Distance from a point to a polyhedron or to a polygon

Question

I have a surface which is a polyhedron and I want to find the minimal distance between it and a given point P. Since the polyhedron is defined by many polygons in a 3d space, one way that occurs to me is to compare the distance to each polygon and choose the shortest distance. Still I am not sure about it.

Answer 1

Implementations of Gilbert–Johnson–Keerthi:
http://www.comlab.ox.ac.uk/stephen.cameron/distances/gjk2.4/
http://code.google.com/p/gjkd/