We develop algorithms to compute edge sequences, Voronoi diagrams, shortest path maps, the Frechet 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 Frechet distance of a non-convex polyhedral surface.
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