Simple Characterization of LR-visibility Polygons

  • Xuehou Tan
  • Jing Zhang
  • Bo Jiang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7033)


A simple polygon P is LR-visible if there are two points s, t on the boundary of P such that every point on the clockwise boundary of P from s to t is visible from some point of the other boundary of P from t to s and visa versa. In this paper, we give a simple, explict characterization of LR-visibility polygons. It is obtained by mapping the structure of non-redundant components used in determining LR-visibility into a set of directed chords of a circle. Using our characterization, we further develop a simple O(n) time algorithm for determining whether a given polygon is LR-visible. This greatly simplifies the existing algorithms for determining whether a simple polygon is LR-visible and for reporting all pairs s and t which admit LR-visibility as well.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Xuehou Tan
    • 1
    • 2
  • Jing Zhang
    • 1
  • Bo Jiang
    • 1
  1. 1.School of Information Science and TechnologyDalian Maritime UniversityDalianChina
  2. 2.School of Information Science and TechnologyTokai UniversityHiratsukaJapan

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