A faster algorithm for computing straight skeletons

Abstract

We present a new algorithm for computing the straight skeleton of a polygon. For a polygon with n vertices, among which r are reflex vertices, we give a deterministic algorithm that reduces the straight skeleton computation to a motorcycle graph computation in O(n(log n) logr) time. It improves on the previously best known algorithm for this reduction, which is randomized, and runs in expected O(n √ h+ 1 log2n) time for a polygon with h holes. Using known motorcycle graph algorithms, our result yields improved time bounds for computing straight skeletons. In particular, we can compute the straight skeleton of a nondegenerate polygon in O(n(log n) logr + r4/3+ϵ) time for any ϵ > 0. On degenerate input, our time bound increases to O(n(log n) logr + r17/11+ϵ ).