public void ComputeDifferentials(RayDifferential ray)
{
if (ray.HasDifferentials)
{
// Estimate screen space change in $\pt{}$ and $(u,v)$
// Compute auxiliary intersection points with plane
double d = -(n ^ new Vector (p.x, p.y, p.z));
Vector rxv = new Vector (ray.RxOrigin.x, ray.RxOrigin.y, ray.RxOrigin.z);
double tx = -((n ^ rxv) + d) / (n ^ ray.RxDirection);
if (double.IsNaN (tx))
{
dudx = dvdx = 0.0;
dudy = dvdy = 0.0;
dpdx = new Vector ();
dpdy = new Vector ();
}
Point px = ray.RxOrigin + tx * ray.RxDirection;
Vector ryv = new Vector (ray.RyOrigin.x, ray.RyOrigin.y, ray.RyOrigin.z);
double ty = -((n ^ ryv) + d) / (n ^ ray.RyDirection);
if (double.IsNaN (ty))
{
dudx = dvdx = 0.0;
dudy = dvdy = 0.0;
dpdx = new Vector ();
dpdy = new Vector ();
}
Point py = ray.RyOrigin + ty * ray.RyDirection;
dpdx = px - p;
dpdy = py - p;
// Compute $(u,v)$ offsets at auxiliary points
// Initialize _A_, _Bx_, and _By_ matrices for offset computation
double[][] A = new double[2][];
A[0] = new double[2];
A[1] = new double[2];
double[] Bx = new double[2], By = new double[2];
int[] axes = new int[2];
if (Math.Abs (n.x) > Math.Abs (n.y) && Math.Abs (n.x) > Math.Abs (n.z))
{
axes[0] = 1;
axes[1] = 2;
} else if (Math.Abs (n.y) > Math.Abs (n.z))
{
axes[0] = 0;
axes[1] = 2;
} else
{
axes[0] = 0;
axes[1] = 1;
}
// Initialize matrices for chosen projection plane
A[0][0] = dpdu[axes[0]];
A[0][1] = dpdv[axes[0]];
A[1][0] = dpdu[axes[1]];
A[1][1] = dpdv[axes[1]];
Bx[0] = px[axes[0]] - p[axes[0]];
Bx[1] = px[axes[1]] - p[axes[1]];
By[0] = py[axes[0]] - p[axes[0]];
By[1] = py[axes[1]] - p[axes[1]];
if (!Util.SolveLinearSystem2x2 (A, Bx[0], Bx[1], out dudx, out dvdx))
{
dudx = 0.0;
dvdx = 0.0;
}
if (!Util.SolveLinearSystem2x2 (A, By[0], By[1], out dudy, out dvdy))
{
dudy = 0.0;
dvdy = 0.0;
}
} else
{
dudx = dvdx = 0.0;
dudy = dvdy = 0.0;
dpdx = new Vector ();
dpdy = new Vector ();
}
}
