geometry - Fastest way to compute point to triangle distance in 3D?

Question

One obvious method for computing the minimum distance from a point to a 3D triangle is to project the point onto the plane of the triangle, determine the barycentric coordinates of the resulting point, and use them to determine whether the projected point lies within the triangle. If not, clamp its the barycentric coordinates to be in the range [0,1], and that gives you the closest point that lies inside the triangle.

Is there a way to speed this up or simplify it somehow?

Answer 1

There are different approaches to finding the distance from a point P0 to a triangle P1,P2,P3.

1. The 3D method. Project the point onto the plane of the triangle and use barycentric coordinates or some other means of finding the closest point in the triangle. The distance is found in the usual way.

2. The 2D method. Apply a translation/rotation to the points so that P1 is on the origin, P2 is on the z-axis, P3 in the yz plane. Projection is of the point P0 is trivial (neglect the x coordinate). This results in a 2D problem. Using the edge equation it's possible to determine the closest vertex or edge of the triangle. Calculating distance is then easy-peasy.

This paper compares the performance of both with the 2D method winning.