A Faster Algorithm for Computing Straight Skeletons

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