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 (logn)logr) time. It improves on the previously best known algorithm for this reduction, which is randomized, and runs in expected O (-rfnet√h+ 1 log2 n) 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 non-degenerate polygon in O(n (logn) logr+r 4/3+ε ) time for any ε>0. On degenerate input, our time bound increases to O(n (logn) logr+ r17/11+ε ).