differential.h

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/* SPDX-FileCopyrightText: 2011-2022 Blender Foundation
 *
 * SPDX-License-Identifier: Apache-2.0 */
 
#pragma once
 
#include "kernel/types.h"
 
CCL_NAMESPACE_BEGIN
 
/* See "Tracing Ray Differentials", Homan Igehy, 1999. */
 
ccl_device void differential_transfer(ccl_private differential3 *surface_dP,
                                      const differential3 ray_dP,
                                      const float3 ray_D,
                                      const differential3 ray_dD,
                                      const float3 surface_Ng,
                                      const float ray_t)
{
  /* ray differential transfer through homogeneous medium, to
   * compute dPdx/dy at a shading point from the incoming ray */
 
  const float3 tmp = ray_D / dot(ray_D, surface_Ng);
  const float3 tmpx = ray_dP.dx + ray_t * ray_dD.dx;
  const float3 tmpy = ray_dP.dy + ray_t * ray_dD.dy;
 
  surface_dP->dx = tmpx - dot(tmpx, surface_Ng) * tmp;
  surface_dP->dy = tmpy - dot(tmpy, surface_Ng) * tmp;
}
 
ccl_device void differential_incoming(ccl_private differential3 *dI, const differential3 dD)
{
  /* compute dIdx/dy at a shading point, we just need to negate the
   * differential of the ray direction */
 
  dI->dx = -dD.dx;
  dI->dy = -dD.dy;
}
 
ccl_device void differential_dudv(ccl_private differential *du,
                                  ccl_private differential *dv,
                                  float3 dPdu,
                                  float3 dPdv,
                                  differential3 dP,
                                  const float3 Ng)
{
  /* now we have dPdx/dy from the ray differential transfer, and dPdu/dv
   * from the primitive, we can compute dudx/dy and dvdx/dy. these are
   * mainly used for differentials of arbitrary mesh attributes. */
 
  /* find most stable axis to project to 2D */
  const float xn = fabsf(Ng.x);
  const float yn = fabsf(Ng.y);
  const float zn = fabsf(Ng.z);
 
  if (zn < xn || zn < yn) {
    if (yn < xn || yn < zn) {
      dPdu.x = dPdu.y;
      dPdv.x = dPdv.y;
      dP.dx.x = dP.dx.y;
      dP.dy.x = dP.dy.y;
    }
 
    dPdu.y = dPdu.z;
    dPdv.y = dPdv.z;
    dP.dx.y = dP.dx.z;
    dP.dy.y = dP.dy.z;
  }
 
  /* using Cramer's rule, we solve for dudx and dvdx in a 2x2 linear system,
   * and the same for dudy and dvdy. the denominator is the same for both
   * solutions, so we compute it only once.
   *
   * `dP.dx = dPdu * dudx + dPdv * dvdx;`
   * `dP.dy = dPdu * dudy + dPdv * dvdy;` */
 
  float det = (dPdu.x * dPdv.y - dPdv.x * dPdu.y);
 
  if (det != 0.0f) {
    det = 1.0f / det;
  }
 
  du->dx = (dP.dx.x * dPdv.y - dP.dx.y * dPdv.x) * det;
  dv->dx = (dP.dx.y * dPdu.x - dP.dx.x * dPdu.y) * det;
 
  du->dy = (dP.dy.x * dPdv.y - dP.dy.y * dPdv.x) * det;
  dv->dy = (dP.dy.y * dPdu.x - dP.dy.x * dPdu.y) * det;
}
 
ccl_device differential differential_zero()
{
  differential d;
  d.dx = 0.0f;
  d.dy = 0.0f;
 
  return d;
}
 
ccl_device differential3 differential3_zero()
{
  differential3 d;
  d.dx = zero_float3();
  d.dy = zero_float3();
 
  return d;
}
 
/* Compact ray differentials that are just a radius to reduce memory usage and access cost
 * on GPUs, basically cone tracing.
 *
 * See above for more accurate reference implementations of ray differentials. */
 
ccl_device_forceinline float differential_zero_compact()
{
  return 0.0f;
}
 
ccl_device_forceinline float differential_make_compact(const float dD)
{
  return dD;
}
 
ccl_device_forceinline float differential_make_compact(const differential3 dD)
{
  return 0.5f * (len(dD.dx) + len(dD.dy));
}
 
ccl_device_forceinline float differential_make_compact(const dual3 D)
{
  return 0.5f * (len(D.dx) + len(D.dy));
}
 
ccl_device_forceinline float differential_incoming_compact(const float dD)
{
  return dD;
}
 
ccl_device_forceinline float differential_transfer_compact(const float ray_dP,
                                                           const float3 /* ray_D */,
                                                           const float ray_dD,
                                                           const float ray_t)
{
  return ray_dP + ray_t * ray_dD;
}
 
ccl_device_forceinline differential3 differential_from_compact(const float3 D, const float dD)
{
  float3 dx;
  float3 dy;
  make_orthonormals(D, &dx, &dy);
 
  differential3 d;
  d.dx = dD * dx;
  d.dy = dD * dy;
  return d;
}
 
ccl_device void differential_dudv_compact(ccl_private differential *du,
                                          ccl_private differential *dv,
                                          const float3 dPdu,
                                          const float3 dPdv,
                                          const float dP,
                                          const float3 Ng)
{
  /* TODO: can we speed this up? */
  differential_dudv(du, dv, dPdu, dPdv, differential_from_compact(Ng, dP), Ng);
}
 
CCL_NAMESPACE_END