cycles/kernel/camera/projection.h

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/* SPDX-FileCopyrightText: 2009-2010 Sony Pictures Imageworks Inc., et al.
 * SPDX-FileCopyrightText: 2011-2022 Blender Foundation
 *
 * SPDX-License-Identifier: BSD-3-Clause
 *
 * Adapted code from Open Shading Language. */
 
#pragma once
 
#include "util/math.h"
#include "util/types.h"
 
CCL_NAMESPACE_BEGIN
 
/* Spherical coordinates <-> Cartesian direction. */
 
ccl_device float2 direction_to_spherical(float3 dir)
{
  float theta = safe_acosf(dir.z);
  float phi = atan2f(dir.x, dir.y);
 
  return make_float2(theta, phi);
}
 
ccl_device float3 spherical_to_direction(float theta, float phi)
{
  float sin_theta = sinf(theta);
  return make_float3(sin_theta * sinf(phi), sin_theta * cosf(phi), cosf(theta));
}
 
/* Equirectangular coordinates <-> Cartesian direction */
 
ccl_device float2 direction_to_equirectangular_range(float3 dir, float4 range)
{
  if (is_zero(dir))
    return zero_float2();
 
  float u = (atan2f(dir.y, dir.x) - range.y) / range.x;
  float v = (acosf(dir.z / len(dir)) - range.w) / range.z;
 
  return make_float2(u, v);
}
 
ccl_device float3 equirectangular_range_to_direction(float u, float v, float4 range)
{
  float phi = range.x * u + range.y;
  float theta = range.z * v + range.w;
  float sin_theta = sinf(theta);
  return make_float3(sin_theta * cosf(phi), sin_theta * sinf(phi), cosf(theta));
}
 
ccl_device float2 direction_to_equirectangular(float3 dir)
{
  return direction_to_equirectangular_range(dir, make_float4(-M_2PI_F, M_PI_F, -M_PI_F, M_PI_F));
}
 
ccl_device float3 equirectangular_to_direction(float u, float v)
{
  return equirectangular_range_to_direction(u, v, make_float4(-M_2PI_F, M_PI_F, -M_PI_F, M_PI_F));
}
 
ccl_device float2 direction_to_central_cylindrical(float3 dir, float4 range)
{
  const float z = dir.z / len(make_float2(dir.x, dir.y));
  const float theta = atan2f(dir.y, dir.x);
  const float u = inverse_lerp(range.x, range.y, theta);
  const float v = inverse_lerp(range.z, range.w, z);
  return make_float2(u, v);
}
 
ccl_device float3 central_cylindrical_to_direction(float u, float v, float4 range)
{
  const float theta = mix(range.x, range.y, u);
  const float z = mix(range.z, range.w, v);
  return make_float3(cosf(theta), sinf(theta), z);
}
 
/* Fisheye <-> Cartesian direction */
 
ccl_device float2 direction_to_fisheye(float3 dir, float fov)
{
  const float r = atan2f(len(make_float2(dir.y, dir.z)), dir.x) / fov;
  const float2 uv = r * safe_normalize(make_float2(dir.y, dir.z));
  return make_float2(0.5f - uv.x, uv.y + 0.5f);
}
 
ccl_device float3 fisheye_to_direction(float u, float v, float fov)
{
  u = (u - 0.5f) * 2.0f;
  v = (v - 0.5f) * 2.0f;
 
  float r = sqrtf(u * u + v * v);
 
  if (r > 1.0f)
    return zero_float3();
 
  float phi = safe_acosf((r != 0.0f) ? u / r : 0.0f);
  float theta = r * fov * 0.5f;
 
  if (v < 0.0f)
    phi = -phi;
 
  return make_float3(cosf(theta), -cosf(phi) * sinf(theta), sinf(phi) * sinf(theta));
}
 
ccl_device float2 direction_to_fisheye_equisolid(float3 dir, float lens, float width, float height)
{
  const float theta = safe_acosf(dir.x);
  const float r = 2.0f * lens * sinf(theta * 0.5f);
 
  const float2 uv = r * safe_normalize(make_float2(dir.y, dir.z));
  return make_float2(0.5f - uv.x / width, uv.y / height + 0.5f);
}
 
ccl_device_inline float3
fisheye_equisolid_to_direction(float u, float v, float lens, float fov, float width, float height)
{
  u = (u - 0.5f) * width;
  v = (v - 0.5f) * height;
 
  float rmax = 2.0f * lens * sinf(fov * 0.25f);
  float r = sqrtf(u * u + v * v);
 
  if (r > rmax)
    return zero_float3();
 
  float phi = safe_acosf((r != 0.0f) ? u / r : 0.0f);
  float theta = 2.0f * asinf(r / (2.0f * lens));
 
  if (v < 0.0f)
    phi = -phi;
 
  return make_float3(cosf(theta), -cosf(phi) * sinf(theta), sinf(phi) * sinf(theta));
}
 
ccl_device_inline float3 fisheye_lens_polynomial_to_direction(
    float u, float v, float coeff0, float4 coeffs, float fov, float width, float height)
{
  u = (u - 0.5f) * width;
  v = (v - 0.5f) * height;
 
  float r = sqrtf(u * u + v * v);
  float r2 = r * r;
  float4 rr = make_float4(r, r2, r2 * r, r2 * r2);
  float theta = -(coeff0 + dot(coeffs, rr));
 
  if (fabsf(theta) > 0.5f * fov)
    return zero_float3();
 
  float phi = safe_acosf((r != 0.0f) ? u / r : 0.0f);
 
  if (v < 0.0f)
    phi = -phi;
 
  return make_float3(cosf(theta), -cosf(phi) * sinf(theta), sinf(phi) * sinf(theta));
}
 
ccl_device float2 direction_to_fisheye_lens_polynomial(
    float3 dir, float coeff0, float4 coeffs, float width, float height)
{
  const float theta = -safe_acosf(dir.x);
 
  /* Initialize r with the closed-form solution for the special case
   * coeffs.y = coeffs.z = coeffs.w = 0 */
  float r = (theta - coeff0) / coeffs.x;
 
  const float4 diff_coeffs = make_float4(1.0f, 2.0f, 3.0f, 4.0f) * coeffs;
 
  for (int i = 0; i < 20; i++) {
    /*  Newton's method for finding roots
     *
     *  Given is the result theta = distortion_model(r),
     *  we need to find r.
     *  Let F(r) := theta - distortion_model(r).
     *  Then F(r) = 0 <=> distortion_model(r) = theta
     *  Therefore we apply Newton's method for finding a root of F(r).
     *  Newton step for the function F:
     *  r_n+1 = r_n - F(r_n) / F'(r_n)
     *  The addition in the implementation is due to canceling of signs.
     * \{ */
    const float old_r = r, r2 = r * r;
    const float F_r = theta - (coeff0 + dot(coeffs, make_float4(r, r2, r2 * r, r2 * r2)));
    const float dF_r = dot(diff_coeffs, make_float4(1.0f, r, r2, r2 * r));
    r += F_r / dF_r;
 
    /* Early termination if the change is below the threshold */
    if (fabsf(r - old_r) < 1e-6f) {
      break;
    }
  }
 
  const float2 uv = r * safe_normalize(make_float2(dir.y, dir.z));
  return make_float2(0.5f - uv.x / width, uv.y / height + 0.5f);
}
 
/* Mirror Ball <-> Cartesion direction */
 
ccl_device float3 mirrorball_to_direction(float u, float v)
{
  /* point on sphere */
  float3 dir;
 
  dir.x = 2.0f * u - 1.0f;
  dir.z = 2.0f * v - 1.0f;
 
  if (dir.x * dir.x + dir.z * dir.z > 1.0f)
    return zero_float3();
 
  dir.y = -sqrtf(max(1.0f - dir.x * dir.x - dir.z * dir.z, 0.0f));
 
  /* reflection */
  float3 I = make_float3(0.0f, -1.0f, 0.0f);
 
  return 2.0f * dot(dir, I) * dir - I;
}
 
ccl_device float2 direction_to_mirrorball(float3 dir)
{
  /* inverse of mirrorball_to_direction */
  dir.y -= 1.0f;
 
  float div = 2.0f * sqrtf(max(-0.5f * dir.y, 0.0f));
  if (div > 0.0f)
    dir /= div;
 
  float u = 0.5f * (dir.x + 1.0f);
  float v = 0.5f * (dir.z + 1.0f);
 
  return make_float2(u, v);
}
 
/* Single face of a equiangular cube map projection as described in
 * https://blog.google/products/google-ar-vr/bringing-pixels-front-and-center-vr-video/ */
ccl_device float3 equiangular_cubemap_face_to_direction(float u, float v)
{
  u = tanf((0.5f - u) * M_PI_2_F);
  v = tanf((v - 0.5f) * M_PI_2_F);
 
  return normalize(make_float3(1.0f, u, v));
}
 
ccl_device float2 direction_to_equiangular_cubemap_face(float3 dir)
{
  float u = 0.5f - atan2f(dir.y, dir.x) * 2.0f / M_PI_F;
  float v = atan2f(dir.z, dir.x) * 2.0f / M_PI_F + 0.5f;
 
  return make_float2(u, v);
}
 
ccl_device_inline float3 panorama_to_direction(ccl_constant KernelCamera *cam, float u, float v)
{
  switch (cam->panorama_type) {
    case PANORAMA_EQUIRECTANGULAR:
      return equirectangular_range_to_direction(u, v, cam->equirectangular_range);
    case PANORAMA_EQUIANGULAR_CUBEMAP_FACE:
      return equiangular_cubemap_face_to_direction(u, v);
    case PANORAMA_MIRRORBALL:
      return mirrorball_to_direction(u, v);
    case PANORAMA_FISHEYE_EQUIDISTANT:
      return fisheye_to_direction(u, v, cam->fisheye_fov);
    case PANORAMA_FISHEYE_LENS_POLYNOMIAL:
      return fisheye_lens_polynomial_to_direction(u,
                                                  v,
                                                  cam->fisheye_lens_polynomial_bias,
                                                  cam->fisheye_lens_polynomial_coefficients,
                                                  cam->fisheye_fov,
                                                  cam->sensorwidth,
                                                  cam->sensorheight);
    case PANORAMA_CENTRAL_CYLINDRICAL:
      return central_cylindrical_to_direction(u, v, cam->central_cylindrical_range);
    case PANORAMA_FISHEYE_EQUISOLID:
    default:
      return fisheye_equisolid_to_direction(
          u, v, cam->fisheye_lens, cam->fisheye_fov, cam->sensorwidth, cam->sensorheight);
  }
}
 
ccl_device_inline float2 direction_to_panorama(ccl_constant KernelCamera *cam, float3 dir)
{
  switch (cam->panorama_type) {
    case PANORAMA_EQUIRECTANGULAR:
      return direction_to_equirectangular_range(dir, cam->equirectangular_range);
    case PANORAMA_EQUIANGULAR_CUBEMAP_FACE:
      return direction_to_equiangular_cubemap_face(dir);
    case PANORAMA_MIRRORBALL:
      return direction_to_mirrorball(dir);
    case PANORAMA_FISHEYE_EQUIDISTANT:
      return direction_to_fisheye(dir, cam->fisheye_fov);
    case PANORAMA_FISHEYE_LENS_POLYNOMIAL:
      return direction_to_fisheye_lens_polynomial(dir,
                                                  cam->fisheye_lens_polynomial_bias,
                                                  cam->fisheye_lens_polynomial_coefficients,
                                                  cam->sensorwidth,
                                                  cam->sensorheight);
    case PANORAMA_CENTRAL_CYLINDRICAL:
      return direction_to_central_cylindrical(dir, cam->central_cylindrical_range);
    case PANORAMA_FISHEYE_EQUISOLID:
    default:
      return direction_to_fisheye_equisolid(
          dir, cam->fisheye_lens, cam->sensorwidth, cam->sensorheight);
  }
}
 
ccl_device_inline void spherical_stereo_transform(ccl_constant KernelCamera *cam,
                                                  ccl_private float3 *P,
                                                  ccl_private float3 *D)
{
  float interocular_offset = cam->interocular_offset;
 
  /* Interocular offset of zero means either non stereo, or stereo without
   * spherical stereo. */
  kernel_assert(interocular_offset != 0.0f);
 
  if (cam->pole_merge_angle_to > 0.0f) {
    const float pole_merge_angle_from = cam->pole_merge_angle_from,
                pole_merge_angle_to = cam->pole_merge_angle_to;
    float altitude = fabsf(safe_asinf((*D).z));
    if (altitude > pole_merge_angle_to) {
      interocular_offset = 0.0f;
    }
    else if (altitude > pole_merge_angle_from) {
      float fac = (altitude - pole_merge_angle_from) /
                  (pole_merge_angle_to - pole_merge_angle_from);
      float fade = cosf(fac * M_PI_2_F);
      interocular_offset *= fade;
    }
  }
 
  float3 up = make_float3(0.0f, 0.0f, 1.0f);
  float3 side = normalize(cross(*D, up));
  float3 stereo_offset = side * interocular_offset;
 
  *P += stereo_offset;
 
  /* Convergence distance is FLT_MAX in the case of parallel convergence mode,
   * no need to modify direction in this case either. */
  const float convergence_distance = cam->convergence_distance;
 
  if (convergence_distance != FLT_MAX) {
    float3 screen_offset = convergence_distance * (*D);
    *D = normalize(screen_offset - stereo_offset);
  }
}
 
CCL_NAMESPACE_END