public void ComputeDifferentials(RayDifferential ray)
{
if (ray.HasDifferentials)
{
try
{
// Estimate screen space change in $\pt{}$ and $(u,v)$
// Compute auxiliary intersection points with plane
double d = N.Dot(P.ToVector3D());
double tx = -(N.Dot(ray.RxOrigin.ToVector3D()) - d) / N.Dot(ray.RxDirection);
if (double.IsInfinity(tx) || double.IsNaN(tx))
{
throw new InvalidOperationException();
}
Point3D px = (ray.RxOrigin.ToVector3D() + tx * ray.RxDirection).ToPoint3D();
double ty = -(N.Dot(ray.RyOrigin.ToVector3D()) - d) / N.Dot(ray.RyDirection);
if (double.IsInfinity(ty) || double.IsNaN(ty))
{
throw new InvalidOperationException();
}
Point3D py = (ray.RyOrigin.ToVector3D() + ty * ray.RyDirection).ToPoint3D();
Dpdx = (px - P).ToVector3D();
Dpdy = (py - P).ToVector3D();
// Compute $(u,v)$ offsets at auxiliary points
// Choose two dimensions to use for ray offset computation
int[] dim = new int[2];
if (Math.Abs(N.X) > Math.Abs(N.Y) && Math.Abs(N.X) > Math.Abs(N.Z))
{
dim[0] = 1;
dim[1] = 2;
}
else if (Math.Abs(N.Y) > Math.Abs(N.Z))
{
dim[0] = 0;
dim[1] = 2;
}
else
{
dim[0] = 0;
dim[1] = 1;
}
// Initialize _A_, _Bx_, and _By_ matrices for offset computation
double[,] a = new double[2, 2];
a[0, 0] = Dpdu[dim[0]];
a[0, 1] = Dpdv[dim[0]];
a[1, 0] = Dpdu[dim[1]];
a[1, 1] = Dpdv[dim[1]];
//Float A[2][2] = {{dpdu[dim[0]], dpdv[dim[0]]
// },
// {dpdu[dim[1]], dpdv[dim[1]]
// }};
double[] bx = new double[2];
bx[0] = px[dim[0]] - P[dim[0]];
bx[1] = px[dim[1]] - P[dim[1]];
double[] by = new double[2];
by[0] = py[dim[0]] - P[dim[0]];
by[1] = py[dim[1]] - P[dim[1]];
if (PbrtMath.SolveLinearSystem2x2(a, bx, out double du1, out double dv1))
{
Dudx = du1;
Dvdx = dv1;
}
else
{
Dudx = 0.0;
Dvdx = 0.0;
}
if (PbrtMath.SolveLinearSystem2x2(a, by, out double du2, out double dv2))
{
Dudx = du2;
Dvdx = dv2;
}
