bool Face::triangle_intersect(const Ray &r, Hit &h, Vertex *a, Vertex *b, Vertex *c, bool intersect_backfacing) const {
// compute the intersection with the plane of the triangle
Hit h2 = Hit(h);
if (!plane_intersect(r,h2,intersect_backfacing)) return 0;
// figure out the barycentric coordinates:
glm::vec3 Ro = r.getOrigin();
glm::vec3 Rd = r.getDirection();
// [ ax-bx ax-cx Rdx ][ beta ] [ ax-Rox ]
// [ ay-by ay-cy Rdy ][ gamma ] = [ ay-Roy ]
// [ az-bz az-cz Rdz ][ t ] [ az-Roz ]
// solve for beta, gamma, & t using Cramer's rule
glm::mat3 detA_mat(a->get().x-b->get().x,a->get().x-c->get().x,Rd.x,
a->get().y-b->get().y,a->get().y-c->get().y,Rd.y,
a->get().z-b->get().z,a->get().z-c->get().z,Rd.z);
float detA = glm::determinant(detA_mat);
if (fabs(detA) <= 0.000001) return 0;
assert (fabs(detA) >= 0.000001);
glm::mat3 beta_mat(a->get().x-Ro.x,a->get().x-c->get().x,Rd.x,
a->get().y-Ro.y,a->get().y-c->get().y,Rd.y,
a->get().z-Ro.z,a->get().z-c->get().z,Rd.z);
glm::mat3 gamma_mat(a->get().x-b->get().x,a->get().x-Ro.x,Rd.x,
a->get().y-b->get().y,a->get().y-Ro.y,Rd.y,
a->get().z-b->get().z,a->get().z-Ro.z,Rd.z);
float beta = glm::determinant(beta_mat) / detA;
float gamma = glm::determinant(gamma_mat) / detA;
if (beta >= -0.00001 && beta <= 1.00001 &&
gamma >= -0.00001 && gamma <= 1.00001 &&
beta + gamma <= 1.00001) {
h = h2;
// interpolate the texture coordinates
float alpha = 1 - beta - gamma;
float t_s = alpha * a->get_s() + beta * b->get_s() + gamma * c->get_s();
float t_t = alpha * a->get_t() + beta * b->get_t() + gamma * c->get_t();
h.setTextureCoords(t_s,t_t);
assert (h.getT() >= EPSILON);
return 1;
}
return 0;
}
bool Face::triangle_intersect(const Ray &r, Hit &h, Vertex *a, Vertex *b, Vertex *c, bool intersect_backfacing, bool* backfacing_hit) {
*backfacing_hit = false;
// compute the intersection with the plane of the triangle
Hit h2 = Hit(h);
if (!plane_intersect(r,h2,intersect_backfacing, backfacing_hit)) return 0;
// figure out the barycentric coordinates:
Vec3f Ro = r.getOrigin();
Vec3f Rd = r.getDirection();
// [ ax-bx ax-cx Rdx ][ beta ] [ ax-Rox ]
// [ ay-by ay-cy Rdy ][ gamma ] = [ ay-Roy ]
// [ az-bz az-cz Rdz ][ t ] [ az-Roz ]
// solve for beta, gamma, & t using Cramer's rule
double detA = Matrix::det3x3(a->get().x()-b->get().x(),a->get().x()-c->get().x(),Rd.x(),
a->get().y()-b->get().y(),a->get().y()-c->get().y(),Rd.y(),
a->get().z()-b->get().z(),a->get().z()-c->get().z(),Rd.z());
if (fabs(detA) <= 0.000001) return 0;
assert (fabs(detA) >= 0.000001);
double beta = Matrix::det3x3(a->get().x()-Ro.x(),a->get().x()-c->get().x(),Rd.x(),
a->get().y()-Ro.y(),a->get().y()-c->get().y(),Rd.y(),
a->get().z()-Ro.z(),a->get().z()-c->get().z(),Rd.z()) / detA;
double gamma = Matrix::det3x3(a->get().x()-b->get().x(),a->get().x()-Ro.x(),Rd.x(),
a->get().y()-b->get().y(),a->get().y()-Ro.y(),Rd.y(),
a->get().z()-b->get().z(),a->get().z()-Ro.z(),Rd.z()) / detA;
//Case of an intersection
if (beta >= -0.00001 && beta <= 1.00001 &&
gamma >= -0.00001 && gamma <= 1.00001 &&
beta + gamma <= 1.00001) {
h = h2;
// interpolate the texture coordinates
double alpha = 1 - beta - gamma;
double t_s = alpha * a->get_s() + beta * b->get_s() + gamma * c->get_s();
double t_t = alpha * a->get_t() + beta * b->get_t() + gamma * c->get_t();
h.setTextureCoords(t_s,t_t);
assert (h.getT() >= EPSILON);
return 1;
}
return 0;
}