Approximating Weighted Shortest Paths on Polyhedral Surfaces

Shortest path problems are among the fundamental prob lems studied in computational geometry. In this video, we consider the problem of computing a shortest cost path between two points s and t on a (possibly nonconvex) polyhedral surface P. The surface is composed of triangular regions (faces) in which each region has an associated positive weight. The cost of travel through each region is the distance traveled times its weight.