bsdf_ashikhmin_shirley.h

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/*
 * Copyright 2011-2014 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(MicrofacetBsdf *bsdf)
{
  bsdf->alpha_x = clamp(bsdf->alpha_x, 1e-4f, 1.0f);
  bsdf->alpha_y = clamp(bsdf->alpha_y, 1e-4f, 1.0f);
 
  bsdf->type = CLOSURE_BSDF_ASHIKHMIN_SHIRLEY_ID;
  return SD_BSDF | SD_BSDF_HAS_EVAL;
}
 
ccl_device void bsdf_ashikhmin_shirley_blur(ShaderClosure *sc, float roughness)
{
  MicrofacetBsdf *bsdf = (MicrofacetBsdf *)sc;
 
  bsdf->alpha_x = fmaxf(roughness, bsdf->alpha_x);
  bsdf->alpha_y = fmaxf(roughness, bsdf->alpha_y);
}
 
ccl_device_inline float bsdf_ashikhmin_shirley_roughness_to_exponent(float roughness)
{
  return 2.0f / (roughness * roughness) - 2.0f;
}
 
ccl_device_forceinline float3 bsdf_ashikhmin_shirley_eval_reflect(const ShaderClosure *sc,
                                                                  const float3 I,
                                                                  const float3 omega_in,
                                                                  float *pdf)
{
  const MicrofacetBsdf *bsdf = (const MicrofacetBsdf *)sc;
  float3 N = bsdf->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 (fmaxf(bsdf->alpha_x, bsdf->alpha_y) <= 1e-4f)
    return make_float3(0.0f, 0.0f, 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(fabsf(dot(H, I)), 1e-6f);
    float HdotN = fmaxf(dot(H, N), 1e-6f);
 
    /* pump from original paper
     * (first derivative disc., but cancels the HdotI in the pdf nicely) */
    float pump = 1.0f / fmaxf(1e-6f, (HdotI * fmaxf(NdotO, NdotI)));
    /* pump from d-brdf paper */
    /*float pump = 1.0f / fmaxf(1e-4f, ((NdotO + NdotI) * (NdotO*NdotI))); */
 
    float n_x = bsdf_ashikhmin_shirley_roughness_to_exponent(bsdf->alpha_x);
    float n_y = bsdf_ashikhmin_shirley_roughness_to_exponent(bsdf->alpha_y);
 
    if (n_x == n_y) {
      /* isotropic */
      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;
      /* this is p_h / 4(H.I)  (conversion from 'wh measure' to 'wi measure', eq. 8 in paper). */
      *pdf = norm * lobe / HdotI;
    }
    else {
      /* anisotropic */
      float3 X, Y;
      make_orthonormals_tangent(N, bsdf->T, &X, &Y);
 
      float HdotX = dot(H, X);
      float HdotY = dot(H, Y);
      float lobe;
      if (HdotN < 1.0f) {
        float e = (n_x * HdotX * HdotX + n_y * HdotY * HdotY) / (1.0f - HdotN * HdotN);
        lobe = powf(HdotN, e);
      }
      else {
        lobe = 1.0f;
      }
      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_phi * cos_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)
{
  const MicrofacetBsdf *bsdf = (const MicrofacetBsdf *)sc;
  float3 N = bsdf->N;
  int label = LABEL_REFLECT | LABEL_GLOSSY;
 
  float NdotI = dot(N, I);
  if (NdotI > 0.0f) {
 
    float n_x = bsdf_ashikhmin_shirley_roughness_to_exponent(bsdf->alpha_x);
    float n_y = bsdf_ashikhmin_shirley_roughness_to_exponent(bsdf->alpha_y);
 
    /* 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, bsdf->T, &X, &Y);
 
    /* sample spherical coords for h in tangent space */
    float phi;
    float cos_theta;
    if (n_x == n_y) {
      /* isotropic sampling */
      phi = M_2PI_F * randu;
      cos_theta = powf(randv, 1.0f / (n_x + 1.0f));
    }
    else {
      /* 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.x * X + h.y * Y + 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;
 
    if (fmaxf(bsdf->alpha_x, bsdf->alpha_y) <= 1e-4f) {
      /* Some high number for MIS. */
      *pdf = 1e6f;
      *eval = make_float3(1e6f, 1e6f, 1e6f);
      label = LABEL_REFLECT | LABEL_SINGULAR;
    }
    else {
      /* leave the rest to eval_reflect */
      *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;
}
 
CCL_NAMESPACE_END
 
#endif /* __BSDF_ASHIKHMIN_SHIRLEY_H__ */