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)log r) time. It improves on the previously best known algorithm for this reduction, which is randomized, and runs in expected O(nsqrth+ 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)log r + r4/3 + ϵ) time for any ϵ > 0. On degenerate input, our time bound increases to O(n(log n)log r + r17/11 + ϵ).