blender/intern/cycles/kernel/kernel_light.h

/*
 * 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.
 */

CCL_NAMESPACE_BEGIN

/* Light Sample result */

typedef struct LightSample {
  float3 P;       /* position on light, or direction for distant light */
  float3 Ng;      /* normal on light */
  float3 D;       /* direction from shading point to light */
  float t;        /* distance to light (FLT_MAX for distant light) */
  float u, v;     /* parametric coordinate on primitive */
  float pdf;      /* light sampling probability density function */
  float eval_fac; /* intensity multiplier */
  int object;     /* object id for triangle/curve lights */
  int prim;       /* primitive id for triangle/curve lights */
  int shader;     /* shader id */
  int lamp;       /* lamp id */
  LightType type; /* type of light */
} LightSample;

/* Area light sampling */

/* Uses the following paper:
 *
 * Carlos Urena et al.
 * An Area-Preserving Parametrization for Spherical Rectangles.
 *
 * https://www.solidangle.com/research/egsr2013_spherical_rectangle.pdf
 *
 * Note: light_p is modified when sample_coord is true.
 */
ccl_device_inline float rect_light_sample(float3 P,
                                          float3 *light_p,
                                          float3 axisu,
                                          float3 axisv,
                                          float randu,
                                          float randv,
                                          bool sample_coord)
{
  /* In our name system we're using P for the center,
   * which is o in the paper.
   */

  float3 corner = *light_p - axisu * 0.5f - axisv * 0.5f;
  float axisu_len, axisv_len;
  /* Compute local reference system R. */
  float3 x = normalize_len(axisu, &axisu_len);
  float3 y = normalize_len(axisv, &axisv_len);
  float3 z = cross(x, y);
  /* Compute rectangle coords in local reference system. */
  float3 dir = corner - P;
  float z0 = dot(dir, z);
  /* Flip 'z' to make it point against Q. */
  if (z0 > 0.0f) {
    z *= -1.0f;
    z0 *= -1.0f;
  }
  float x0 = dot(dir, x);
  float y0 = dot(dir, y);
  float x1 = x0 + axisu_len;
  float y1 = y0 + axisv_len;
  /* Compute internal angles (gamma_i). */
  float4 diff = make_float4(x0, y1, x1, y0) - make_float4(x1, y0, x0, y1);
  float4 nz = make_float4(y0, x1, y1, x0) * diff;
  nz = nz / sqrt(z0 * z0 * diff * diff + nz * nz);
  float g0 = safe_acosf(-nz.x * nz.y);
  float g1 = safe_acosf(-nz.y * nz.z);
  float g2 = safe_acosf(-nz.z * nz.w);
  float g3 = safe_acosf(-nz.w * nz.x);
  /* Compute predefined constants. */
  float b0 = nz.x;
  float b1 = nz.z;
  float b0sq = b0 * b0;
  float k = M_2PI_F - g2 - g3;
  /* Compute solid angle from internal angles. */
  float S = g0 + g1 - k;

  if (sample_coord) {
    /* Compute cu. */
    float au = randu * S + k;
    float fu = (cosf(au) * b0 - b1) / sinf(au);
    float cu = 1.0f / sqrtf(fu * fu + b0sq) * (fu > 0.0f ? 1.0f : -1.0f);
    cu = clamp(cu, -1.0f, 1.0f);
    /* Compute xu. */
    float xu = -(cu * z0) / max(sqrtf(1.0f - cu * cu), 1e-7f);
    xu = clamp(xu, x0, x1);
    /* Compute yv. */
    float z0sq = z0 * z0;
    float y0sq = y0 * y0;
    float y1sq = y1 * y1;
    float d = sqrtf(xu * xu + z0sq);
    float h0 = y0 / sqrtf(d * d + y0sq);
    float h1 = y1 / sqrtf(d * d + y1sq);
    float hv = h0 + randv * (h1 - h0), hv2 = hv * hv;
    float yv = (hv2 < 1.0f - 1e-6f) ? (hv * d) / sqrtf(1.0f - hv2) : y1;

    /* Transform (xu, yv, z0) to world coords. */
    *light_p = P + xu * x + yv * y + z0 * z;
  }

  /* return pdf */
  if (S != 0.0f)
    return 1.0f / S;
  else
    return 0.0f;
}

ccl_device_inline float3 ellipse_sample(float3 ru, float3 rv, float randu, float randv)
{
  to_unit_disk(&randu, &randv);
  return ru * randu + rv * randv;
}

ccl_device float3 disk_light_sample(float3 v, float randu, float randv)
{
  float3 ru, rv;

  make_orthonormals(v, &ru, &rv);

  return ellipse_sample(ru, rv, randu, randv);
}

ccl_device float3 distant_light_sample(float3 D, float radius, float randu, float randv)
{
  return normalize(D + disk_light_sample(D, randu, randv) * radius);
}

ccl_device float3
sphere_light_sample(float3 P, float3 center, float radius, float randu, float randv)
{
  return disk_light_sample(normalize(P - center), randu, randv) * radius;
}

ccl_device float spot_light_attenuation(float3 dir,
                                        float spot_angle,
                                        float spot_smooth,
                                        LightSample *ls)
{
  float3 I = ls->Ng;

  float attenuation = dot(dir, I);

  if (attenuation <= spot_angle) {
    attenuation = 0.0f;
  }
  else {
    float t = attenuation - spot_angle;

    if (t < spot_smooth && spot_smooth != 0.0f)
      attenuation *= smoothstepf(t / spot_smooth);
  }

  return attenuation;
}

ccl_device float lamp_light_pdf(KernelGlobals *kg, const float3 Ng, const float3 I, float t)
{
  float cos_pi = dot(Ng, I);

  if (cos_pi <= 0.0f)
    return 0.0f;

  return t * t / cos_pi;
}

/* Background Light */

#ifdef __BACKGROUND_MIS__

/* TODO(sergey): In theory it should be all fine to use noinline for all
 * devices, but we're so close to the release so better not screw things
 * up for CPU at least.
 */
#  ifdef __KERNEL_GPU__
ccl_device_noinline
#  else
ccl_device
#  endif
    float3
    background_map_sample(KernelGlobals *kg, float randu, float randv, float *pdf)
{
  /* for the following, the CDF values are actually a pair of floats, with the
   * function value as X and the actual CDF as Y.  The last entry's function
   * value is the CDF total. */
  int res_x = kernel_data.integrator.pdf_background_res_x;
  int res_y = kernel_data.integrator.pdf_background_res_y;
  int cdf_width = res_x + 1;

  /* this is basically std::lower_bound as used by pbrt */
  int first = 0;
  int count = res_y;

  while (count > 0) {
    int step = count >> 1;
    int middle = first + step;

    if (kernel_tex_fetch(__light_background_marginal_cdf, middle).y < randv) {
      first = middle + 1;
      count -= step + 1;
    }
    else
      count = step;
  }

  int index_v = max(0, first - 1);
  kernel_assert(index_v >= 0 && index_v < res_y);

  float2 cdf_v = kernel_tex_fetch(__light_background_marginal_cdf, index_v);
  float2 cdf_next_v = kernel_tex_fetch(__light_background_marginal_cdf, index_v + 1);
  float2 cdf_last_v = kernel_tex_fetch(__light_background_marginal_cdf, res_y);

  /* importance-sampled V direction */
  float dv = inverse_lerp(cdf_v.y, cdf_next_v.y, randv);
  float v = (index_v + dv) / res_y;

  /* this is basically std::lower_bound as used by pbrt */
  first = 0;
  count = res_x;
  while (count > 0) {
    int step = count >> 1;
    int middle = first + step;

    if (kernel_tex_fetch(__light_background_conditional_cdf, index_v * cdf_width + middle).y <
        randu) {
      first = middle + 1;
      count -= step + 1;
    }
    else
      count = step;
  }

  int index_u = max(0, first - 1);
  kernel_assert(index_u >= 0 && index_u < res_x);

  float2 cdf_u = kernel_tex_fetch(__light_background_conditional_cdf,
                                  index_v * cdf_width + index_u);
  float2 cdf_next_u = kernel_tex_fetch(__light_background_conditional_cdf,
                                       index_v * cdf_width + index_u + 1);
  float2 cdf_last_u = kernel_tex_fetch(__light_background_conditional_cdf,
                                       index_v * cdf_width + res_x);

  /* importance-sampled U direction */
  float du = inverse_lerp(cdf_u.y, cdf_next_u.y, randu);
  float u = (index_u + du) / res_x;

  /* compute pdf */
  float denom = cdf_last_u.x * cdf_last_v.x;
  float sin_theta = sinf(M_PI_F * v);

  if (sin_theta == 0.0f || denom == 0.0f)
    *pdf = 0.0f;
  else
    *pdf = (cdf_u.x * cdf_v.x) / (M_2PI_F * M_PI_F * sin_theta * denom);

  /* compute direction */
  return equirectangular_to_direction(u, v);
}

/* TODO(sergey): Same as above, after the release we should consider using
 * 'noinline' for all devices.
 */
#  ifdef __KERNEL_GPU__
ccl_device_noinline
#  else
ccl_device
#  endif
    float
    background_map_pdf(KernelGlobals *kg, float3 direction)
{
  float2 uv = direction_to_equirectangular(direction);
  int res_x = kernel_data.integrator.pdf_background_res_x;
  int res_y = kernel_data.integrator.pdf_background_res_y;
  int cdf_width = res_x + 1;

  float sin_theta = sinf(uv.y * M_PI_F);

  if (sin_theta == 0.0f)
    return 0.0f;

  int index_u = clamp(float_to_int(uv.x * res_x), 0, res_x - 1);
  int index_v = clamp(float_to_int(uv.y * res_y), 0, res_y - 1);

  /* pdfs in V direction */
  float2 cdf_last_u = kernel_tex_fetch(__light_background_conditional_cdf,
                                       index_v * cdf_width + res_x);
  float2 cdf_last_v = kernel_tex_fetch(__light_background_marginal_cdf, res_y);

  float denom = cdf_last_u.x * cdf_last_v.x;

  if (denom == 0.0f)
    return 0.0f;

  /* pdfs in U direction */
  float2 cdf_u = kernel_tex_fetch(__light_background_conditional_cdf,
                                  index_v * cdf_width + index_u);
  float2 cdf_v = kernel_tex_fetch(__light_background_marginal_cdf, index_v);

  return (cdf_u.x * cdf_v.x) / (M_2PI_F * M_PI_F * sin_theta * denom);
}

ccl_device_inline bool background_portal_data_fetch_and_check_side(
    KernelGlobals *kg, float3 P, int index, float3 *lightpos, float3 *dir)
{
  int portal = kernel_data.integrator.portal_offset + index;
  const ccl_global KernelLight *klight = &kernel_tex_fetch(__lights, portal);

  *lightpos = make_float3(klight->co[0], klight->co[1], klight->co[2]);
  *dir = make_float3(klight->area.dir[0], klight->area.dir[1], klight->area.dir[2]);

  /* Check whether portal is on the right side. */
  if (dot(*dir, P - *lightpos) > 1e-4f)
    return true;

  return false;
}

ccl_device_inline float background_portal_pdf(
    KernelGlobals *kg, float3 P, float3 direction, int ignore_portal, bool *is_possible)
{
  float portal_pdf = 0.0f;

  int num_possible = 0;
  for (int p = 0; p < kernel_data.integrator.num_portals; p++) {
    if (p == ignore_portal)
      continue;

    float3 lightpos, dir;
    if (!background_portal_data_fetch_and_check_side(kg, P, p, &lightpos, &dir))
      continue;

    /* There's a portal that could be sampled from this position. */
    if (is_possible) {
      *is_possible = true;
    }
    num_possible++;

    int portal = kernel_data.integrator.portal_offset + p;
    const ccl_global KernelLight *klight = &kernel_tex_fetch(__lights, portal);
    float3 axisu = make_float3(
        klight->area.axisu[0], klight->area.axisu[1], klight->area.axisu[2]);
    float3 axisv = make_float3(
        klight->area.axisv[0], klight->area.axisv[1], klight->area.axisv[2]);
    bool is_round = (klight->area.invarea < 0.0f);

    if (!ray_quad_intersect(P,
                            direction,
                            1e-4f,
                            FLT_MAX,
                            lightpos,
                            axisu,
                            axisv,
                            dir,
                            NULL,
                            NULL,
                            NULL,
                            NULL,
                            is_round))
      continue;

    if (is_round) {
      float t;
      float3 D = normalize_len(lightpos - P, &t);
      portal_pdf += fabsf(klight->area.invarea) * lamp_light_pdf(kg, dir, -D, t);
    }
    else {
      portal_pdf += rect_light_sample(P, &lightpos, axisu, axisv, 0.0f, 0.0f, false);
    }
  }

  if (ignore_portal >= 0) {
    /* We have skipped a portal that could be sampled as well. */
    num_possible++;
  }

  return (num_possible > 0) ? portal_pdf / num_possible : 0.0f;
}

ccl_device int background_num_possible_portals(KernelGlobals *kg, float3 P)
{
  int num_possible_portals = 0;
  for (int p = 0; p < kernel_data.integrator.num_portals; p++) {
    float3 lightpos, dir;
    if (background_portal_data_fetch_and_check_side(kg, P, p, &lightpos, &dir))
      num_possible_portals++;
  }
  return num_possible_portals;
}

ccl_device float3 background_portal_sample(KernelGlobals *kg,
                                           float3 P,
                                           float randu,
                                           float randv,
                                           int num_possible,
                                           int *sampled_portal,
                                           float *pdf)
{
  /* Pick a portal, then re-normalize randv. */
  randv *= num_possible;
  int portal = (int)randv;
  randv -= portal;

  /* TODO(sergey): Some smarter way of finding portal to sample
   * is welcome.
   */
  for (int p = 0; p < kernel_data.integrator.num_portals; p++) {
    /* Search for the sampled portal. */
    float3 lightpos, dir;
    if (!background_portal_data_fetch_and_check_side(kg, P, p, &lightpos, &dir))
      continue;

    if (portal == 0) {
      /* p is the portal to be sampled. */
      int portal = kernel_data.integrator.portal_offset + p;
      const ccl_global KernelLight *klight = &kernel_tex_fetch(__lights, portal);
      float3 axisu = make_float3(
          klight->area.axisu[0], klight->area.axisu[1], klight->area.axisu[2]);
      float3 axisv = make_float3(
          klight->area.axisv[0], klight->area.axisv[1], klight->area.axisv[2]);
      bool is_round = (klight->area.invarea < 0.0f);

      float3 D;
      if (is_round) {
        lightpos += ellipse_sample(axisu * 0.5f, axisv * 0.5f, randu, randv);
        float t;
        D = normalize_len(lightpos - P, &t);
        *pdf = fabsf(klight->area.invarea) * lamp_light_pdf(kg, dir, -D, t);
      }
      else {
        *pdf = rect_light_sample(P, &lightpos, axisu, axisv, randu, randv, true);
        D = normalize(lightpos - P);
      }

      *pdf /= num_possible;
      *sampled_portal = p;
      return D;
    }

    portal--;
  }

  return make_float3(0.0f, 0.0f, 0.0f);
}

ccl_device_inline float3
background_light_sample(KernelGlobals *kg, float3 P, float randu, float randv, float *pdf)
{
  /* Probability of sampling portals instead of the map. */
  float portal_sampling_pdf = kernel_data.integrator.portal_pdf;

  /* Check if there are portals in the scene which we can sample. */
  if (portal_sampling_pdf > 0.0f) {
    int num_portals = background_num_possible_portals(kg, P);
    if (num_portals > 0) {
      if (portal_sampling_pdf == 1.0f || randu < portal_sampling_pdf) {
        if (portal_sampling_pdf < 1.0f) {
          randu /= portal_sampling_pdf;
        }
        int portal;
        float3 D = background_portal_sample(kg, P, randu, randv, num_portals, &portal, pdf);
        if (num_portals > 1) {
          /* Ignore the chosen portal, its pdf is already included. */
          *pdf += background_portal_pdf(kg, P, D, portal, NULL);
        }
        /* We could also have sampled the map, so combine with MIS. */
        if (portal_sampling_pdf < 1.0f) {
          float cdf_pdf = background_map_pdf(kg, D);
          *pdf = (portal_sampling_pdf * (*pdf) + (1.0f - portal_sampling_pdf) * cdf_pdf);
        }
        return D;
      }
      else {
        /* Sample map, but with nonzero portal_sampling_pdf for MIS. */
        randu = (randu - portal_sampling_pdf) / (1.0f - portal_sampling_pdf);
      }
    }
    else {
      /* We can't sample a portal.
       * Check if we can sample the map instead.
       */
      if (portal_sampling_pdf == 1.0f) {
        /* Use uniform as a fallback if we can't sample the map. */
        *pdf = 1.0f / M_4PI_F;
        return sample_uniform_sphere(randu, randv);
      }
      else {
        portal_sampling_pdf = 0.0f;
      }
    }
  }

  float3 D = background_map_sample(kg, randu, randv, pdf);
  /* Use MIS if portals could be sampled as well. */
  if (portal_sampling_pdf > 0.0f) {
    float portal_pdf = background_portal_pdf(kg, P, D, -1, NULL);
    *pdf = (portal_sampling_pdf * portal_pdf + (1.0f - portal_sampling_pdf) * (*pdf));
  }
  return D;
}

ccl_device float background_light_pdf(KernelGlobals *kg, float3 P, float3 direction)
{
  /* Probability of sampling portals instead of the map. */
  float portal_sampling_pdf = kernel_data.integrator.portal_pdf;

  float portal_pdf = 0.0f, map_pdf = 0.0f;
  if (portal_sampling_pdf > 0.0f) {
    /* Evaluate PDF of sampling this direction by portal sampling. */
    bool is_possible = false;
    portal_pdf = background_portal_pdf(kg, P, direction, -1, &is_possible) * portal_sampling_pdf;
    if (!is_possible) {
      /* Portal sampling is not possible here because all portals point to the wrong side.
       * If map sampling is possible, it would be used instead,
       * otherwise fallback sampling is used. */
      if (portal_sampling_pdf == 1.0f) {
        return kernel_data.integrator.pdf_lights / M_4PI_F;
      }
      else {
        /* Force map sampling. */
        portal_sampling_pdf = 0.0f;
      }
    }
  }
  if (portal_sampling_pdf < 1.0f) {
    /* Evaluate PDF of sampling this direction by map sampling. */
    map_pdf = background_map_pdf(kg, direction) * (1.0f - portal_sampling_pdf);
  }
  return (portal_pdf + map_pdf) * kernel_data.integrator.pdf_lights;
}
#endif

/* Regular Light */

ccl_device_inline bool lamp_light_sample(
    KernelGlobals *kg, int lamp, float randu, float randv, float3 P, LightSample *ls)
{
  const ccl_global KernelLight *klight = &kernel_tex_fetch(__lights, lamp);
  LightType type = (LightType)klight->type;
  ls->type = type;
  ls->shader = klight->shader_id;
  ls->object = PRIM_NONE;
  ls->prim = PRIM_NONE;
  ls->lamp = lamp;
  ls->u = randu;
  ls->v = randv;

  if (type == LIGHT_DISTANT) {
    /* distant light */
    float3 lightD = make_float3(klight->co[0], klight->co[1], klight->co[2]);
    float3 D = lightD;
    float radius = klight->distant.radius;
    float invarea = klight->distant.invarea;

    if (radius > 0.0f)
      D = distant_light_sample(D, radius, randu, randv);

    ls->P = D;
    ls->Ng = D;
    ls->D = -D;
    ls->t = FLT_MAX;

    float costheta = dot(lightD, D);
    ls->pdf = invarea / (costheta * costheta * costheta);
    ls->eval_fac = ls->pdf;
  }
#ifdef __BACKGROUND_MIS__
  else if (type == LIGHT_BACKGROUND) {
    /* infinite area light (e.g. light dome or env light) */
    float3 D = -background_light_sample(kg, P, randu, randv, &ls->pdf);

    ls->P = D;
    ls->Ng = D;
    ls->D = -D;
    ls->t = FLT_MAX;
    ls->eval_fac = 1.0f;
  }
#endif
  else {
    ls->P = make_float3(klight->co[0], klight->co[1], klight->co[2]);

    if (type == LIGHT_POINT || type == LIGHT_SPOT) {
      float radius = klight->spot.radius;

      if (radius > 0.0f)
        /* sphere light */
        ls->P += sphere_light_sample(P, ls->P, radius, randu, randv);

      ls->D = normalize_len(ls->P - P, &ls->t);
      ls->Ng = -ls->D;

      float invarea = klight->spot.invarea;
      ls->eval_fac = (0.25f * M_1_PI_F) * invarea;
      ls->pdf = invarea;

      if (type == LIGHT_SPOT) {
        /* spot light attenuation */
        float3 dir = make_float3(klight->spot.dir[0], klight->spot.dir[1], klight->spot.dir[2]);
        ls->eval_fac *= spot_light_attenuation(
            dir, klight->spot.spot_angle, klight->spot.spot_smooth, ls);
        if (ls->eval_fac == 0.0f) {
          return false;
        }
      }
      float2 uv = map_to_sphere(ls->Ng);
      ls->u = uv.x;
      ls->v = uv.y;

      ls->pdf *= lamp_light_pdf(kg, ls->Ng, -ls->D, ls->t);
    }
    else {
      /* area light */
      float3 axisu = make_float3(
          klight->area.axisu[0], klight->area.axisu[1], klight->area.axisu[2]);
      float3 axisv = make_float3(
          klight->area.axisv[0], klight->area.axisv[1], klight->area.axisv[2]);
      float3 D = make_float3(klight->area.dir[0], klight->area.dir[1], klight->area.dir[2]);
      float invarea = fabsf(klight->area.invarea);
      bool is_round = (klight->area.invarea < 0.0f);

      if (dot(ls->P - P, D) > 0.0f) {
        return false;
      }

      float3 inplane;

      if (is_round) {
        inplane = ellipse_sample(axisu * 0.5f, axisv * 0.5f, randu, randv);
        ls->P += inplane;
        ls->pdf = invarea;
      }
      else {
        inplane = ls->P;
        ls->pdf = rect_light_sample(P, &ls->P, axisu, axisv, randu, randv, true);
        inplane = ls->P - inplane;
      }

      ls->u = dot(inplane, axisu) * (1.0f / dot(axisu, axisu)) + 0.5f;
      ls->v = dot(inplane, axisv) * (1.0f / dot(axisv, axisv)) + 0.5f;

      ls->Ng = D;
      ls->D = normalize_len(ls->P - P, &ls->t);

      ls->eval_fac = 0.25f * invarea;
      if (is_round) {
        ls->pdf *= lamp_light_pdf(kg, D, -ls->D, ls->t);
      }
    }
  }

  ls->pdf *= kernel_data.integrator.pdf_lights;

  return (ls->pdf > 0.0f);
}

ccl_device bool lamp_light_eval(
    KernelGlobals *kg, int lamp, float3 P, float3 D, float t, LightSample *ls)
{
  const ccl_global KernelLight *klight = &kernel_tex_fetch(__lights, lamp);
  LightType type = (LightType)klight->type;
  ls->type = type;
  ls->shader = klight->shader_id;
  ls->object = PRIM_NONE;
  ls->prim = PRIM_NONE;
  ls->lamp = lamp;
  /* todo: missing texture coordinates */
  ls->u = 0.0f;
  ls->v = 0.0f;

  if (!(ls->shader & SHADER_USE_MIS))
    return false;

  if (type == LIGHT_DISTANT) {
    /* distant light */
    float radius = klight->distant.radius;

    if (radius == 0.0f)
      return false;
    if (t != FLT_MAX)
      return false;

    /* a distant light is infinitely far away, but equivalent to a disk
     * shaped light exactly 1 unit away from the current shading point.
     *
     *     radius              t^2/cos(theta)
     *  <---------->           t = sqrt(1^2 + tan(theta)^2)
     *       tan(th)           area = radius*radius*pi
     *       <----->
     *        \    |           (1 + tan(theta)^2)/cos(theta)
     *         \   |           (1 + tan(acos(cos(theta)))^2)/cos(theta)
     *       t  \th| 1         simplifies to
     *           \-|           1/(cos(theta)^3)
     *            \|           magic!
     *             P
     */

    float3 lightD = make_float3(klight->co[0], klight->co[1], klight->co[2]);
    float costheta = dot(-lightD, D);
    float cosangle = klight->distant.cosangle;

    if (costheta < cosangle)
      return false;

    ls->P = -D;
    ls->Ng = -D;
    ls->D = D;
    ls->t = FLT_MAX;

    /* compute pdf */
    float invarea = klight->distant.invarea;
    ls->pdf = invarea / (costheta * costheta * costheta);
    ls->eval_fac = ls->pdf;
  }
  else if (type == LIGHT_POINT || type == LIGHT_SPOT) {
    float3 lightP = make_float3(klight->co[0], klight->co[1], klight->co[2]);

    float radius = klight->spot.radius;

    /* sphere light */
    if (radius == 0.0f)
      return false;

    if (!ray_aligned_disk_intersect(P, D, t, lightP, radius, &ls->P, &ls->t)) {
      return false;
    }

    ls->Ng = -D;
    ls->D = D;

    float invarea = klight->spot.invarea;
    ls->eval_fac = (0.25f * M_1_PI_F) * invarea;
    ls->pdf = invarea;

    if (type == LIGHT_SPOT) {
      /* spot light attenuation */
      float3 dir = make_float3(klight->spot.dir[0], klight->spot.dir[1], klight->spot.dir[2]);
      ls->eval_fac *= spot_light_attenuation(
          dir, klight->spot.spot_angle, klight->spot.spot_smooth, ls);

      if (ls->eval_fac == 0.0f)
        return false;
    }
    float2 uv = map_to_sphere(ls->Ng);
    ls->u = uv.x;
    ls->v = uv.y;

    /* compute pdf */
    if (ls->t != FLT_MAX)
      ls->pdf *= lamp_light_pdf(kg, ls->Ng, -ls->D, ls->t);
  }
  else if (type == LIGHT_AREA) {
    /* area light */
    float invarea = fabsf(klight->area.invarea);
    bool is_round = (klight->area.invarea < 0.0f);
    if (invarea == 0.0f)
      return false;

    float3 axisu = make_float3(
        klight->area.axisu[0], klight->area.axisu[1], klight->area.axisu[2]);
    float3 axisv = make_float3(
        klight->area.axisv[0], klight->area.axisv[1], klight->area.axisv[2]);
    float3 Ng = make_float3(klight->area.dir[0], klight->area.dir[1], klight->area.dir[2]);

    /* one sided */
    if (dot(D, Ng) >= 0.0f)
      return false;

    float3 light_P = make_float3(klight->co[0], klight->co[1], klight->co[2]);

    if (!ray_quad_intersect(
            P, D, 0.0f, t, light_P, axisu, axisv, Ng, &ls->P, &ls->t, &ls->u, &ls->v, is_round)) {
      return false;
    }

    ls->D = D;
    ls->Ng = Ng;
    if (is_round) {
      ls->pdf = invarea * lamp_light_pdf(kg, Ng, -D, ls->t);
    }
    else {
      ls->pdf = rect_light_sample(P, &light_P, axisu, axisv, 0, 0, false);
    }
    ls->eval_fac = 0.25f * invarea;
  }
  else {
    return false;
  }

  ls->pdf *= kernel_data.integrator.pdf_lights;

  return true;
}

/* Triangle Light */

/* returns true if the triangle is has motion blur or an instancing transform applied */
ccl_device_inline bool triangle_world_space_vertices(
    KernelGlobals *kg, int object, int prim, float time, float3 V[3])
{
  bool has_motion = false;
  const int object_flag = kernel_tex_fetch(__object_flag, object);

  if (object_flag & SD_OBJECT_HAS_VERTEX_MOTION && time >= 0.0f) {
    motion_triangle_vertices(kg, object, prim, time, V);
    has_motion = true;
  }
  else {
    triangle_vertices(kg, prim, V);
  }

#ifdef __INSTANCING__
  if (!(object_flag & SD_OBJECT_TRANSFORM_APPLIED)) {
#  ifdef __OBJECT_MOTION__
    float object_time = (time >= 0.0f) ? time : 0.5f;
    Transform tfm = object_fetch_transform_motion_test(kg, object, object_time, NULL);
#  else
    Transform tfm = object_fetch_transform(kg, object, OBJECT_TRANSFORM);
#  endif
    V[0] = transform_point(&tfm, V[0]);
    V[1] = transform_point(&tfm, V[1]);
    V[2] = transform_point(&tfm, V[2]);
    has_motion = true;
  }
#endif
  return has_motion;
}

ccl_device_inline float triangle_light_pdf_area(KernelGlobals *kg,
                                                const float3 Ng,
                                                const float3 I,
                                                float t)
{
  float pdf = kernel_data.integrator.pdf_triangles;
  float cos_pi = fabsf(dot(Ng, I));

  if (cos_pi == 0.0f)
    return 0.0f;

  return t * t * pdf / cos_pi;
}

ccl_device_forceinline float triangle_light_pdf(KernelGlobals *kg, ShaderData *sd, float t)
{
  /* A naive heuristic to decide between costly solid angle sampling
   * and simple area sampling, comparing the distance to the triangle plane
   * to the length of the edges of the triangle. */

  float3 V[3];
  bool has_motion = triangle_world_space_vertices(kg, sd->object, sd->prim, sd->time, V);

  const float3 e0 = V[1] - V[0];
  const float3 e1 = V[2] - V[0];
  const float3 e2 = V[2] - V[1];
  const float longest_edge_squared = max(len_squared(e0), max(len_squared(e1), len_squared(e2)));
  const float3 N = cross(e0, e1);
  const float distance_to_plane = fabsf(dot(N, sd->I * t)) / dot(N, N);

  if (longest_edge_squared > distance_to_plane * distance_to_plane) {
    /* sd contains the point on the light source
     * calculate Px, the point that we're shading */
    const float3 Px = sd->P + sd->I * t;
    const float3 v0_p = V[0] - Px;
    const float3 v1_p = V[1] - Px;
    const float3 v2_p = V[2] - Px;

    const float3 u01 = safe_normalize(cross(v0_p, v1_p));
    const float3 u02 = safe_normalize(cross(v0_p, v2_p));
    const float3 u12 = safe_normalize(cross(v1_p, v2_p));

    const float alpha = fast_acosf(dot(u02, u01));
    const float beta = fast_acosf(-dot(u01, u12));
    const float gamma = fast_acosf(dot(u02, u12));
    const float solid_angle = alpha + beta + gamma - M_PI_F;

    /* pdf_triangles is calculated over triangle area, but we're not sampling over its area */
    if (UNLIKELY(solid_angle == 0.0f)) {
      return 0.0f;
    }
    else {
      float area = 1.0f;
      if (has_motion) {
        /* get the center frame vertices, this is what the PDF was calculated from */
        triangle_world_space_vertices(kg, sd->object, sd->prim, -1.0f, V);
        area = triangle_area(V[0], V[1], V[2]);
      }
      else {
        area = 0.5f * len(N);
      }
      const float pdf = area * kernel_data.integrator.pdf_triangles;
      return pdf / solid_angle;
    }
  }
  else {
    float pdf = triangle_light_pdf_area(kg, sd->Ng, sd->I, t);
    if (has_motion) {
      const float area = 0.5f * len(N);
      if (UNLIKELY(area == 0.0f)) {
        return 0.0f;
      }
      /* scale the PDF.
       * area = the area the sample was taken from
       * area_pre = the are from which pdf_triangles was calculated from */
      triangle_world_space_vertices(kg, sd->object, sd->prim, -1.0f, V);
      const float area_pre = triangle_area(V[0], V[1], V[2]);
      pdf = pdf * area_pre / area;
    }
    return pdf;
  }
}

ccl_device_forceinline void triangle_light_sample(KernelGlobals *kg,
                                                  int prim,
                                                  int object,
                                                  float randu,
                                                  float randv,
                                                  float time,
                                                  LightSample *ls,
                                                  const float3 P)
{
  /* A naive heuristic to decide between costly solid angle sampling
   * and simple area sampling, comparing the distance to the triangle plane
   * to the length of the edges of the triangle. */

  float3 V[3];
  bool has_motion = triangle_world_space_vertices(kg, object, prim, time, V);

  const float3 e0 = V[1] - V[0];
  const float3 e1 = V[2] - V[0];
  const float3 e2 = V[2] - V[1];
  const float longest_edge_squared = max(len_squared(e0), max(len_squared(e1), len_squared(e2)));
  const float3 N0 = cross(e0, e1);
  float Nl = 0.0f;
  ls->Ng = safe_normalize_len(N0, &Nl);
  float area = 0.5f * Nl;

  /* flip normal if necessary */
  const int object_flag = kernel_tex_fetch(__object_flag, object);
  if (object_flag & SD_OBJECT_NEGATIVE_SCALE_APPLIED) {
    ls->Ng = -ls->Ng;
  }
  ls->eval_fac = 1.0f;
  ls->shader = kernel_tex_fetch(__tri_shader, prim);
  ls->object = object;
  ls->prim = prim;
  ls->lamp = LAMP_NONE;
  ls->shader |= SHADER_USE_MIS;
  ls->type = LIGHT_TRIANGLE;

  float distance_to_plane = fabsf(dot(N0, V[0] - P) / dot(N0, N0));

  if (longest_edge_squared > distance_to_plane * distance_to_plane) {
    /* see James Arvo, "Stratified Sampling of Spherical Triangles"
     * http://www.graphics.cornell.edu/pubs/1995/Arv95c.pdf */

    /* project the triangle to the unit sphere
     * and calculate its edges and angles */
    const float3 v0_p = V[0] - P;
    const float3 v1_p = V[1] - P;
    const float3 v2_p = V[2] - P;

    const float3 u01 = safe_normalize(cross(v0_p, v1_p));
    const float3 u02 = safe_normalize(cross(v0_p, v2_p));
    const float3 u12 = safe_normalize(cross(v1_p, v2_p));

    const float3 A = safe_normalize(v0_p);
    const float3 B = safe_normalize(v1_p);
    const float3 C = safe_normalize(v2_p);

    const float cos_alpha = dot(u02, u01);
    const float cos_beta = -dot(u01, u12);
    const float cos_gamma = dot(u02, u12);

    /* calculate dihedral angles */
    const float alpha = fast_acosf(cos_alpha);
    const float beta = fast_acosf(cos_beta);
    const float gamma = fast_acosf(cos_gamma);
    /* the area of the unit spherical triangle = solid angle */
    const float solid_angle = alpha + beta + gamma - M_PI_F;

    /* precompute a few things
     * these could be re-used to take several samples
     * as they are independent of randu/randv */
    const float cos_c = dot(A, B);
    const float sin_alpha = fast_sinf(alpha);
    const float product = sin_alpha * cos_c;

    /* Select a random sub-area of the spherical triangle
     * and calculate the third vertex C_ of that new triangle */
    const float phi = randu * solid_angle - alpha;
    float s, t;
    fast_sincosf(phi, &s, &t);
    const float u = t - cos_alpha;
    const float v = s + product;

    const float3 U = safe_normalize(C - dot(C, A) * A);

    float q = 1.0f;
    const float det = ((v * s + u * t) * sin_alpha);
    if (det != 0.0f) {
      q = ((v * t - u * s) * cos_alpha - v) / det;
    }
    const float temp = max(1.0f - q * q, 0.0f);

    const float3 C_ = safe_normalize(q * A + sqrtf(temp) * U);

    /* Finally, select a random point along the edge of the new triangle
     * That point on the spherical triangle is the sampled ray direction */
    const float z = 1.0f - randv * (1.0f - dot(C_, B));
    ls->D = z * B + safe_sqrtf(1.0f - z * z) * safe_normalize(C_ - dot(C_, B) * B);

    /* calculate intersection with the planar triangle */
    if (!ray_triangle_intersect(P,
                                ls->D,
                                FLT_MAX,
#if defined(__KERNEL_SSE2__) && defined(__KERNEL_SSE__)
                                (ssef *)V,
#else
                                V[0],
                                V[1],
                                V[2],
#endif
                                &ls->u,
                                &ls->v,
                                &ls->t)) {
      ls->pdf = 0.0f;
      return;
    }

    ls->P = P + ls->D * ls->t;

    /* pdf_triangles is calculated over triangle area, but we're sampling over solid angle */
    if (UNLIKELY(solid_angle == 0.0f)) {
      ls->pdf = 0.0f;
      return;
    }
    else {
      if (has_motion) {
        /* get the center frame vertices, this is what the PDF was calculated from */
        triangle_world_space_vertices(kg, object, prim, -1.0f, V);
        area = triangle_area(V[0], V[1], V[2]);
      }
      const float pdf = area * kernel_data.integrator.pdf_triangles;
      ls->pdf = pdf / solid_angle;
    }
  }
  else {
    /* compute random point in triangle */
    randu = sqrtf(randu);

    const float u = 1.0f - randu;
    const float v = randv * randu;
    const float t = 1.0f - u - v;
    ls->P = u * V[0] + v * V[1] + t * V[2];
    /* compute incoming direction, distance and pdf */
    ls->D = normalize_len(ls->P - P, &ls->t);
    ls->pdf = triangle_light_pdf_area(kg, ls->Ng, -ls->D, ls->t);
    if (has_motion && area != 0.0f) {
      /* scale the PDF.
       * area = the area the sample was taken from
       * area_pre = the are from which pdf_triangles was calculated from */
      triangle_world_space_vertices(kg, object, prim, -1.0f, V);
      const float area_pre = triangle_area(V[0], V[1], V[2]);
      ls->pdf = ls->pdf * area_pre / area;
    }
    ls->u = u;
    ls->v = v;
  }
}

/* Light Distribution */

ccl_device int light_distribution_sample(KernelGlobals *kg, float *randu)
{
  /* This is basically std::upper_bound as used by pbrt, to find a point light or
   * triangle to emit from, proportional to area. a good improvement would be to
   * also sample proportional to power, though it's not so well defined with
   * arbitrary shaders. */
  int first = 0;
  int len = kernel_data.integrator.num_distribution + 1;
  float r = *randu;

  while (len > 0) {
    int half_len = len >> 1;
    int middle = first + half_len;

    if (r < kernel_tex_fetch(__light_distribution, middle).totarea) {
      len = half_len;
    }
    else {
      first = middle + 1;
      len = len - half_len - 1;
    }
  }

  /* Clamping should not be needed but float rounding errors seem to
   * make this fail on rare occasions. */
  int index = clamp(first - 1, 0, kernel_data.integrator.num_distribution - 1);

  /* Rescale to reuse random number. this helps the 2D samples within
   * each area light be stratified as well. */
  float distr_min = kernel_tex_fetch(__light_distribution, index).totarea;
  float distr_max = kernel_tex_fetch(__light_distribution, index + 1).totarea;
  *randu = (r - distr_min) / (distr_max - distr_min);

  return index;
}

/* Generic Light */

ccl_device bool light_select_reached_max_bounces(KernelGlobals *kg, int index, int bounce)
{
  return (bounce > kernel_tex_fetch(__lights, index).max_bounces);
}

ccl_device_noinline bool light_sample(
    KernelGlobals *kg, float randu, float randv, float time, float3 P, int bounce, LightSample *ls)
{
  /* sample index */
  int index = light_distribution_sample(kg, &randu);

  /* fetch light data */
  const ccl_global KernelLightDistribution *kdistribution = &kernel_tex_fetch(__light_distribution,
                                                                              index);
  int prim = kdistribution->prim;

  if (prim >= 0) {
    int object = kdistribution->mesh_light.object_id;
    int shader_flag = kdistribution->mesh_light.shader_flag;

    triangle_light_sample(kg, prim, object, randu, randv, time, ls, P);
    ls->shader |= shader_flag;
    return (ls->pdf > 0.0f);
  }
  else {
    int lamp = -prim - 1;

    if (UNLIKELY(light_select_reached_max_bounces(kg, lamp, bounce))) {
      return false;
    }

    return lamp_light_sample(kg, lamp, randu, randv, P, ls);
  }
}

ccl_device int light_select_num_samples(KernelGlobals *kg, int index)
{
  return kernel_tex_fetch(__lights, index).samples;
}

CCL_NAMESPACE_END