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				/*
				* Copyright 2011-2013 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
				*/

				#ifndef __BSDF_ASHIKHMIN_SHIRLEY_H__
				#define __BSDF_ASHIKHMIN_SHIRLEY_H__

				/*
				ASHIKHMIN SHIRLEY BSDF

				Implementation of
				Michael Ashikhmin and Peter Shirley: "An Anisotropic Phong BRDF Model" (2000)

				The Fresnel factor is missing to get a separable bsdf (intensity*color), as is
				the case with all other microfacet-based BSDF implementations in Cycles.

				Other than that, the implementation directly follows the paper.
				*/

				CCL_NAMESPACE_BEGIN

				ccl_device int bsdf_ashikhmin_shirley_setup(ShaderClosure *sc)
				{
				/* store roughness. could already convert to exponent to save some cycles
				* in eval, but this is more consistent with other bsdfs and shader_blur. */
				sc->data0 = clamp(sc->data0, 1e-4f, 1.0f);
				sc->data1 = sc->data0;

				sc->type = CLOSURE_BSDF_ASHIKHMIN_SHIRLEY_ID;
				return SD_BSDF \| SD_BSDF_HAS_EVAL \| SD_BSDF_GLOSSY;
				}

				ccl_device int bsdf_ashikhmin_shirley_aniso_setup(ShaderClosure *sc)
				{
				/* store roughness. could already convert to exponent to save some cycles
				* in eval, but this is more consistent with other bsdfs and shader_blur. */
				sc->data0 = clamp(sc->data0, 1e-4f, 1.0f);
				sc->data1 = clamp(sc->data1, 1e-4f, 1.0f);

				sc->type = CLOSURE_BSDF_ASHIKHMIN_SHIRLEY_ANISO_ID;
				return SD_BSDF \| SD_BSDF_HAS_EVAL \| SD_BSDF_GLOSSY;
				}

				ccl_device void bsdf_ashikhmin_shirley_blur(ShaderClosure *sc, float roughness)
				{
				sc->data0 = fmaxf(roughness, sc->data0); /* clamp roughness */
				sc->data1 = fmaxf(roughness, sc->data1);
				}

				ccl_device_inline float bsdf_ashikhmin_shirley_roughness_to_exponent(float roughness)
				{
				return 2.0f / (roughness*roughness) - 2.0f;
				}

				ccl_device float3 bsdf_ashikhmin_shirley_eval_reflect(const ShaderClosure sc, const float3 I, const float3 omega_in, float pdf)
				{
				float3 N = sc->N;

				float NdotI = dot(N, I); /* in Cycles/OSL convention I is omega_out */
				float NdotO = dot(N, omega_in); /* and consequently we use for O omaga_in ;) */

				float out = 0.0f;

				if (NdotI > 0.0f && NdotO > 0.0f) {
				NdotI = fmaxf(NdotI, 1e-6f);
				NdotO = fmaxf(NdotO, 1e-6f);
				float3 H = normalize(omega_in + I);
				float HdotI = fmaxf(dot(H, I), 1e-6f);
				float HdotN = fmaxf(dot(H, N), 1e-6f);

				float pump = 1.0f / fmaxf(1e-6f, (HdotIfmaxf(NdotO, NdotI))); / pump from original paper (first derivative disc., but cancels the HdotI in the pdf nicely) */
				/float pump = 1.0f / fmaxf(1e-4f, ((NdotO + NdotI) (NdotONdotI))); / /* pump from d-brdf paper */

				float n_x = bsdf_ashikhmin_shirley_roughness_to_exponent(sc->data0);
				float n_y = bsdf_ashikhmin_shirley_roughness_to_exponent(sc->data1);

				if (n_x == n_y) { /* => isotropic case */
				float e = n_x;
				float lobe = powf(HdotN, e);
				float norm = (n_x + 1.0f) / (8.0f * M_PI_F);

				out = NdotO * norm * lobe * pump;
				pdf = norm lobe / HdotI; /* this is p_h / 4(H.I) (conversion from 'wh measure' to 'wi measure', eq. 8 in paper) */
				}
				else { /* => ANisotropic case */
				float3 X, Y;
				make_orthonormals_tangent(N, sc->T, &X, &Y);

				float HdotX = dot(H, X);
				float HdotY = dot(H, Y);
				float e = (n_x * HdotXHdotX + n_y HdotYHdotY) / (1.0f - HdotNHdotN);
				float lobe = powf(HdotN, e);
				float norm = sqrtf((n_x + 1.0f)(n_y + 1.0f)) / (8.0f M_PI_F);

				out = NdotO * norm * lobe * pump;
				pdf = norm lobe / HdotI;
				}
				}

				return make_float3(out, out, out);
				}

				ccl_device float3 bsdf_ashikhmin_shirley_eval_transmit(const ShaderClosure sc, const float3 I, const float3 omega_in, float pdf)
				{
				return make_float3(0.0f, 0.0f, 0.0f);
				}

				ccl_device_inline void bsdf_ashikhmin_shirley_sample_first_quadrant(float n_x, float n_y, float randu, float randv, float phi, float cos_theta)
				{
				phi = atanf(sqrtf((n_x + 1.0f) / (n_y + 1.0f)) tanf(M_PI_2_F * randu));
				float cos_phi = cosf(*phi);
				float sin_phi = sinf(*phi);
				cos_theta = powf(randv, 1.0f / (n_x cos_phicos_phi + n_y sin_phi*sin_phi + 1.0f));
				}

				ccl_device int bsdf_ashikhmin_shirley_sample(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)
				{
				float3 N = sc->N;

				float NdotI = dot(N, I);
				if (NdotI > 0.0f) {

				float n_x = bsdf_ashikhmin_shirley_roughness_to_exponent(sc->data0);
				float n_y = bsdf_ashikhmin_shirley_roughness_to_exponent(sc->data1);

				/* get x,y basis on the surface for anisotropy */
				float3 X, Y;

				if(n_x == n_y)
				make_orthonormals(N, &X, &Y);
				else
				make_orthonormals_tangent(N, sc->T, &X, &Y);

				/* sample spherical coords for h in tangent space */
				float phi;
				float cos_theta;
				if (n_x == n_y) { /* => simple isotropic sampling */
				phi = M_2PI_F * randu;
				cos_theta = powf(randv, 1.0f / (n_x + 1.0f));
				}
				else { /* => more complex anisotropic sampling */
				if (randu < 0.25f) { /* first quadrant */
				float remapped_randu = 4.0f * randu;
				bsdf_ashikhmin_shirley_sample_first_quadrant(n_x, n_y, remapped_randu, randv, &phi, &cos_theta);
				}
				else if (randu < 0.5f) { /* second quadrant */
				float remapped_randu = 4.0f * (.5f - randu);
				bsdf_ashikhmin_shirley_sample_first_quadrant(n_x, n_y, remapped_randu, randv, &phi, &cos_theta);
				phi = M_PI_F - phi;
				}
				else if (randu < 0.75f) { /* third quadrant */
				float remapped_randu = 4.0f * (randu - 0.5f);
				bsdf_ashikhmin_shirley_sample_first_quadrant(n_x, n_y, remapped_randu, randv, &phi, &cos_theta);
				phi = M_PI_F + phi;
				}
				else { /* fourth quadrant */
				float remapped_randu = 4.0f * (1.0f - randu);
				bsdf_ashikhmin_shirley_sample_first_quadrant(n_x, n_y, remapped_randu, randv, &phi, &cos_theta);
				phi = 2.0f * M_PI_F - phi;
				}
				}

				/* get half vector in tangent space */
				float sin_theta = sqrtf(fmaxf(0.0f, 1.0f - cos_theta*cos_theta));
				float cos_phi = cosf(phi);
				float sin_phi = sinf(phi); /* no sqrt(1-cos^2) here b/c it causes artifacts */
				float3 h = make_float3(
				sin_theta * cos_phi,
				sin_theta * sin_phi,
				cos_theta
				);

				/* half vector to world space */
				float3 H = h.xX + h.yY + h.z*N;
				float HdotI = dot(H, I);
				if (HdotI < 0.0f) H = -H;

				/* reflect I on H to get omega_in */
				omega_in = -I + (2.0f HdotI) * H;

				/* leave the rest to eval_reflect */
				/* (could maybe optimize a few things by manual inlining, but I doubt it would make much difference) */
				eval = bsdf_ashikhmin_shirley_eval_reflect(sc, I, omega_in, pdf);

				#ifdef __RAY_DIFFERENTIALS__
				/* just do the reflection thing for now */
				domega_in_dx = (2.0f dot(N, dIdx)) * N - dIdx;
				domega_in_dy = (2.0f dot(N, dIdy)) * N - dIdy;
				#endif
				}

				return LABEL_REFLECT \| LABEL_GLOSSY;
				}


				CCL_NAMESPACE_END

				#endif /* __BSDF_ASHIKHMIN_SHIRLEY_H__ */