A Faster Algorithm for Computing Straight Skeletons

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8737)


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 \(O(n \sqrt{h+1}\log^2 n)\) 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 + r 17/11 + ε ).


Fast Algorithm Computational Geometry Medial Axis Vertical Edge Simple Polygon 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.The Hong Kong University of Science and TechnologyKowloonHong Kong
  2. 2.King Abdullah University of Science and TechnologyThuwalSaudi Arabia

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