Discrete & Computational Geometry

, Volume 32, Issue 3, pp 401–415 | Cite as

Hierarchical Decompositions and Circular Ray Shooting in Simple Polygons

  • Siu-Wing ChengEmail author
  • Otfried CheongEmail author
  • Hazel EverettEmail author
  • René van OostrumEmail author


A hierarchical decomposition of a simple polygon is introduced. The hierarchy has logarithmic depth, linear size, and its regions have at most three neighbors. Using this hierarchy, circular ray shooting queries in a simple polygon on n vertices can be answered in O(log2 n) query time and O(n log n) space. If the radius of the circle is fixed, the query time can be improved to O(log n) and the space to O(n).


Linear Size Query Time Simple Polygon Hierarchical Decomposition Logarithmic Depth 
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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of Computer Science, Hong Kong University of Science & Technology, Clear Water Bay, KowloonHong Kong
  2. 2.Department of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600 MB EindhovenThe Netherlands
  3. 3.LORIA, 615 rue du Jardin Botanique, B.P. 101, 54602 Villers-lès-Nancy cedexFrance
  4. 4.Institute of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB UtrechtThe Netherlands

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