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 randomised, 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 nondegenerate polygon in O(n (log n) log r + r^(4/3 + ε)) time for any ε > 0. On degenerate input, our time bound increases to O(n (log n) log r + r^(17/11 + ε))
Date of Award  May 6 2014 

Original language  English (US) 

Awarding Institution   Computer, Electrical and Mathematical Science and Engineering


Supervisor  Antoine Vigneron (Supervisor) 

 straight skeleton
 algorithm
 computional geometry
 theory