blender/intern/cycles/kernel/light/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.
 */

#pragma once

#include "kernel/geom/geom.h"
#include "kernel/light/light_background.h"
#include "kernel/sample/sample_mapping.h"

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;

/* Regular Light */

template<bool in_volume_segment>
ccl_device_inline bool light_sample(KernelGlobals kg,
                                    const int lamp,
                                    const float randu,
                                    const float randv,
                                    const float3 P,
                                    const uint32_t path_flag,
                                    ccl_private LightSample *ls)
{
  const ccl_global KernelLight *klight = &kernel_tex_fetch(__lights, lamp);
  if (path_flag & PATH_RAY_SHADOW_CATCHER_PASS) {
    if (klight->shader_id & SHADER_EXCLUDE_SHADOW_CATCHER) {
      return false;
    }
  }

  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 (in_volume_segment && (type == LIGHT_DISTANT || type == LIGHT_BACKGROUND)) {
    /* Distant lights in a volume get a dummy sample, position will not actually
     * be used in that case. Only when sampling from a specific scatter position
     * do we actually need to evaluate these. */
    ls->P = zero_float3();
    ls->Ng = zero_float3();
    ls->D = zero_float3();
    ls->pdf = true;
    ls->t = FLT_MAX;
    return true;
  }

  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->Ng);
        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 Ng = 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 (!in_volume_segment) {
        if (dot(ls->P - P, Ng) > 0.0f) {
          return false;
        }
      }

      float3 inplane;

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

        float3 sample_axisu = axisu;
        float3 sample_axisv = axisv;

        if (klight->area.tan_spread > 0.0f) {
          if (!light_spread_clamp_area_light(
                  P, Ng, &ls->P, &sample_axisu, &sample_axisv, klight->area.tan_spread)) {
            return false;
          }
        }

        ls->pdf = rect_light_sample(P, &ls->P, sample_axisu, sample_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 = Ng;
      ls->D = normalize_len(ls->P - P, &ls->t);

      ls->eval_fac = 0.25f * invarea;

      if (klight->area.tan_spread > 0.0f) {
        /* Area Light spread angle attenuation */
        ls->eval_fac *= light_spread_attenuation(
            ls->D, ls->Ng, klight->area.tan_spread, klight->area.normalize_spread);
      }

      if (is_round) {
        ls->pdf *= lamp_light_pdf(kg, Ng, -ls->D, ls->t);
      }
    }
  }

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

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

ccl_device bool lights_intersect(KernelGlobals kg,
                                 ccl_private const Ray *ccl_restrict ray,
                                 ccl_private Intersection *ccl_restrict isect,
                                 const int last_prim,
                                 const int last_object,
                                 const int last_type,
                                 const uint32_t path_flag)
{
  for (int lamp = 0; lamp < kernel_data.integrator.num_all_lights; lamp++) {
    const ccl_global KernelLight *klight = &kernel_tex_fetch(__lights, lamp);

    if (path_flag & PATH_RAY_CAMERA) {
      if (klight->shader_id & SHADER_EXCLUDE_CAMERA) {
        continue;
      }
    }
    else {
      if (!(klight->shader_id & SHADER_USE_MIS)) {
        continue;
      }
    }

    if (path_flag & PATH_RAY_SHADOW_CATCHER_PASS) {
      if (klight->shader_id & SHADER_EXCLUDE_SHADOW_CATCHER) {
        continue;
      }
    }

    LightType type = (LightType)klight->type;
    float t = 0.0f, u = 0.0f, v = 0.0f;

    if (type == LIGHT_POINT || type == LIGHT_SPOT) {
      /* Sphere light. */
      const float3 lightP = make_float3(klight->co[0], klight->co[1], klight->co[2]);
      const float radius = klight->spot.radius;
      if (radius == 0.0f) {
        continue;
      }

      float3 P;
      if (!ray_aligned_disk_intersect(ray->P, ray->D, ray->t, lightP, radius, &P, &t)) {
        continue;
      }
    }
    else if (type == LIGHT_AREA) {
      /* Area light. */
      const float invarea = fabsf(klight->area.invarea);
      const bool is_round = (klight->area.invarea < 0.0f);
      if (invarea == 0.0f) {
        continue;
      }

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

      /* One sided. */
      if (dot(ray->D, Ng) >= 0.0f) {
        continue;
      }

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

      float3 P;
      if (!ray_quad_intersect(
              ray->P, ray->D, 0.0f, ray->t, light_P, axisu, axisv, Ng, &P, &t, &u, &v, is_round)) {
        continue;
      }
    }
    else {
      continue;
    }

    if (t < isect->t &&
        !(last_prim == lamp && last_object == OBJECT_NONE && last_type == PRIMITIVE_LAMP)) {
      isect->t = t;
      isect->u = u;
      isect->v = v;
      isect->type = PRIMITIVE_LAMP;
      isect->prim = lamp;
      isect->object = OBJECT_NONE;
    }
  }

  return isect->prim != PRIM_NONE;
}

ccl_device bool light_sample_from_distant_ray(KernelGlobals kg,
                                              const float3 ray_D,
                                              const int lamp,
                                              ccl_private LightSample *ccl_restrict ls)
{
  ccl_global const KernelLight *klight = &kernel_tex_fetch(__lights, lamp);
  const int shader = klight->shader_id;
  const float radius = klight->distant.radius;
  const LightType type = (LightType)klight->type;

  if (type != LIGHT_DISTANT) {
    return false;
  }
  if (!(shader & SHADER_USE_MIS)) {
    return false;
  }
  if (radius == 0.0f) {
    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, ray_D);
  float cosangle = klight->distant.cosangle;

  if (costheta < cosangle)
    return false;

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

  /* compute pdf */
  float invarea = klight->distant.invarea;
  ls->pdf = invarea / (costheta * costheta * costheta);
  ls->pdf *= kernel_data.integrator.pdf_lights;
  ls->eval_fac = ls->pdf;

  return true;
}

ccl_device bool light_sample_from_intersection(KernelGlobals kg,
                                               ccl_private const Intersection *ccl_restrict isect,
                                               const float3 ray_P,
                                               const float3 ray_D,
                                               ccl_private LightSample *ccl_restrict ls)
{
  const int lamp = isect->prim;
  ccl_global const 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->t = isect->t;
  ls->P = ray_P + ray_D * ls->t;
  ls->D = ray_D;

  if (type == LIGHT_POINT || type == LIGHT_SPOT) {
    ls->Ng = -ray_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->Ng);

      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);

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

    ls->u = isect->u;
    ls->v = isect->v;
    ls->D = ray_D;
    ls->Ng = Ng;

    const bool is_round = (klight->area.invarea < 0.0f);
    if (is_round) {
      ls->pdf = invarea * lamp_light_pdf(kg, Ng, -ray_D, ls->t);
    }
    else {
      float3 sample_axisu = axisu;
      float3 sample_axisv = axisv;

      if (klight->area.tan_spread > 0.0f) {
        if (!light_spread_clamp_area_light(
                ray_P, Ng, &light_P, &sample_axisu, &sample_axisv, klight->area.tan_spread)) {
          return false;
        }
      }

      ls->pdf = rect_light_sample(ray_P, &light_P, sample_axisu, sample_axisv, 0, 0, false);
    }
    ls->eval_fac = 0.25f * invarea;

    if (klight->area.tan_spread > 0.0f) {
      /* Area Light spread angle attenuation */
      ls->eval_fac *= light_spread_attenuation(
          ls->D, ls->Ng, klight->area.tan_spread, klight->area.normalize_spread);
      if (ls->eval_fac == 0.0f) {
        return false;
      }
    }
  }
  else {
    kernel_assert(!"Invalid lamp type in light_sample_from_intersection");
    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);
  }

  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;
  }
  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,
                                                ccl_private const 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;
  }
}

template<bool in_volume_segment>
ccl_device_forceinline void triangle_light_sample(KernelGlobals kg,
                                                  int prim,
                                                  int object,
                                                  float randu,
                                                  float randv,
                                                  float time,
                                                  ccl_private 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 (!in_volume_segment && (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. From Eric Heitz's "A Low-Distortion Map Between Triangle
     * and Square" */
    float u = randu;
    float v = randv;
    if (v > u) {
      u *= 0.5f;
      v -= u;
    }
    else {
      v *= 0.5f;
      u -= v;
    }

    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, ccl_private 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;

  do {
    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;
    }
  } while (len > 0);

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

template<bool in_volume_segment>
ccl_device_noinline bool light_distribution_sample(KernelGlobals kg,
                                                   float randu,
                                                   const float randv,
                                                   const float time,
                                                   const float3 P,
                                                   const int bounce,
                                                   const uint32_t path_flag,
                                                   ccl_private LightSample *ls)
{
  /* Sample light index from distribution. */
  const int index = light_distribution_sample(kg, &randu);
  ccl_global const KernelLightDistribution *kdistribution = &kernel_tex_fetch(__light_distribution,
                                                                              index);
  const int prim = kdistribution->prim;

  if (prim >= 0) {
    /* Mesh light. */
    const int object = kdistribution->mesh_light.object_id;

    /* Exclude synthetic meshes from shadow catcher pass. */
    if ((path_flag & PATH_RAY_SHADOW_CATCHER_PASS) &&
        !(kernel_tex_fetch(__object_flag, object) & SD_OBJECT_SHADOW_CATCHER)) {
      return false;
    }

    const int shader_flag = kdistribution->mesh_light.shader_flag;
    triangle_light_sample<in_volume_segment>(kg, prim, object, randu, randv, time, ls, P);
    ls->shader |= shader_flag;
    return (ls->pdf > 0.0f);
  }

  const int lamp = -prim - 1;

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

  return light_sample<in_volume_segment>(kg, lamp, randu, randv, P, path_flag, ls);
}

ccl_device_inline bool light_distribution_sample_from_volume_segment(KernelGlobals kg,
                                                                     float randu,
                                                                     const float randv,
                                                                     const float time,
                                                                     const float3 P,
                                                                     const int bounce,
                                                                     const uint32_t path_flag,
                                                                     ccl_private LightSample *ls)
{
  return light_distribution_sample<true>(kg, randu, randv, time, P, bounce, path_flag, ls);
}

ccl_device_inline bool light_distribution_sample_from_position(KernelGlobals kg,
                                                               float randu,
                                                               const float randv,
                                                               const float time,
                                                               const float3 P,
                                                               const int bounce,
                                                               const uint32_t path_flag,
                                                               ccl_private LightSample *ls)
{
  return light_distribution_sample<false>(kg, randu, randv, time, P, bounce, path_flag, ls);
}

ccl_device_inline bool light_distribution_sample_new_position(KernelGlobals kg,
                                                              const float randu,
                                                              const float randv,
                                                              const float time,
                                                              const float3 P,
                                                              ccl_private LightSample *ls)
{
  /* Sample a new position on the same light, for volume sampling. */
  if (ls->type == LIGHT_TRIANGLE) {
    triangle_light_sample<false>(kg, ls->prim, ls->object, randu, randv, time, ls, P);
    return (ls->pdf > 0.0f);
  }
  else {
    return light_sample<false>(kg, ls->lamp, randu, randv, P, 0, ls);
  }
}

CCL_NAMESPACE_END