blender/intern/cycles/kernel/svm/bsdf_microfacet.h

/* 
 * Adapted from Open Shading Language with this license: 
 * 
 * Copyright (c) 2009-2010 Sony Pictures Imageworks Inc., et al. 
 * All Rights Reserved. 
 * 
 * Modifications Copyright 2011, Blender Foundation. 
 *  
 * Redistribution and use in source and binary forms, with or without 
 * modification, are permitted provided that the following conditions are 
 * met: 
 * * Redistributions of source code must retain the above copyright 
 *   notice, this list of conditions and the following disclaimer. 
 * * Redistributions in binary form must reproduce the above copyright 
 *   notice, this list of conditions and the following disclaimer in the 
 *   documentation and/or other materials provided with the distribution. 
 * * Neither the name of Sony Pictures Imageworks nor the names of its 
 *   contributors may be used to endorse or promote products derived from 
 *   this software without specific prior written permission. 
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 
 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT 
 * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT 
 * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE 
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 
*/

#ifndef __BSDF_MICROFACET_H__
#define __BSDF_MICROFACET_H__

CCL_NAMESPACE_BEGIN

/* GGX */

typedef struct BsdfMicrofacetGGXClosure {
	//float3 m_N;
	float m_ag;
	float m_eta;
} BsdfMicrofacetGGXClosure;

__device void bsdf_microfacet_ggx_setup(ShaderData *sd, ShaderClosure *sc, float ag, float eta, bool refractive)
{
	float m_ag = clamp(ag, 1e-4f, 1.0f);
	float m_eta = eta;

	sc->data0 = m_ag;
	sc->data1 = m_eta;

	if(refractive)
		sc->type = CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
	else
		sc->type = CLOSURE_BSDF_MICROFACET_GGX_ID;

	sd->flag |= SD_BSDF|SD_BSDF_HAS_EVAL|SD_BSDF_GLOSSY;
}

__device void bsdf_microfacet_ggx_blur(ShaderClosure *sc, float roughness)
{
	float m_ag = sc->data0;
	m_ag = fmaxf(roughness, m_ag);
	sc->data0 = m_ag;
}

__device float3 bsdf_microfacet_ggx_eval_reflect(const ShaderData *sd, const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf)
{
	float m_ag = sc->data0;
	//float m_eta = sc->data1;
	int m_refractive = sc->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
	float3 m_N = sd->N;

	if(m_refractive) return make_float3 (0, 0, 0);
	float cosNO = dot(m_N, I);
	float cosNI = dot(m_N, omega_in);
	if(cosNI > 0 && cosNO > 0) {
		// get half vector
		float3 Hr = normalize(omega_in + I);
		// eq. 20: (F*G*D)/(4*in*on)
		// eq. 33: first we calculate D(m) with m=Hr:
		float alpha2 = m_ag * m_ag;
		float cosThetaM = dot(m_N, Hr);
		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 + sqrtf(1 + alpha2 * (1 - cosNO * cosNO) / (cosNO * cosNO)));
		float G1i = 2 / (1 + sqrtf(1 + alpha2 * (1 - cosNI * cosNI) / (cosNI * cosNI))); 
		float G = G1o * G1i;
		float out = (G * D) * 0.25f / cosNO;
		// eq. 24
		float pm = D * cosThetaM;
		// convert into pdf of the sampled direction
		// eq. 38 - but see also:
		// eq. 17 in http://www.graphics.cornell.edu/~bjw/wardnotes.pdf
		*pdf = pm * 0.25f / dot(Hr, I);
		return make_float3 (out, out, out);
	}
	return make_float3 (0, 0, 0);
}

__device float3 bsdf_microfacet_ggx_eval_transmit(const ShaderData *sd, const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf)
{
	float m_ag = sc->data0;
	float m_eta = sc->data1;
	int m_refractive = sc->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
	float3 m_N = sd->N;

	if(!m_refractive) return make_float3 (0, 0, 0);
	float cosNO = dot(m_N, I);
	float cosNI = dot(m_N, omega_in);
	if(cosNO <= 0 || cosNI >= 0)
		return make_float3 (0, 0, 0); // vectors on same side -- not possible
	// 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_ag * m_ag;
	float cosThetaM = dot(m_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 + sqrtf(1 + alpha2 * (1 - cosNO * cosNO) / (cosNO * cosNO)));
	float G1i = 2 / (1 + sqrtf(1 + alpha2 * (1 - cosNI * cosNI) / (cosNI * cosNI))); 
	float G = G1o * G1i;
	// probability
	float invHt2 = 1 / dot(ht, ht);
	*pdf = D * fabsf(cosThetaM) * (fabsf(cosHI) * (m_eta * m_eta)) * invHt2;
	float out = (fabsf(cosHI * cosHO) * (m_eta * m_eta) * (G * D) * invHt2) / cosNO;
	return make_float3 (out, out, out);
}

__device float bsdf_microfacet_ggx_albedo(const ShaderData *sd, const ShaderClosure *sc, const float3 I)
{
	return 1.0f;
}

__device int bsdf_microfacet_ggx_sample(const ShaderData *sd, const ShaderClosure *sc, float randu, float randv, float3 *eval, float3 *omega_in, float3 *domega_in_dx, float3 *domega_in_dy, float *pdf)
{
	float m_ag = sc->data0;
	float m_eta = sc->data1;
	int m_refractive = sc->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
	float3 m_N = sd->N;

	float cosNO = dot(m_N, sd->I);
	if(cosNO > 0) {
		float3 X, Y, Z = m_N;
		make_orthonormals(Z, &X, &Y);
		// generate a random microfacet normal m
		// eq. 35,36:
		// we take advantage of cos(atan(x)) == 1/sqrt(1+x^2)
		//tttt  and sin(atan(x)) == x/sqrt(1+x^2)
		float alpha2 = m_ag * m_ag;
		float tanThetaM2 = alpha2 * randu / (1 - randu);
		float cosThetaM  = 1 / sqrtf(1 + tanThetaM2);
		float sinThetaM  = cosThetaM * sqrtf(tanThetaM2);
		float phiM = 2 * M_PI_F * randv;
		float3 m = (cosf(phiM) * sinThetaM) * X +
				 (sinf(phiM) * sinThetaM) * Y +
							   cosThetaM  * Z;
		if(!m_refractive) {
			float cosMO = dot(m, sd->I);
			if(cosMO > 0) {
				// eq. 39 - compute actual reflected direction
				*omega_in = 2 * cosMO * m - sd->I;
				if(dot(sd->Ng, *omega_in) > 0) {
					// microfacet normal is visible to this ray
					// eq. 33
					float cosThetaM2 = cosThetaM * cosThetaM;
					float cosThetaM4 = cosThetaM2 * cosThetaM2;
					float D = alpha2 / (M_PI_F * cosThetaM4 * (alpha2 + tanThetaM2) * (alpha2 + tanThetaM2));
					// eq. 24
					float pm = D * cosThetaM;
					// convert into pdf of the sampled direction
					// eq. 38 - but see also:
					// eq. 17 in http://www.graphics.cornell.edu/~bjw/wardnotes.pdf
					*pdf = pm * 0.25f / cosMO;
					// eval BRDF*cosNI
					float cosNI = dot(m_N, *omega_in);
					// eq. 34: now calculate G1(i,m) and G1(o,m)
					float G1o = 2 / (1 + sqrtf(1 + alpha2 * (1 - cosNO * cosNO) / (cosNO * cosNO)));
					float G1i = 2 / (1 + sqrtf(1 + alpha2 * (1 - cosNI * cosNI) / (cosNI * cosNI))); 
					float G = G1o * G1i;
					// eq. 20: (F*G*D)/(4*in*on)
					float out = (G * D) * 0.25f / cosNO;
					*eval = make_float3(out, out, out);
#ifdef __RAY_DIFFERENTIALS__
					*domega_in_dx = (2 * dot(m, sd->dI.dx)) * m - sd->dI.dx;
					*domega_in_dy = (2 * dot(m, sd->dI.dy)) * m - sd->dI.dy;
					// Since there is some blur to this reflection, make the
					// derivatives a bit bigger. In theory this varies with the
					// roughness but the exact relationship is complex and
					// requires more ops than are practical.
					*domega_in_dx *= 10.0f;
					*domega_in_dy *= 10.0f;
#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
			bool inside;
			fresnel_dielectric(m_eta, m, sd->I, &R, &T,
#ifdef __RAY_DIFFERENTIALS__
				sd->dI.dx, sd->dI.dy, &dRdx, &dRdy, &dTdx, &dTdy,
#endif
				&inside);
			
			if(!inside) {
				*omega_in = T;
#ifdef __RAY_DIFFERENTIALS__
				*domega_in_dx = dTdx;
				*domega_in_dy = dTdy;
#endif
				// eq. 33
				float cosThetaM2 = cosThetaM * cosThetaM;
				float cosThetaM4 = cosThetaM2 * cosThetaM2;
				float D = alpha2 / (M_PI_F * cosThetaM4 * (alpha2 + tanThetaM2) * (alpha2 + tanThetaM2));
				// eq. 24
				float pm = D * cosThetaM;
				// eval BRDF*cosNI
				float cosNI = dot(m_N, *omega_in);
				// eq. 34: now calculate G1(i,m) and G1(o,m)
				float G1o = 2 / (1 + sqrtf(1 + alpha2 * (1 - cosNO * cosNO) / (cosNO * cosNO)));
				float G1i = 2 / (1 + sqrtf(1 + alpha2 * (1 - cosNI * cosNI) / (cosNI * cosNI))); 
				float G = G1o * G1i;
				// eq. 21
				float cosHI = dot(m, *omega_in);
				float cosHO = dot(m, sd->I);
				float Ht2 = m_eta * cosHI + cosHO;
				Ht2 *= Ht2;
				float out = (fabsf(cosHI * cosHO) * (m_eta * m_eta) * (G * D)) / (cosNO * Ht2);
				// eq. 38 and eq. 17
				*pdf = pm * (m_eta * m_eta) * fabsf(cosHI) / Ht2;
				*eval = make_float3(out, out, out);
#ifdef __RAY_DIFFERENTIALS__
				// Since there is some blur to this refraction, make the
				// derivatives a bit bigger. In theory this varies with the
				// roughness but the exact relationship is complex and
				// requires more ops than are practical.
				*domega_in_dx *= 10.0f;
				*domega_in_dy *= 10.0f;
#endif
			}
		}
	}
	return (m_refractive) ? LABEL_TRANSMIT|LABEL_GLOSSY : LABEL_REFLECT|LABEL_GLOSSY;
}

/* BECKMANN */

typedef struct BsdfMicrofacetBeckmannClosure {
	//float3 m_N;
	float m_ab;
	float m_eta;
} BsdfMicrofacetBeckmannClosure;

__device void bsdf_microfacet_beckmann_setup(ShaderData *sd, ShaderClosure *sc, float ab, float eta, bool refractive)
{
	float m_ab = clamp(ab, 1e-4f, 1.0f);
	float m_eta = eta;

	sc->data0 = m_ab;
	sc->data1 = m_eta;

	if(refractive)
		sc->type = CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID;
	else
		sc->type = CLOSURE_BSDF_MICROFACET_BECKMANN_ID;

	sd->flag |= SD_BSDF|SD_BSDF_HAS_EVAL|SD_BSDF_GLOSSY;
}

__device void bsdf_microfacet_beckmann_blur(ShaderClosure *sc, float roughness)
{
	float m_ab = sc->data0;
	m_ab = fmaxf(roughness, m_ab);
	sc->data0 = m_ab;
}

__device float3 bsdf_microfacet_beckmann_eval_reflect(const ShaderData *sd, const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf)
{
	float m_ab = sc->data0;
	//float m_eta = sc->data1;
	int m_refractive = sc->type == CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID;
	float3 m_N = sd->N;

	if(m_refractive) return make_float3 (0, 0, 0);
	float cosNO = dot(m_N, I);
	float cosNI = dot(m_N, omega_in);
	if(cosNO > 0 && cosNI > 0) {
	   // get half vector
	   float3 Hr = normalize(omega_in + I);
	   // eq. 20: (F*G*D)/(4*in*on)
	   // eq. 25: first we calculate D(m) with m=Hr:
	   float alpha2 = m_ab * m_ab;
	   float cosThetaM = dot(m_N, Hr);
	   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 * sqrtf((1 - cosNO * cosNO) / (cosNO * cosNO)));
	   float ai = 1 / (m_ab * 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;
	   float out = (G * D) * 0.25f / cosNO;
	   // eq. 24
	   float pm = D * cosThetaM;
	   // convert into pdf of the sampled direction
	   // eq. 38 - but see also:
	   // eq. 17 in http://www.graphics.cornell.edu/~bjw/wardnotes.pdf
	   *pdf = pm * 0.25f / dot(Hr, I);
	   return make_float3 (out, out, out);
	}
	return make_float3 (0, 0, 0);
}

__device float3 bsdf_microfacet_beckmann_eval_transmit(const ShaderData *sd, const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf)
{
	float m_ab = sc->data0;
	float m_eta = sc->data1;
	int m_refractive = sc->type == CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID;
	float3 m_N = sd->N;

	if(!m_refractive) return make_float3 (0, 0, 0);
	float cosNO = dot(m_N, I);
	float cosNI = dot(m_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 = dot(m_N, Ht);
	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 * sqrtf((1 - cosNO * cosNO) / (cosNO * cosNO)));
	float ai = 1 / (m_ab * 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 invHt2 = 1 / dot(ht, ht);
	*pdf = D * fabsf(cosThetaM) * (fabsf(cosHI) * (m_eta * m_eta)) * invHt2;
	float out = (fabsf(cosHI * cosHO) * (m_eta * m_eta) * (G * D) * invHt2) / cosNO;
	return make_float3 (out, out, out);
}

__device float bsdf_microfacet_beckmann_albedo(const ShaderData *sd, const ShaderClosure *sc, const float3 I)
{
	return 1.0f;
}

__device int bsdf_microfacet_beckmann_sample(const ShaderData *sd, const ShaderClosure *sc, float randu, float randv, float3 *eval, float3 *omega_in, float3 *domega_in_dx, float3 *domega_in_dy, float *pdf)
{
	float m_ab = sc->data0;
	float m_eta = sc->data1;
	int m_refractive = sc->type == CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID;
	float3 m_N = sd->N;

	float cosNO = dot(m_N, sd->I);
	if(cosNO > 0) {
		float3 X, Y, Z = m_N;
		make_orthonormals(Z, &X, &Y);
		// generate a random microfacet normal m
		// eq. 35,36:
		// we take advantage of cos(atan(x)) == 1/sqrt(1+x^2)
		//tttt  and sin(atan(x)) == x/sqrt(1+x^2)
		float alpha2 = m_ab * m_ab;
		float tanThetaM = sqrtf(-alpha2 * logf(1 - randu));
		float cosThetaM = 1 / sqrtf(1 + tanThetaM * tanThetaM);
		float sinThetaM = cosThetaM * tanThetaM;
		float phiM = 2 * M_PI_F * randv;
		float3 m = (cosf(phiM) * sinThetaM) * X +
				 (sinf(phiM) * sinThetaM) * Y +
							   cosThetaM  * Z;

		if(!m_refractive) {
			float cosMO = dot(m, sd->I);
			if(cosMO > 0) {
				// eq. 39 - compute actual reflected direction
				*omega_in = 2 * cosMO * m - sd->I;
				if(dot(sd->Ng, *omega_in) > 0) {
					// microfacet normal is visible to this ray
					// eq. 25
					float cosThetaM2 = cosThetaM * cosThetaM;
					float tanThetaM2 = tanThetaM * tanThetaM;
					float cosThetaM4 = cosThetaM2 * cosThetaM2;
					float D = expf(-tanThetaM2 / alpha2) / (M_PI_F * alpha2 *  cosThetaM4);
					// eq. 24
					float pm = D * cosThetaM;
					// convert into pdf of the sampled direction
					// eq. 38 - but see also:
					// eq. 17 in http://www.graphics.cornell.edu/~bjw/wardnotes.pdf
					*pdf = pm * 0.25f / cosMO;
					// Eval BRDF*cosNI
					float cosNI = dot(m_N, *omega_in);
					// eq. 26, 27: now calculate G1(i,m) and G1(o,m)
					float ao = 1 / (m_ab * sqrtf((1 - cosNO * cosNO) / (cosNO * cosNO)));
					float ai = 1 / (m_ab * 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: (F*G*D)/(4*in*on)
					float out = (G * D) * 0.25f / cosNO;
					*eval = make_float3(out, out, out);
#ifdef __RAY_DIFFERENTIALS__
					*domega_in_dx = (2 * dot(m, sd->dI.dx)) * m - sd->dI.dx;
					*domega_in_dy = (2 * dot(m, sd->dI.dy)) * m - sd->dI.dy;
					// Since there is some blur to this reflection, make the
					// derivatives a bit bigger. In theory this varies with the
					// roughness but the exact relationship is complex and
					// requires more ops than are practical.
					*domega_in_dx *= 10.0f;
					*domega_in_dy *= 10.0f;
#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
			bool inside;
			fresnel_dielectric(m_eta, m, sd->I, &R, &T,
#ifdef __RAY_DIFFERENTIALS__
				sd->dI.dx, sd->dI.dy, &dRdx, &dRdy, &dTdx, &dTdy,
#endif
				&inside);

			if(!inside) {
				*omega_in = T;
#ifdef __RAY_DIFFERENTIALS__
				*domega_in_dx = dTdx;
				*domega_in_dy = dTdy;
#endif

				// eq. 33
				float cosThetaM2 = cosThetaM * cosThetaM;
				float tanThetaM2 = tanThetaM * tanThetaM;
				float cosThetaM4 = cosThetaM2 * cosThetaM2;
				float D = expf(-tanThetaM2 / alpha2) / (M_PI_F * alpha2 *  cosThetaM4);
				// eq. 24
				float pm = D * cosThetaM;
				// eval BRDF*cosNI
				float cosNI = dot(m_N, *omega_in);
				// eq. 26, 27: now calculate G1(i,m) and G1(o,m)
				float ao = 1 / (m_ab * sqrtf((1 - cosNO * cosNO) / (cosNO * cosNO)));
				float ai = 1 / (m_ab * 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. 21
				float cosHI = dot(m, *omega_in);
				float cosHO = dot(m, sd->I);
				float Ht2 = m_eta * cosHI + cosHO;
				Ht2 *= Ht2;
				float out = (fabsf(cosHI * cosHO) * (m_eta * m_eta) * (G * D)) / (cosNO * Ht2);
				// eq. 38 and eq. 17
				*pdf = pm * (m_eta * m_eta) * fabsf(cosHI) / Ht2;
				*eval = make_float3(out, out, out);
#ifdef __RAY_DIFFERENTIALS__
				// Since there is some blur to this refraction, make the
				// derivatives a bit bigger. In theory this varies with the
				// roughness but the exact relationship is complex and
				// requires more ops than are practical.
				*domega_in_dx *= 10.0f;
				*domega_in_dy *= 10.0f;
#endif
			}
		}
	}
	return (m_refractive) ? LABEL_TRANSMIT|LABEL_GLOSSY : LABEL_REFLECT|LABEL_GLOSSY;
}

CCL_NAMESPACE_END

#endif /* __BSDF_MICROFACET_H__ */