bsdf_microfacet_multi_impl.h

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/*
 * 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.
 */
 
/* Evaluate the BSDF from wi to wo.
 * Evaluation is split into the analytical single-scattering BSDF and the multi-scattering BSDF,
 * which is evaluated stochastically through a random walk. At each bounce (except for the first
 * one), the amount of reflection from here towards wo is evaluated before bouncing again.
 *
 * Because of the random walk, the evaluation is not deterministic, but its expected value is equal
 * to the correct BSDF, which is enough for Monte-Carlo rendering. The PDF also can't be determined
 * analytically, so the single-scattering PDF plus a diffuse term to account for the
 * multi-scattered energy is used. In combination with MIS, that is enough to produce an unbiased
 * result, although the balance heuristic isn't necessarily optimal anymore.
 */
ccl_device_forceinline float3 MF_FUNCTION_FULL_NAME(mf_eval)(float3 wi,
                                                             float3 wo,
                                                             const bool wo_outside,
                                                             const float3 color,
                                                             const float alpha_x,
                                                             const float alpha_y,
                                                             ccl_addr_space uint *lcg_state,
                                                             const float eta,
                                                             bool use_fresnel,
                                                             const float3 cspec0)
{
  /* Evaluating for a shallower incoming direction produces less noise, and the properties of the
   * BSDF guarantee reciprocity. */
  bool swapped = false;
#ifdef MF_MULTI_GLASS
  if (wi.z * wo.z < 0.0f) {
    /* Glass transmission is a special case and requires the directions to change hemisphere. */
    if (-wo.z < wi.z) {
      swapped = true;
      float3 tmp = -wo;
      wo = -wi;
      wi = tmp;
    }
  }
  else
#endif
      if (wo.z < wi.z) {
    swapped = true;
    float3 tmp = wo;
    wo = wi;
    wi = tmp;
  }
 
  if (wi.z < 1e-5f || (wo.z < 1e-5f && wo_outside) || (wo.z > -1e-5f && !wo_outside))
    return make_float3(0.0f, 0.0f, 0.0f);
 
  const float2 alpha = make_float2(alpha_x, alpha_y);
 
  float lambda_r = mf_lambda(-wi, alpha);
  float shadowing_lambda = mf_lambda(wo_outside ? wo : -wo, alpha);
 
  /* Analytically compute single scattering for lower noise. */
  float3 eval;
  float3 throughput = make_float3(1.0f, 1.0f, 1.0f);
  const float3 wh = normalize(wi + wo);
#ifdef MF_MULTI_GLASS
  eval = mf_eval_phase_glass(-wi, lambda_r, wo, wo_outside, alpha, eta);
  if (wo_outside)
    eval *= -lambda_r / (shadowing_lambda - lambda_r);
  else
    eval *= -lambda_r * beta(-lambda_r, shadowing_lambda + 1.0f);
#else /* MF_MULTI_GLOSSY */
  const float G2 = 1.0f / (1.0f - (lambda_r + 1.0f) + shadowing_lambda);
  float val = G2 * 0.25f / wi.z;
  if (alpha.x == alpha.y)
    val *= D_ggx(wh, alpha.x);
  else
    val *= D_ggx_aniso(wh, alpha);
  eval = make_float3(val, val, val);
#endif
 
  float F0 = fresnel_dielectric_cos(1.0f, eta);
  if (use_fresnel) {
    throughput = interpolate_fresnel_color(wi, wh, eta, F0, cspec0);
 
    eval *= throughput;
  }
 
  float3 wr = -wi;
  float hr = 1.0f;
  float C1_r = 1.0f;
  float G1_r = 0.0f;
  bool outside = true;
 
  for (int order = 0; order < 10; order++) {
    /* Sample microfacet height. */
    float height_rand = lcg_step_float_addrspace(lcg_state);
    if (!mf_sample_height(wr, &hr, &C1_r, &G1_r, &lambda_r, height_rand))
      break;
    /* Sample microfacet normal. */
    float vndf_rand_y = lcg_step_float_addrspace(lcg_state);
    float vndf_rand_x = lcg_step_float_addrspace(lcg_state);
    float3 wm = mf_sample_vndf(-wr, alpha, vndf_rand_x, vndf_rand_y);
 
#ifdef MF_MULTI_GLASS
    if (order == 0 && use_fresnel) {
      /* Evaluate amount of scattering towards wo on this microfacet. */
      float3 phase;
      if (outside)
        phase = mf_eval_phase_glass(wr, lambda_r, wo, wo_outside, alpha, eta);
      else
        phase = mf_eval_phase_glass(wr, lambda_r, -wo, !wo_outside, alpha, 1.0f / eta);
 
      eval = throughput * phase *
             mf_G1(wo_outside ? wo : -wo,
                   mf_C1((outside == wo_outside) ? hr : -hr),
                   shadowing_lambda);
    }
#endif
    if (order > 0) {
      /* Evaluate amount of scattering towards wo on this microfacet. */
      float3 phase;
#ifdef MF_MULTI_GLASS
      if (outside)
        phase = mf_eval_phase_glass(wr, lambda_r, wo, wo_outside, alpha, eta);
      else
        phase = mf_eval_phase_glass(wr, lambda_r, -wo, !wo_outside, alpha, 1.0f / eta);
#else /* MF_MULTI_GLOSSY */
      phase = mf_eval_phase_glossy(wr, lambda_r, wo, alpha) * throughput;
#endif
      eval += throughput * phase *
              mf_G1(wo_outside ? wo : -wo,
                    mf_C1((outside == wo_outside) ? hr : -hr),
                    shadowing_lambda);
    }
    if (order + 1 < 10) {
      /* Bounce from the microfacet. */
#ifdef MF_MULTI_GLASS
      bool next_outside;
      float3 wi_prev = -wr;
      float phase_rand = lcg_step_float_addrspace(lcg_state);
      wr = mf_sample_phase_glass(-wr, outside ? eta : 1.0f / eta, wm, phase_rand, &next_outside);
      if (!next_outside) {
        outside = !outside;
        wr = -wr;
        hr = -hr;
      }
 
      if (use_fresnel && !next_outside) {
        throughput *= color;
      }
      else if (use_fresnel && order > 0) {
        throughput *= interpolate_fresnel_color(wi_prev, wm, eta, F0, cspec0);
      }
#else /* MF_MULTI_GLOSSY */
      if (use_fresnel && order > 0) {
        throughput *= interpolate_fresnel_color(-wr, wm, eta, F0, cspec0);
      }
      wr = mf_sample_phase_glossy(-wr, &throughput, wm);
#endif
 
      lambda_r = mf_lambda(wr, alpha);
 
      if (!use_fresnel)
        throughput *= color;
 
      C1_r = mf_C1(hr);
      G1_r = mf_G1(wr, C1_r, lambda_r);
    }
  }
 
  if (swapped)
    eval *= fabsf(wi.z / wo.z);
  return eval;
}
 
/* Perform a random walk on the microsurface starting from wi, returning the direction in which the
 * walk escaped the surface in wo. The function returns the throughput between wi and wo. Without
 * reflection losses due to coloring or fresnel absorption in conductors, the sampling is optimal.
 */
ccl_device_forceinline float3 MF_FUNCTION_FULL_NAME(mf_sample)(float3 wi,
                                                               float3 *wo,
                                                               const float3 color,
                                                               const float alpha_x,
                                                               const float alpha_y,
                                                               ccl_addr_space uint *lcg_state,
                                                               const float eta,
                                                               bool use_fresnel,
                                                               const float3 cspec0)
{
  const float2 alpha = make_float2(alpha_x, alpha_y);
 
  float3 throughput = make_float3(1.0f, 1.0f, 1.0f);
  float3 wr = -wi;
  float lambda_r = mf_lambda(wr, alpha);
  float hr = 1.0f;
  float C1_r = 1.0f;
  float G1_r = 0.0f;
  bool outside = true;
 
  float F0 = fresnel_dielectric_cos(1.0f, eta);
  if (use_fresnel) {
    throughput = interpolate_fresnel_color(wi, normalize(wi + wr), eta, F0, cspec0);
  }
 
  int order;
  for (order = 0; order < 10; order++) {
    /* Sample microfacet height. */
    float height_rand = lcg_step_float_addrspace(lcg_state);
    if (!mf_sample_height(wr, &hr, &C1_r, &G1_r, &lambda_r, height_rand)) {
      /* The random walk has left the surface. */
      *wo = outside ? wr : -wr;
      return throughput;
    }
    /* Sample microfacet normal. */
    float vndf_rand_y = lcg_step_float_addrspace(lcg_state);
    float vndf_rand_x = lcg_step_float_addrspace(lcg_state);
    float3 wm = mf_sample_vndf(-wr, alpha, vndf_rand_x, vndf_rand_y);
 
    /* First-bounce color is already accounted for in mix weight. */
    if (!use_fresnel && order > 0)
      throughput *= color;
 
      /* Bounce from the microfacet. */
#ifdef MF_MULTI_GLASS
    bool next_outside;
    float3 wi_prev = -wr;
    float phase_rand = lcg_step_float_addrspace(lcg_state);
    wr = mf_sample_phase_glass(-wr, outside ? eta : 1.0f / eta, wm, phase_rand, &next_outside);
    if (!next_outside) {
      hr = -hr;
      wr = -wr;
      outside = !outside;
    }
 
    if (use_fresnel) {
      if (!next_outside) {
        throughput *= color;
      }
      else {
        float3 t_color = interpolate_fresnel_color(wi_prev, wm, eta, F0, cspec0);
 
        if (order == 0)
          throughput = t_color;
        else
          throughput *= t_color;
      }
    }
#else /* MF_MULTI_GLOSSY */
    if (use_fresnel) {
      float3 t_color = interpolate_fresnel_color(-wr, wm, eta, F0, cspec0);
 
      if (order == 0)
        throughput = t_color;
      else
        throughput *= t_color;
    }
    wr = mf_sample_phase_glossy(-wr, &throughput, wm);
#endif
 
    /* Update random walk parameters. */
    lambda_r = mf_lambda(wr, alpha);
    G1_r = mf_G1(wr, C1_r, lambda_r);
  }
  *wo = make_float3(0.0f, 0.0f, 1.0f);
  return make_float3(0.0f, 0.0f, 0.0f);
}
 
#undef MF_MULTI_GLASS
#undef MF_MULTI_GLOSSY
#undef MF_PHASE_FUNCTION