Shortest path problems on a polyhedral surface

Abstract

We develop algorithms to compute edge sequences, Voronoi diagrams, shortest path maps, the Fréchet distance, and the diameter of a polyhedral surface. Distances on the surface are measured by the length of a Euclidean shortest path. Our main result is a linear factor speedup for the computation of all shortest path edge sequences and the diameter of a convex polyhedral surface. This speedup is achieved with kinetic Voronoi diagrams. We also use the star unfolding to compute a shortest path map and the Fréchet distance of a non-convex polyhedral surface. © 2009 Springer Berlin Heidelberg.