public virtual double Pdf(Point p, Vector wi)
{
// Intersect sample ray with area light geometry
DifferentialGeometry dgLight;
Ray ray = new Ray(p, wi, 1e-3d);
ray.depth = -1; // temporary hack to ignore alpha mask
double thit, rayEpsilon;
if (!Intersect(ray, out thit, out rayEpsilon, out dgLight)) return 0.0d;
// Convert light sample weight to solid angle measure
double pdf = Geometry.DistanceSquared(p, ray.GetPointAt(thit)) / ( Geometry.AbsDot(dgLight.nn, -wi) * Area());
if (Double.IsInfinity(pdf)) pdf = 0.0d;
return pdf;
}
public override bool IntersectP(Ray r)
{
// Compute $\VEC{s}_1$
// Get triangle vertices in _p1_, _p2_, and _p3_
Point p1 = mesh.p[v[0]];
Point p2 = mesh.p[v[1]];
Point p3 = mesh.p[v[2]];
Vector e1 = p2 - p1;
Vector e2 = p3 - p1;
Vector s1 = Geometry.Cross(r.d, e2);
double divisor = Geometry.Dot(s1, e1);
if (divisor == 0.0d)
return false;
double invDivisor = 1.0d / divisor;
// Compute first barycentric coordinate
Vector d = r.o - p1;
double b1 = Geometry.Dot(d, s1) * invDivisor;
if (b1 < 0.0d || b1 > 1.0d)
return false;
// Compute second barycentric coordinate
Vector s2 = Geometry.Cross(d, e1);
double b2 = Geometry.Dot(r.d, s2) * invDivisor;
if (b2 < 0.0d || b1 + b2 > 1.0d)
return false;
// Compute _t_ to intersection point
double t = Geometry.Dot(e2, s2) * invDivisor;
if (t < r.mint || t > r.maxt)
return false;
// Test shadow r intersection against alpha texture, if present
if (r.depth != -1 && mesh.alphaTexture != null)
{
// Compute triangle partial derivatives
Vector dpdu, dpdv;
double[,] uvs = new double[3, 2];
GetUVs(uvs);
// Compute deltas for triangle partial derivatives
double du1 = uvs[0, 0] - uvs[2, 0];
double du2 = uvs[1, 0] - uvs[2, 0];
double dv1 = uvs[0, 1] - uvs[2, 1];
double dv2 = uvs[1, 1] - uvs[2, 1];
Vector dp1 = p1 - p3, dp2 = p2 - p3;
double determinant = du1 * dv2 - dv1 * du2;
if (determinant == 0.0d)
{
// Handle zero determinant for triangle partial derivative matrix
Geometry.CoordinateSystem(Geometry.Normalize(Geometry.Cross(e2, e1)), out dpdu, out dpdv);
}
else
{
double invdet = 1.0d / determinant;
dpdu = (dv2 * dp1 - dv1 * dp2) * invdet;
dpdv = (-du2 * dp1 + du1 * dp2) * invdet;
}
// Interpolate $(u,v)$ triangle parametric coordinates
double b0 = 1 - b1 - b2;
double tu = b0 * uvs[0, 0] + b1 * uvs[1, 0] + b2 * uvs[2, 0];
double tv = b0 * uvs[0, 1] + b1 * uvs[1, 1] + b2 * uvs[2, 1];
DifferentialGeometry dgLocal = new DifferentialGeometry(r.GetPointAt(t), dpdu, dpdv, new Normal(0, 0, 0), new Normal(0, 0, 0), tu, tv, this);
if (mesh.alphaTexture.Evaluate(dgLocal) == 0.0d)
return false;
}
return true;
}
public override Point Sample(Point p, double u1, double u2, ref Normal ns)
{
// Compute coordinate system for sphere sampling
Point Pcenter = ObjectToWorld.Apply(new Point(0, 0, 0));
Vector wc = Geometry.Normalize(Pcenter - p);
Vector wcX, wcY;
Geometry.CoordinateSystem(wc, out wcX, out wcY);
// Sample uniformly on sphere if $\pt{}$ is inside it
if (Geometry.DistanceSquared(p, Pcenter) - radius * radius < 1e-4f)
return Sample(u1, u2, ref ns);
// Sample sphere uniformly inside subtended cone
double sinThetaMax2 = radius * radius / Geometry.DistanceSquared(p, Pcenter);
double cosThetaMax = Math.Sqrt(Math.Max(0.0d, 1.0d - sinThetaMax2));
DifferentialGeometry dgSphere;
double thit, rayEpsilon;
Point ps;
Ray r = new Ray(p, MonteCarlo.UniformSampleCone(u1, u2, cosThetaMax, wcX, wcY, wc), 1e-3d);
if (!Intersect(r, out thit, out rayEpsilon, out dgSphere))
thit = Geometry.Dot(Pcenter - p, Geometry.Normalize(r.d));
ps = r.GetPointAt(thit);
ns = new Normal(Geometry.Normalize(ps - Pcenter));
if (ReverseOrientation) ns *= -1.0d;
return ps;
}
