area.h

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/* SPDX-FileCopyrightText: 2011-2022 Blender Foundation
 *
 * SPDX-License-Identifier: Apache-2.0 */
 
#pragma once
 
#include "kernel/light/common.h"
 
#include "util/math_intersect.h"
 
CCL_NAMESPACE_BEGIN
 
/* Importance sampling.
 *
 * An Area-Preserving Parametrization for Spherical Rectangles.
 * Carlos Urena et al.
 *
 * NOTE: light_p is modified when sample_coord is true. */
ccl_device_inline float area_light_rect_sample(const float3 P,
                                               ccl_private float3 *light_p,
                                               const float3 axis_u,
                                               const float len_u,
                                               const float3 axis_v,
                                               const float len_v,
                                               const float2 rand,
                                               bool sample_coord)
{
  /* Compute local reference system R. */
  const float3 x = axis_u;
  const float3 y = axis_v;
  float3 z = cross(x, y);
  /* Compute rectangle coords in local reference system. */
  const float3 dir = *light_p - P;
  float z0 = dot(dir, z);
  /* Flip 'z' to make it point against Q. */
  if (z0 > 0.0f) {
    z *= -1.0f;
    z0 *= -1.0f;
  }
  const float xc = dot(dir, x);
  const float yc = dot(dir, y);
  const float x0 = xc - 0.5f * len_u;
  const float x1 = xc + 0.5f * len_u;
  const float y0 = yc - 0.5f * len_v;
  const float y1 = yc + 0.5f * len_v;
  /* Compute predefined constants. */
  float4 nz = make_float4(-y0, x1, y1, -x0);
  nz /= sqrt(nz * nz + z0 * z0);
  /* The original paper uses `acos()` to compute the internal angles here, and then computes the
   * solid angle as their sum minus 2*pi. However, for very small rectangles, this results in
   * excessive cancellation error since the sum will be almost 2*pi as well.
   * This can be avoided by using that `asin(x) = pi/2 - acos(x)`. */
  const float g0 = safe_asinf(-nz.x * nz.y);
  const float g1 = safe_asinf(-nz.y * nz.z);
  const float g2 = safe_asinf(-nz.z * nz.w);
  const float g3 = safe_asinf(-nz.w * nz.x);
  const float S = -(g0 + g1 + g2 + g3);
 
  if (sample_coord) {
    /* Compute predefined constants. */
    const float b0 = nz.x;
    const float b1 = nz.z;
    const float b0sq = b0 * b0;
    /* Compute cu.
     * In the original paper, an additional constant k is involved here. However, just like above,
     * it causes cancellation issues. The same `asin()` terms from above can be used instead, and
     * the extra +pi that would remain in the expression for au can be removed by flipping the sign
     * of cos(au) and sin(au), which also cancels if we flip the sign of b1 in the fu term. */
    const float au = rand.x * S + g2 + g3;
    const float fu = safe_divide(cosf(au) * b0 + b1, sinf(au));
    float cu = copysignf(1.0f / sqrtf(fu * fu + b0sq), fu);
    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. */
    const float d2 = sqr(xu) + sqr(z0);
    const float h0 = y0 / sqrtf(d2 + sqr(y0));
    const float h1 = y1 / sqrtf(d2 + sqr(y1));
    const float hv = h0 + rand.y * (h1 - h0);
    const float hv2 = hv * hv;
    const float yv = (hv2 < 1.0f - 1e-6f) ? hv * sqrtf(d2 / (1.0f - hv2)) : y1;
 
    /* Transform (xu, yv, z0) to world coords. */
    *light_p = P + xu * x + yv * y + z0 * z;
  }
 
  /* return pdf */
  if (S < 1e-5f || reduce_min(sqr(nz)) > 0.99999f) {
    /* The solid angle is too small to be computed accurately in single precision.
     * As a fallback, approximate it using the planar sampling PDF,
     * for such tiny lights the difference is irrelevant.
     *
     * A threshold of 1e-5 was found to be the smallest option that avoids structured
     * artifacts at all tested parameter combinations. The additional check of nz is
     * needed for the case where the light is viewed from grazing angles, see e.g. #98930.
     */
    const float t = len(dir);
    return safe_divide(-t * t * t, (z0 * len_u * len_v));
  }
  return 1.0f / S;
}
 
/* Light spread. */
 
ccl_device float area_light_spread_attenuation(const float3 D,
                                               const float3 lightNg,
                                               const float tan_half_spread,
                                               const float normalize_spread)
{
  /* Model a soft-box grid, computing the ratio of light not hidden by the
   * slats of the grid at a given angle. (see D10594). */
  const float tan_a = tan_angle(-D, lightNg);
 
  if (tan_half_spread == 0.0f) {
    /* The factor M_PI_F comes from integrating the radiance over the hemisphere */
    return (tan_a > 1e-5f) ? 0.0f : M_PI_F;
  }
 
  return max((tan_half_spread - tan_a) * normalize_spread, 0.0f);
}
 
/* Compute the minimal rectangle, circle or ellipse that covers the valid sample region, to reduce
 * noise with low spread. */
ccl_device bool area_light_spread_clamp_light(const float3 P,
                                              const float3 lightNg,
                                              ccl_private float3 *lightP,
                                              ccl_private float3 *axis_u,
                                              ccl_private float *len_u,
                                              ccl_private float3 *axis_v,
                                              ccl_private float *len_v,
                                              const float tan_half_spread,
                                              ccl_private bool *sample_rectangle)
{
  /* Distance from shading point to area light plane and the closest point on that plane. */
  const float t = dot(lightNg, P - *lightP);
  const float3 closest_P = P - t * lightNg;
 
  /* Radius of circle on area light that actually affects the shading point. */
  const float r_spread = t * tan_half_spread;
 
  /* Local uv coordinates of closest point. */
  const float spread_u = dot(*axis_u, closest_P - *lightP);
  const float spread_v = dot(*axis_v, closest_P - *lightP);
 
  const bool is_round = !(*sample_rectangle) && (*len_u == *len_v);
 
  /* Whether we should sample the spread circle. */
  bool sample_spread = (r_spread == 0.0f);
  if (is_round && !sample_spread) {
    /* Distance between the centers of the disk light and the valid region circle. */
    const float dist = len(make_float2(spread_u, spread_v));
 
    /* Radius of the disk light. */
    const float r = *len_u * 0.5f;
 
    if (dist >= r + r_spread) {
      /* Two circles are outside each other or touch externally. */
      return false;
    }
 
    sample_spread = (dist <= fabsf(r - r_spread)) && (r_spread < r);
    if (dist > fabsf(r - r_spread)) {
      /* Two circles intersect. Find the smallest rectangle that covers the intersection */
      const float len_u_ = r + r_spread - dist;
      const float len_v_ = (fabsf(sqr(r) - sqr(r_spread)) >= sqr(dist)) ?
                               2.0f * fminf(r, r_spread) :
                               sqrtf(sqr(2.0f * r_spread) -
                                     sqr(dist + (sqr(r_spread) - sqr(r)) / dist));
 
      const float rect_area = len_u_ * len_v_;
      const float circle_area = M_PI_F * sqr(r);
      const float spread_area = M_PI_F * sqr(r_spread);
 
      /* Sample the shape with minimal area. */
      if (rect_area < fminf(circle_area, spread_area)) {
        *sample_rectangle = true;
        *axis_u = normalize(*lightP - closest_P);
        *axis_v = rotate_around_axis(*axis_u, lightNg, M_PI_2_F);
        *len_u = len_u_;
        *len_v = len_v_;
        *lightP = 0.5f * (*lightP + closest_P + *axis_u * (r_spread - r));
        return true;
      }
 
      sample_spread = (spread_area < circle_area);
    }
  }
  else if (!is_round && !sample_spread) {
    /* Compute rectangle encompassing the circle that affects the shading point,
     * clamped to the bounds of the area light. */
    const float min_u = max(spread_u - r_spread, -*len_u * 0.5f);
    const float max_u = min(spread_u + r_spread, *len_u * 0.5f);
    const float min_v = max(spread_v - r_spread, -*len_v * 0.5f);
    const float max_v = min(spread_v + r_spread, *len_v * 0.5f);
 
    /* Skip if rectangle is empty. */
    if (min_u >= max_u || min_v >= max_v) {
      return false;
    }
 
    const float rect_len_u = max_u - min_u;
    const float rect_len_v = max_v - min_v;
 
    const float rect_area = rect_len_u * rect_len_v;
    const float ellipse_area = (*sample_rectangle) ? FLT_MAX : M_PI_4_F * (*len_u) * (*len_v);
    const float spread_area = M_PI_F * sqr(r_spread);
 
    /* Sample the shape with minimal area. */
    /* NOTE: we don't switch to spread circle sampling for rectangle light because rectangle light
     * supports solid angle sampling, which has less variance than sampling the area. If ellipse
     * area light also supports solid angle sampling, `*sample_rectangle ||` could be deleted. */
    if (*sample_rectangle || rect_area < fminf(ellipse_area, spread_area)) {
      *sample_rectangle = true;
 
      /* Compute new area light center position and axes from rectangle in local
       * uv coordinates. */
      const float new_center_u = 0.5f * (min_u + max_u);
      const float new_center_v = 0.5f * (min_v + max_v);
 
      *len_u = rect_len_u;
      *len_v = rect_len_v;
      *lightP = *lightP + *axis_u * new_center_u + *axis_v * new_center_v;
      return true;
    }
    *sample_rectangle = false;
    sample_spread = (spread_area < ellipse_area);
  }
 
  if (sample_spread) {
    *sample_rectangle = false;
    *lightP = *lightP + *axis_u * spread_u + *axis_v * spread_v;
    *len_u = r_spread * 2.0f;
    *len_v = r_spread * 2.0f;
    return true;
  }
 
  /* Don't clamp. */
  return true;
}
 
ccl_device_forceinline bool area_light_is_ellipse(const ccl_global KernelAreaLight *light)
{
  return light->invarea < 0.0f;
}
 
/* Common API. */
/* Compute `eval_fac` and `pdf`. Also sample a new position on the light if `sample_coord`. */
template<bool in_volume_segment>
ccl_device_inline bool area_light_eval(const ccl_global KernelLight *klight,
                                       const float3 ray_P,
                                       ccl_private float3 *light_P,
                                       ccl_private LightSample *ccl_restrict ls,
                                       const float2 rand,
                                       bool sample_coord)
{
  float3 axis_u = klight->area.axis_u;
  float3 axis_v = klight->area.axis_v;
  float len_u = klight->area.len_u;
  float len_v = klight->area.len_v;
 
  const float3 Ng = klight->area.dir;
  const float invarea = fabsf(klight->area.invarea);
  bool sample_rectangle = (klight->area.invarea > 0.0f);
 
  float3 light_P_new = *light_P;
 
  if (in_volume_segment) {
    light_P_new += sample_rectangle ?
                       rectangle_sample(axis_u * len_u * 0.5f, axis_v * len_v * 0.5f, rand) :
                       ellipse_sample(axis_u * len_u * 0.5f, axis_v * len_v * 0.5f, rand);
    ls->pdf = invarea;
  }
  else {
    if (klight->area.normalize_spread > 0) {
      if (!area_light_spread_clamp_light(ray_P,
                                         Ng,
                                         &light_P_new,
                                         &axis_u,
                                         &len_u,
                                         &axis_v,
                                         &len_v,
                                         klight->area.tan_half_spread,
                                         &sample_rectangle))
      {
        return false;
      }
    }
 
    if (sample_rectangle) {
      ls->pdf = area_light_rect_sample(
          ray_P, &light_P_new, axis_u, len_u, axis_v, len_v, rand, sample_coord);
    }
    else {
      if (klight->area.tan_half_spread == 0.0f) {
        ls->pdf = 1.0f;
      }
      else {
        if (sample_coord) {
          light_P_new += ellipse_sample(axis_u * len_u * 0.5f, axis_v * len_v * 0.5f, rand);
        }
        ls->pdf = 4.0f * M_1_PI_F / (len_u * len_v);
      }
    }
  }
 
  if (sample_coord) {
    *light_P = light_P_new;
    ls->D = safe_normalize_len(*light_P - ray_P, &ls->t);
  }
 
  /* Convert radiant flux to radiance. */
  ls->eval_fac = M_1_PI_F * invarea;
 
  if (klight->area.normalize_spread > 0) {
    /* Area Light spread angle attenuation */
    ls->eval_fac *= area_light_spread_attenuation(
        ls->D, Ng, klight->area.tan_half_spread, klight->area.normalize_spread);
  }
 
  if (in_volume_segment || (!sample_rectangle && klight->area.tan_half_spread > 0)) {
    ls->pdf *= light_pdf_area_to_solid_angle(Ng, -ls->D, ls->t);
  }
 
  return in_volume_segment || ls->eval_fac > 0;
}
 
template<bool in_volume_segment>
ccl_device_inline bool area_light_sample(const ccl_global KernelLight *klight,
                                         const float2 rand,
                                         const float3 P,
                                         ccl_private LightSample *ls)
{
  ls->P = klight->co;
  ls->Ng = klight->area.dir;
 
  if (!in_volume_segment) {
    if (dot(ls->P - P, ls->Ng) > 0.0f) {
      return false;
    }
  }
 
  if (!area_light_eval<in_volume_segment>(klight, P, &ls->P, ls, rand, true)) {
    return false;
  }
 
  const float3 inplane = ls->P - klight->co;
  float light_u = dot(inplane, klight->area.axis_u);
  float light_v = dot(inplane, klight->area.axis_v);
 
  if (!in_volume_segment && klight->area.normalize_spread > 0) {
    const bool is_ellipse = area_light_is_ellipse(&klight->area);
 
    /* Check whether the sampled point lies outside of the area light.
     * For very small area lights, numerical issues can cause this to be
     * slightly off since the sampling logic clamps the result right at the border,
     * so allow for a small margin of error. */
    const float len_u_epsilon = ((0.5f + 1e-7f) * klight->area.len_u + 1e-6f);
    const float len_v_epsilon = ((0.5f + 1e-7f) * klight->area.len_v + 1e-6f);
    if (is_ellipse && (sqr(light_u / len_u_epsilon) + sqr(light_v / len_v_epsilon) > 1.0f)) {
      return false;
    }
    if (!is_ellipse && (fabsf(light_u) > len_u_epsilon || fabsf(light_v) > len_v_epsilon)) {
      return false;
    }
  }
 
  light_u /= klight->area.len_u;
  light_v /= klight->area.len_v;
 
  /* NOTE: Return barycentric coordinates in the same notation as Embree and OptiX. */
  ls->u = light_v + 0.5f;
  ls->v = -light_u - light_v;
 
  return true;
}
 
ccl_device_forceinline void area_light_mnee_sample_update(const ccl_global KernelLight *klight,
                                                          ccl_private LightSample *ls,
                                                          const float3 P)
{
  if (klight->area.tan_half_spread == 0) {
    /* Update position on the light to keep the direction fixed. */
    area_light_eval<false>(klight, P, &ls->P, ls, zero_float2(), true);
  }
  else {
    ls->D = safe_normalize_len(ls->P - P, &ls->t);
    area_light_eval<false>(klight, P, &ls->P, ls, zero_float2(), false);
    /* Convert pdf to be in area measure. */
    ls->pdf /= light_pdf_area_to_solid_angle(ls->Ng, -ls->D, ls->t);
  }
}
 
ccl_device_inline bool area_light_intersect(const ccl_global KernelLight *klight,
                                            const ccl_private Ray *ccl_restrict ray,
                                            ccl_private float *t,
                                            ccl_private float *u,
                                            ccl_private float *v)
{
  /* Area light. */
  const float invarea = fabsf(klight->area.invarea);
  const bool is_ellipse = area_light_is_ellipse(&klight->area);
  if (invarea == 0.0f) {
    return false;
  }
 
  const float3 inv_extent_u = klight->area.axis_u / klight->area.len_u;
  const float3 inv_extent_v = klight->area.axis_v / klight->area.len_v;
  const float3 Ng = klight->area.dir;
 
  /* One sided. */
  if (dot(ray->D, Ng) >= 0.0f) {
    return false;
  }
 
  const float3 light_P = klight->co;
 
  float3 P;
  return ray_quad_intersect(ray->P,
                            ray->D,
                            ray->tmin,
                            ray->tmax,
                            light_P,
                            inv_extent_u,
                            inv_extent_v,
                            Ng,
                            &P,
                            t,
                            u,
                            v,
                            is_ellipse);
}
 
ccl_device_inline bool area_light_sample_from_intersection(
    const ccl_global KernelLight *klight,
    const ccl_private Intersection *ccl_restrict isect,
    const float3 ray_P,
    const float3 ray_D,
    ccl_private LightSample *ccl_restrict ls)
{
  ls->u = isect->u;
  ls->v = isect->v;
  ls->D = ray_D;
  ls->Ng = klight->area.dir;
 
  float3 light_P = klight->co;
  return area_light_eval<false>(klight, ray_P, &light_P, ls, zero_float2(), false);
}
 
/* Returns the maximal distance between the light center and the boundary. */
ccl_device_forceinline float area_light_max_extent(const ccl_global KernelAreaLight *light)
{
  return 0.5f * (area_light_is_ellipse(light) ? fmaxf(light->len_u, light->len_v) :
                                                len(make_float2(light->len_u, light->len_v)));
}
 
/* Find the ray segment lit by the area light. */
ccl_device_inline bool area_light_valid_ray_segment(const ccl_global KernelAreaLight *light,
                                                    float3 P,
                                                    float3 D,
                                                    ccl_private Interval<float> *t_range)
{
  bool valid;
  const float tan_half_spread = light->tan_half_spread;
  float3 axis = light->dir;
 
  const bool angle_almost_zero = (tan_half_spread < 1e-5f);
  if (angle_almost_zero) {
    /* Map to local coordinate of the light. Do not use `itfm` in `KernelLight` as there might be
     * additional scaling in the light size. */
    const Transform tfm = make_transform(light->axis_u, light->axis_v, axis);
    P = transform_point(&tfm, P);
    D = transform_direction(&tfm, D);
    axis = make_float3(0.0f, 0.0f, 1.0f);
 
    const float half_len_u = 0.5f * light->len_u;
    const float half_len_v = 0.5f * light->len_v;
    if (area_light_is_ellipse(light)) {
      valid = ray_infinite_cylinder_intersect(P, D, half_len_u, half_len_v, t_range);
    }
    else {
      const float3 bbox_min = make_float3(-half_len_u, -half_len_v, 0.0f);
      const float3 bbox_max = make_float3(half_len_u, half_len_v, FLT_MAX);
      valid = ray_aabb_intersect(bbox_min, bbox_max, P, D, t_range);
    }
  }
  else {
    /* Conservative estimation with the smallest possible cone covering the whole spread. */
    const float3 apex_to_point = P + area_light_max_extent(light) / tan_half_spread * axis;
    const float cos_angle_sq = 1.0f / (1.0f + sqr(tan_half_spread));
 
    valid = ray_cone_intersect(axis, apex_to_point, D, cos_angle_sq, t_range);
  }
 
  /* Limit the range to the positive side of the area light. */
  return valid && ray_plane_intersect(axis, P, D, t_range);
}
 
template<bool in_volume_segment>
ccl_device_forceinline bool area_light_tree_parameters(const ccl_global KernelLight *klight,
                                                       const float3 centroid,
                                                       const float3 P,
                                                       const float3 N,
                                                       const float3 bcone_axis,
                                                       ccl_private float &cos_theta_u,
                                                       ccl_private float2 &distance,
                                                       ccl_private float3 &point_to_centroid)
{
  /* TODO: a cheap substitute for minimal distance between point and primitive. Does it worth the
   * overhead to compute the accurate minimal distance? */
  float min_distance;
  point_to_centroid = safe_normalize_len(centroid - P, &min_distance);
  distance = make_float2(min_distance, min_distance);
 
  cos_theta_u = FLT_MAX;
 
  const float3 extentu = klight->area.axis_u * klight->area.len_u;
  const float3 extentv = klight->area.axis_v * klight->area.len_v;
  for (int i = 0; i < 4; i++) {
    const float3 corner = ((i & 1) - 0.5f) * extentu + 0.5f * ((i & 2) - 1) * extentv + centroid;
    float distance_point_to_corner;
    const float3 point_to_corner = safe_normalize_len(corner - P, &distance_point_to_corner);
    cos_theta_u = fminf(cos_theta_u, dot(point_to_centroid, point_to_corner));
    if (!in_volume_segment) {
      distance.x = fmaxf(distance.x, distance_point_to_corner);
    }
  }
 
  const bool front_facing = dot(bcone_axis, point_to_centroid) < 0;
  const bool shape_above_surface = dot(N, centroid - P) + fabsf(dot(N, extentu)) +
                                       fabsf(dot(N, extentv)) >
                                   0;
 
  return front_facing && shape_above_surface;
}
 
CCL_NAMESPACE_END