bool Triangle::Intersect(const Ray &ray, float *tHit, float *rayEpsilon,
DifferentialGeometry *dg) const {
PBRT_RAY_TRIANGLE_INTERSECTION_TEST(const_cast<Ray *>(&ray), const_cast<Triangle *>(this));
// Compute $\VEC{s}_1$
// Get triangle vertices in _p1_, _p2_, and _p3_
const Point &p1 = mesh->p[v[0]];
const Point &p2 = mesh->p[v[1]];
const Point &p3 = mesh->p[v[2]];
Vector e1 = p2 - p1;
Vector e2 = p3 - p1;
Vector s1 = Cross(ray.d, e2);
float divisor = Dot(s1, e1);
if (divisor == 0.)
return false;
float invDivisor = 1.f / divisor;
// Compute first barycentric coordinate
Vector d = ray.o - p1;
float b1 = Dot(d, s1) * invDivisor;
if (b1 < 0. || b1 > 1.)
return false;
// Compute second barycentric coordinate
Vector s2 = Cross(d, e1);
float b2 = Dot(ray.d, s2) * invDivisor;
if (b2 < 0. || b1 + b2 > 1.)
return false;
// Compute _t_ to intersection point
float t = Dot(e2, s2) * invDivisor;
if (t < ray.mint || t > ray.maxt)
return false;
// Compute triangle partial derivatives
Vector dpdu, dpdv;
float uvs[3][2];
GetUVs(uvs);
// Compute deltas for triangle partial derivatives
float du1 = uvs[0][0] - uvs[2][0];
float du2 = uvs[1][0] - uvs[2][0];
float dv1 = uvs[0][1] - uvs[2][1];
float dv2 = uvs[1][1] - uvs[2][1];
Vector dp1 = p1 - p3, dp2 = p2 - p3;
float determinant = du1 * dv2 - dv1 * du2;
if (determinant == 0.f) {
// Handle zero determinant for triangle partial derivative matrix
CoordinateSystem(Normalize(Cross(e2, e1)), &dpdu, &dpdv);
}
else {
float invdet = 1.f / determinant;
dpdu = ( dv2 * dp1 - dv1 * dp2) * invdet;
dpdv = (-du2 * dp1 + du1 * dp2) * invdet;
}
// Interpolate $(u,v)$ triangle parametric coordinates
float b0 = 1 - b1 - b2;
float tu = b0*uvs[0][0] + b1*uvs[1][0] + b2*uvs[2][0];
float tv = b0*uvs[0][1] + b1*uvs[1][1] + b2*uvs[2][1];
// Test intersection against alpha texture, if present
if (ray.depth != -1) {
if (mesh->alphaTexture) {
DifferentialGeometry dgLocal(ray(t), dpdu, dpdv,
Normal(0,0,0), Normal(0,0,0),
tu, tv, this);
if (mesh->alphaTexture->Evaluate(dgLocal) == 0.f)
return false;
}
}
// Fill in _DifferentialGeometry_ from triangle hit
*dg = DifferentialGeometry(ray(t), dpdu, dpdv,
Normal(0,0,0), Normal(0,0,0),
tu, tv, this);
*tHit = t;
*rayEpsilon = 1e-3f * *tHit;
PBRT_RAY_TRIANGLE_INTERSECTION_HIT(const_cast<Ray *>(&ray), t);
return true;
}
bool Heightfield2::TriangleIntersect(const Ray &ray, float *tHit, float *rayEpsilon, DifferentialGeometry *dg, int index[]) const{
PBRT_RAY_TRIANGLE_INTERSECTION_TEST(const_cast<Ray *>(&ray), const_cast<Triangle *>(this));
// Get triangle vertices in _p1_, _p2_, and _p3_
const Point &p1o = point[index[0]];
const Point &p2o = point[index[1]];
const Point &p3o = point[index[2]];
const Point &p1 = (*ObjectToWorld)(p1o);
const Point &p2 = (*ObjectToWorld)(p2o);
const Point &p3 = (*ObjectToWorld)(p3o);
Vector e1 = p2 - p1;
Vector e2 = p3 - p1;
Vector s1 = Cross(ray.d, e2);
float divisor = Dot(s1, e1);
if (divisor == 0.)
return false;
float invDivisor = 1.f / divisor;
// Compute first barycentric coordinate
Vector s = ray.o - p1;
float b1 = Dot(s, s1) * invDivisor;
if (b1 < 0. || b1 > 1.)
return false;
// Compute second barycentric coordinate
Vector s2 = Cross(s, e1);
float b2 = Dot(ray.d, s2) * invDivisor;
if (b2 < 0. || b1 + b2 > 1.)
return false;
// Compute _t_ to intersection point
float t = Dot(e2, s2) * invDivisor;
if (t < ray.mint || t > ray.maxt)
return false;
// Compute triangle partial derivatives
Vector dpdu, dpdv;
// Compute deltas for triangle partial derivatives
float du1 = p1o.x - p3o.x;
float du2 = p2o.x - p3o.x;
float dv1 = p1o.y - p3o.y;
float dv2 = p2o.y - p3o.y;
Vector dp1 = p1 - p3, dp2 = p2 - p3;
float determinant = du1 * dv2 - dv1 * du2;
if (determinant == 0.f) {
// Handle zero determinant for triangle partial derivative matrix
CoordinateSystem(Normalize(Cross(e2, e1)), &dpdu, &dpdv);
}
else {
float invdet = 1.f / determinant;
dpdu = ( dv2 * dp1 - dv1 * dp2) * invdet;
dpdv = (-du2 * dp1 + du1 * dp2) * invdet;
}
// Interpolate $(u,v)$ triangle parametric coordinates
float b0 = 1 - b1 - b2;
float tu = b0*p1o.x + b1*p2o.x + b2*p3o.x;
float tv = b0*p1o.y + b1*p2o.y + b2*p3o.y;
// Fill in _DifferentialGeometry_ from triangle hit
*dg = DifferentialGeometry(ray(t), dpdu, dpdv,
Normal(0,0,0), Normal(0,0,0),
tu, tv, this);
*tHit = t;
*rayEpsilon = 1e-3f * *tHit;
ray.maxt = t;
PBRT_RAY_TRIANGLE_INTERSECTION_HIT(const_cast<Ray *>(&ray), t);
return true;
}
