/*
* Finds the point on a line segment closest to a given point.
*
* Solves the equation system that minimizes the point-line distance.
* https://math.stackexchange.com/questions/846054/closest-points-on-two-line-segments
*/
public static Vect3 FindClosestLinePoint(Vect3 lineStart, Vect3 lineEnd, Vect3 point)
{
Vect3 lineVector = lineEnd - lineStart;
double lineVectorSquared = Vect3.Dot(lineVector, lineVector);
double pointToLineVectorDotProduct = Vect3.Dot((point - lineStart), lineVector);
double vectorScalingFactor = pointToLineVectorDotProduct / lineVectorSquared;
// Clamps the result to the line segment distance [0,1]
// 0 is lineStart, 1 applies the entire lineVector from lineStart towards lineEnd.
vectorScalingFactor = vectorScalingFactor < 0 ? 0 : vectorScalingFactor;
vectorScalingFactor = vectorScalingFactor > 1 ? 1 : vectorScalingFactor;
return(lineStart + lineVector * vectorScalingFactor);
}
/*
* Calculates Line/Face intersections using the Möller-Trumbore intersection algorithm.
*
* https://en.wikipedia.org/wiki/Möller–Trumbore_intersection_algorithm
*/
public static bool rayIntersectsTriangle(Vect3 rayOrigin,
Vect3 rayVector,
Vect3 vertex0,
Vect3 vertex1,
Vect3 vertex2)
{
double EPSILON = 1e-6;
Vect3 edge1 = vertex1 - vertex0;
Vect3 edge2 = vertex2 - vertex0;
double a, f, u, v;
Vect3 h = Vect3.Cross(rayVector, edge2);
a = Vect3.Dot(edge1, h);
if (a > -EPSILON && a < EPSILON)
{
return(false); // This ray is parallel to this triangle.
}
f = 1.0 / a;
Vect3 s = rayOrigin - vertex0;
u = f * Vect3.Dot(s, h);
if (u < 0.0 || u > 1.0)
{
return(false);
}
Vect3 q = Vect3.Cross(s, edge1);
v = f * Vect3.Dot(rayVector, q);
if (v < 0.0 || u + v > 1.0)
{
return(false);
}
double t = f * Vect3.Dot(edge2, q);
return(t > EPSILON);
}
