Efficient computation of geodesic shortest paths

Abstract

This paper describes an efficient algorithm for the geodesic shortest path problem, i.e. the problem of finding shortest paths between pairs of points on the surface of a 3-dimensional polyhedron such that the path is constrained to lie on the surface of the polyhedron. We use the wave-front method and show an O(nlog2n) time bound for this problem, when there are O(n) vertices and edges on the polyhedron.