv_wz2 = 1.0f / (w.z*w.z);
+	const float2 wa = make_float2(w.x, w.y)*alpha;
+	float v = sqrtf(1.0f + dot(wa, wa) * inv_wz2);
+	if(w.z <= 0.0f)
+		v = -v;
+
+	return 0.5f*(v - 1.0f);
+}
+
+/* Height distribution CDF (based on page 4 of the supplemental implementation). */
+ccl_device_inline float mf_invC1(const float h)
+{
+	return 2.0f * saturate(h) - 1.0f;
+}
+
+ccl_device_inline float mf_C1(const float h)
+{
+	return saturate(0.5f * (h + 1.0f));
+}
+
+/* Masking function (based on page 16 of the supplemental implementation). */
+ccl_device_inline float mf_G1(const float3 w, const float C1, const float lambda)
+{
+	if(w.z > 0.9999f)
+		return 1.0f;
+	if(w.z < 1e-5f)
+		return 0.0f;
+	return powf(C1, lambda);
+}
+
+/* Sampling from the visible height distribution (based on page 17 of the supplemental implementation). */
+ccl_device_inline bool mf_sample_height(const float3 w, float *h, float *C1, float *G1, float *lambda, const float U)
+{
+	if(w.z > 0.9999f)
+		return false;
+	if(w.z < -0.9999f) {
+		*C1 *= U;
+		*h = mf_invC1(*C1);
+		*G1 = mf_G1(w, *C1, *lambda);
+	}
+	else if(fabsf(w.z) >= 0.0001f) {
+		if(U > 1.0f - *G1)
+			return false;
+		if(*lambda >= 0.0f) {
+			*C1 = 1.0f;
+		}
+		else {
+			*C1 *= powf(1.0f-U, -1.0f / *lambda);
+		}
+		*h = mf_invC1(*C1);
+		*G1 = mf_G1(w, *C1, *lambda);
+	}
+	return true;
+}
+
+/* === PDF approximations for the different phase functions. ===
+ * As explained in bsdf_microfacet_multi_impl.h, using approximations with MIS still produces an unbiased result. */
+
+/* Approximation for the albedo of the single-scattering GGX distribution,
+ * the missing energy is then approximated as a diffuse reflection for the PDF. */
+ccl_device_inline float mf_ggx_albedo(float r)
+{
+	float albedo = 0.806495f*expf(-1.98712f*r*r) + 0.199531f;
+	albedo -= ((((((1.76741f*r - 8.43891f)*r + 15.784f)*r - 14.398f)*r + 6.45221f)*r - 1.19722f)*r + 0.027803f)*r + 0.00568739f;
+	return saturate(albedo);
+}
+
+ccl_device_inline float mf_ggx_pdf(const float3 wi, const float3 wo, const float alpha)
+{
+	return 0.25f * D_ggx(normalize(wi+wo), alpha) / ((1.0f + mf_lambda(wi, make_float2(alpha, alpha))) * wi.z) + (1.0f - mf_ggx_albedo(alpha)) * wo.z;
+}
+
+ccl_device_inline float mf_ggx_aniso_pdf(const float3 wi, const float3 wo, const float2 alpha)
+{
+	return 0.25f * D_ggx_aniso(normalize(wi+wo), alpha) / ((1.0f + mf_lambda(wi, alpha)) * wi.z) + (1.0f - mf_ggx_albedo(sqrtf(alpha.x*alpha.y))) * wo.z;
+}
+
+ccl_device_inline float mf_diffuse_pdf(const float3 wo)
+{
+	return M_1_PI_F * wo.z;
+}
+
+ccl_device_inline float mf_glass_pdf(const float3 wi, const float3 wo, const float alpha, const float eta)
+{
+	float3 wh;
+	float fresnel;
+	if(wi.z*wo.z > 0.0f) {
+		wh = normalize(wi + wo);
+		fresnel = fresnel_dielectric_cos(dot(wi, wh), eta);
+	}
+	else {
+		wh = normalize(wi + wo*eta);
+		fresnel = 1.0f - fresnel_dielectric_cos(dot(wi, wh), eta);
+	}
+	if(wh.z < 0.0f)
+		wh = -wh;
+	float3 r_wi = (wi.z < 0.0f)? -wi: wi;
+	return fresnel * max(0.0f, dot(r_wi, wh)) * D_ggx(wh, alpha) / ((1.0f + mf_lambda(r_wi, make_float2(alpha, alpha))) * r_wi.z) + fabsf(wo.z);
+}
+
+/* === Actual random walk implementations, one version of mf_eval and mf_sample per phase function. === */
+
+#define MF_NAME_JOIN(x,y) x ## _ ## y
+#define MF_NAME_EVAL(x,y) MF_NAME_JOIN(x,y)
+#define MF_FUNCTION_FULL_NAME(prefix) MF_NAME_EVAL(prefix, MF_PHASE_FUNCTION)
+
+#define MF_PHASE_FUNCTION glass
+#define MF_MULTI_GLASS
+#include "bsdf_microfacet_multi_impl.h"
+
+/* The diffuse phase function is not implemented as a node yet. */
+#if 0
+#define MF_PHASE_FUNCTION diffuse
+#define MF_MULTI_DIFFUSE
+#include "bsdf_microfacet_multi_impl.h"
+#endif
+
+#define MF_PHASE_FUNCTION glossy
+#define MF_MULTI_GLOSSY
+#include "bsdf_microfacet_multi_impl.h"
+
+ccl_device void bsdf_microfacet_multi_ggx_blur(ShaderClosure *sc, float roughness)
+{
+	sc->data0 = fmaxf(roughness, sc->data0); /* alpha_x */
+	sc->data1 = fmaxf(roughness, sc->data1); /* alpha_y */
+}
+
+/* === Closure implementations === */
+
+/* Multiscattering GGX Glossy closure */
+
+ccl_device int bsdf_microfacet_multi_ggx_common_setup(ShaderClosure *sc)
+{
+	sc->data0 = clamp(sc->data0, 1e-4f, 1.0f); /* alpha */
+	sc->data1 = clamp(sc->data1, 1e-4f, 1.0f);
+	sc->custom1 = saturate(sc->custom1); /* color */
+	sc->custom2 = saturate(sc->custom2);
+	sc->custom3 = saturate(sc->custom3);
+
+	sc->type = CLOSURE_BSDF_MICROFACET_MULTI_GGX_ID;
+
+	return SD_BSDF|SD_BSDF_HAS_EVAL|SD_BSDF_NEEDS_LCG|SD_BSDF_HAS_CUSTOM;
+}
+
+ccl_device int bsdf_microfacet_multi_ggx_aniso_setup(ShaderClosure *sc)
+{
+	if(sc->T == make_float3(0.0f, 0.0f, 0.0f))
+		sc->T = make_float3(1.0f, 0.0f, 0.0f);
+
+	return bsdf_microfacet_multi_ggx_common_setup(sc);
+}
+
+ccl_device int bsdf_microfacet_multi_ggx_setup(ShaderClosure *sc)
+{
+	sc->data1 = sc->data0;
+
+	return bsdf_microfacet_multi_ggx_common_setup(sc);
+}
+
+ccl_device float3 bsdf_microfacet_multi_ggx_eval_transmit(const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf, uint *lcg_state) {
+	*pdf = 0.0f;
+	return make_float3(0.0f, 0.0f, 0.0f);
+}
+
+ccl_device float3 bsdf_microfacet_multi_ggx_eval_reflect(const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf, uint *lcg_state) {
+	bool is_aniso = (sc->data0 != sc->data1);
+	float3 X, Y, Z;
+	Z = sc->N;
+	if(is_aniso)
+		make_orthonormals_tangent(Z, sc->T, &X, &Y);
+	else
+		make_orthonormals(Z, &X, &Y);
+
+	float3 localI = make_float3(dot(I, X), dot(I, Y), dot(I, Z));
+	float3 localO = make_float3(dot(omega_in, X), dot(omega_in, Y), dot(omega_in, Z));
+
+	if(is_aniso)
+		*pdf = mf_ggx_aniso_pdf(localI, localO, make_float2(sc->data0, sc->data1));
+	else
+		*pdf = mf_ggx_pdf(localI, localO, sc->data0);
+	return mf_eval_glossy(localI, localO, true, make_float3(sc->custom1, sc->custom2, sc->custom3), sc->data0, sc->data1, lcg_state, NULL, NULL);
+}
+
+ccl_device int bsdf_microfacet_multi_ggx_sample(KernelGlobals *kg, 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, uint *lcg_state)
+{
+	bool is_aniso = (sc->data0 != sc->data1);
+	float3 X, Y, Z;
+	Z = sc->N;
+	if(is_aniso)
+		make_orthonormals_tangent(Z, sc->T, &X, &Y);
+	else
+		make_orthonormals(Z, &X, &Y);
+
+	float3 localI = make_float3(dot(I, X), dot(I, Y), dot(I, Z));
+	float3 localO;
+
+	*eval = mf_sample_glossy(localI, &localO, make_float3(sc->custom1, sc->custom2, sc->custom3), sc->data0, sc->data1, lcg_state, NULL, NULL);
+	if(is_aniso)
+		*pdf = mf_ggx_aniso_pdf(localI, localO, make_float2(sc->data0, sc->data1));
+	else
+		*pdf = mf_ggx_pdf(localI, localO, sc->data0);
+	*eval *= *pdf;
+
+	*omega_in = X*localO.x + Y*localO.y + Z*localO.z;
+	return LABEL_REFLECT|LABEL_GLOSSY;
+}
+
+/* Multiscattering GGX Glass closure */
+
+ccl_device int bsdf_microfacet_multi_ggx_glass_setup(ShaderClosure *sc)
+{
+	sc->data0 = clamp(sc->data0, 1e-4f, 1.0f); /* alpha */
+	sc->data1 = sc->data0;
+	sc->data2 = max(0.0f, sc->data2); /* ior */
+	sc->custom1 = saturate(sc->custom1); /* color */
+	sc->custom2 = saturate(sc->custom2);
+	sc->custom3 = saturate(sc->custom3);
+
+	sc->type = CLOSURE_BSDF_MICROFACET_MULTI_GGX_GLASS_ID;
+
+	return SD_BSDF|SD_BSDF_HAS_EVAL|SD_BSDF_NEEDS_LCG|SD_BSDF_HAS_CUSTOM;
+}
+
+ccl_device float3 bsdf_microfacet_multi_ggx_glass_eval_transmit(const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf, uint *lcg_state) {
+	float3 X, Y, Z;
+	Z = sc->N;
+	make_orthonormals(Z, &X, &Y);
+
+	float3 localI = make_float3(dot(I, X), dot(I, Y), dot(I, Z));
+	float3 localO = make_float3(dot(omega_in, X), dot(omega_in, Y), dot(omega_in, Z));
+
+	*pdf = mf_glass_pdf(localI, localO, sc->data0, sc->data2);
+	return mf_eval_glass(localI, localO, false, make_float3(sc->custom1, sc->custom2, sc->custom3), sc->data0, sc->data1, lcg_state, sc->data2);
+}
+
+ccl_device float3 bsdf_microfacet_multi_ggx_glass_eval_reflect(const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf, uint *lcg_state) {
+	float3 X, Y, Z;
+	Z = sc->N;
+	make_orthonormals(Z, &X, &Y);
+
+	float3 localI = make_float3(dot(I, X), dot(I, Y), dot(I, Z));
+	float3 localO = make_float3(dot(omega_in, X), dot(omega_in, Y), dot(omega_in, Z));
+
+	*pdf = mf_glass_pdf(localI, localO, sc->data0, sc->data2);
+	return mf_eval_glass(localI, localO, true, make_float3(sc->custom1, sc->custom2, sc->custom3), sc->data0, sc->data1, lcg_state, sc->data2);
+}
+
+ccl_device int bsdf_microfacet_multi_ggx_glass_sample(KernelGlobals *kg, 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, uint *lcg_state)
+{
+	float3 X, Y, Z;
+	Z = sc->N;
+	make_orthonormals(Z, &X, &Y);
+
+	float3 localI = make_float3(dot(I, X), dot(I, Y), dot(I, Z));
+	float3 localO;
+
+	*eval = mf_sample_glass(localI, &localO, make_float3(sc->custom1, sc->custom2, sc->custom3), sc->data0, sc->data1, lcg_state, sc->data2);
+	*pdf = mf_glass_pdf(localI, localO, sc->data0, sc->data2);
+	*eval *= *pdf;
+
+	*omega_in = X*localO.x + Y*localO.y + Z*localO.z;
+	if(localO.z*localI.z > 0.0f)
+		return LABEL_REFLECT|LABEL_GLOSSY;
+	else
+		return LABEL_TRANSMIT|LABEL_GLOSSY;
+}
+
+CCL_NAMESPACE_END