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/*
* Copyright 2011, Blender Foundation.
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
CCL_NAMESPACE_BEGIN
/* See "Tracing Ray Differentials", Homan Igehy, 1999. */
__device void differential_transfer(differential3 *dP_, const differential3 dP, float3 D, const differential3 dD, float3 Ng, float t)
{
/* ray differential transfer through homogenous medium, to
* compute dPdx/dy at a shading point from the incoming ray */
float3 tmp = D/dot(D, Ng);
float3 tmpx = dP.dx + t*dD.dx;
float3 tmpy = dP.dy + t*dD.dy;
dP_->dx = tmpx - dot(tmpx, Ng)*tmp;
dP_->dy = tmpy - dot(tmpy, Ng)*tmp;
}
__device void differential_incoming(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;
}
__device void differential_dudv(differential *du, differential *dv, float3 dPdu, float3 dPdv, differential3 dP, 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 */
float xn= fabsf(Ng.x);
float yn= fabsf(Ng.y);
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_NAMESPACE_END
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