template<class T> Tuple<Vector<T,2>,Vector<T,3>> Triangle<Vector<T,2>>::
closest_point(const Vector<T,2>& location) const
{
TV closest;
Vector<T,3> weights = barycentric_coordinates(location);
// project closest point to the triangle if it's not already inside it
if(weights.x<0){
T a23=interpolation_fraction(simplex(X[1],X[2]),location); // Check edge X[1]--X[2]
if(a23<0){
if(weights.z<0){ // Closest point is on edge X[0]--X[1]
T a12=clamp<T>(interpolation_fraction(simplex(X[0],X[1]),location),0,1);weights=Vector<T,3>(1-a12,a12,0);closest=weights.x*X[0]+weights.y*X[1];}
else{weights=Vector<T,3>(0,1,0);closest=X[1];}} // Closest point is X[1]
else if(a23>1){
if(weights.y<0){ // Closest point is on edge X[0]--X[2]
T a13=clamp<T>(interpolation_fraction(simplex(X[0],X[2]),location),0,1);weights=Vector<T,3>(1-a13,0,a13);closest=weights.x*X[0]+weights.z*X[2];}
else{weights=Vector<T,3>(0,0,1);closest=X[2];}} // Closest point is X[2]
else{weights=Vector<T,3>(0,1-a23,a23);closest=weights.y*X[1]+weights.z*X[2];}} // Closest point is on edge X[1]--X[2]
else if(weights.y<0){
T a13=interpolation_fraction(simplex(X[0],X[2]),location); // Check edge X[0]--X[2]
if(a13<0){
if(weights.z<0){ // Closest point is on edge X[0]--X[1]
T a12=clamp<T>(interpolation_fraction(simplex(X[0],X[1]),location),0,1);weights=Vector<T,3>(1-a12,a12,0);closest=weights.x*X[0]+weights.y*X[1];}
else{weights=Vector<T,3>(1,0,0);closest=X[0];}} // Closest point is X[0]
else if(a13>1){weights=Vector<T,3>(0,0,1);closest=X[2];} // Closest point is X[2]
else{weights=Vector<T,3>(1-a13,0,a13);closest=weights.x*X[0]+weights.z*X[2];}} // Closest point is on edge X[0]--X[2]
else if(weights.z<0){ // Closest point is on edge X[0]--X[1]
T a12=clamp<T>(interpolation_fraction(simplex(X[0],X[1]),location),0,1);weights=Vector<T,3>(1-a12,a12,0);closest=weights.x*X[0]+weights.y*X[1];}
else
closest=weights.x*X[0]+weights.y*X[1]+weights.z*X[2]; // Point is interior to the triangle
return tuple(closest,weights);
}
bool Triangle::intersect(const Ray& r, LocalGeometry& lgeo) {
Mat4 TInv = this->transform.inverse();
Vec3 dir = as_vec3(TInv*as_vec4(r.direction));
Vec4 origin = TInv*r.origin;
if (cross(dir, normal).is_zero())
return false;
double t = dot(as_vec3(origin-A), normal)/dot(dir, normal);
if (t < 0.0)
return false;
else {
Vec4 point = origin + (as_vec4(dir) * t);
Vec3 bar_coords = barycentric_coordinates(A, B, C, point);
double alpha = bar_coords.el(0);
double beta = bar_coords.el(1);
double gamma = bar_coords.el(2);
if (alpha < 0.0 || beta < 0.0 || gamma < 0.0)
return false;
else {
lgeo.normal = submatrix(transform).inverse().transpose() * normal;
lgeo.point = transform * point;
lgeo.geo = this;
return true;
}
}
}
void compute_closest_points(const Vec3d& P, Vec3d& pa, Vec3d& pb){
switch(size_){
//If the simplex has 4 points, it means that the last point added,
//most likely lies on the previous simplex, a triangle. We instead
//use the last simplex to compute the closest points.
case 4:{
const uchar* pos = p_pos[(bits_ ^ (1 << last_sb_))];
const Vec3d& aA = a_[pos[0]];
const Vec3d& aB = a_[pos[1]];
const Vec3d& aC = a_[pos[2]];
const Vec3d& bA = b_[pos[0]];
const Vec3d& bB = b_[pos[1]];
const Vec3d& bC = b_[pos[2]];
const Vec3d& A = p_[pos[0]];
const Vec3d& B = p_[pos[1]];
const Vec3d& C = p_[pos[2]];
auto bary = barycentric_coordinates(P, A, B, C);
pa = aA * bary[0] + aB * bary[1] + aC * bary[2];
pb = bA * bary[0] + bB * bary[1] + bC * bary[2];
break;
}
case 3:{
const uchar* pos = p_pos[(bits_ ^ (1 << last_sb_))];
const Vec3d& aA = a_[last_sb_];
const Vec3d& aB = a_[pos[0]];
const Vec3d& aC = a_[pos[1]];
const Vec3d& bA = b_[last_sb_];
const Vec3d& bB = b_[pos[0]];
const Vec3d& bC = b_[pos[1]];
const Vec3d& A = p_[last_sb_];
const Vec3d& B = p_[pos[0]];
const Vec3d& C = p_[pos[1]];
auto bary = barycentric_coordinates(P, A, B, C);
pa = aA * bary[0] + aB * bary[1] + aC * bary[2];
pb = bA * bary[0] + bB * bary[1] + bC * bary[2];
break;
}
case 2:{
const uchar* pos = p_pos[(bits_ ^ (1 << last_sb_))];
const Vec3d& aA = a_[last_sb_];
const Vec3d& aB = a_[pos[0]];
const Vec3d& bA = b_[last_sb_];
const Vec3d& bB = b_[pos[0]];
double u, v;
{
const Vec3d& A = p_[last_sb_];
const Vec3d& B = p_[pos[0]];
auto AB = B - A;
v = dot(AB, P - A) / AB.length2();
u = 1.0 - v;
}
pa = aA * u + aB * v;
pb = bA * u + bB * v;
break;
}
case 1:{
pa = a_[last_sb_];
pb = b_[last_sb_];
break;
}
default:
break;
}
}