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Algorithmica

, Volume 47, Issue 2, pp 159–182 | Cite as

Motorcycle Graphs and Straight Skeletons

  • Siu-Wing Cheng
  • Antoine Vigneron
Article

Abstract

We present a new algorithm to compute motorcycle graphs. It runs in \(O(n \sqrt{n}\log n)\) time when n is the number of motorcycles. We give a new characterization of the straight skeleton of a nondegenerate polygon. For a polygon with n vertices and h holes, we show that it yields a randomized algorithm that reduces the straight skeleton computation to a motorcycle graph computation in expected \(O(n\sqrt{h+1}\log^2 n)\) time. Combining these results, we can compute the straight skeleton of a nondegenerate polygon with h holes and with n vertices, among which r are reflex vertices, in \(O(n\sqrt{h+1}\log^2 n+r \sqrt{r} \log r)\) expected time. In particular, we cancompute the straight skeleton of a nondegenerate polygon with n vertices in \(O(n\sqrt{n}\log^2n)\) expected time.

Keywords

Impact Event Medial Axis Switching Event Simple Polygon Support Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Department of Computer Science, Hong Kong University of Science and Technology, Clear Water BayKowloonHong Kong
  2. 2.Unite Mathematiques et Informatique Appliquees, INRA, Domaine de Vilvert, F-78352Jouy-en-Josas cedexFrance

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