Computing the minimum visible vertex distance between two polygons

Preliminar version
  • Alok Aggarwal
  • Shlomo Moran
  • Peter W. Shor
  • Subhash Suri
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 382)


Given two non-intersecting simple polygons P and Q with n and m vertices, respectively, a vertex of P is said to be visible from a vertex of Q if the segment joining these vertices does not properly intersect any edge of these polygons. The problem of finding a closest visible pair of vertices requires finding two vertices, pP and qQ, that are visible to each other and that are closest to each other among all such pairs. In this paper, we present an O((n+m) log log(n+m)) time algorithm; this improves upon an earlier result of Wang and Chan by an O(log(n+m)/ log log(n+m)) factor.

Key Words

Closest pair visible polygons totally-monotone window-trees link-distance 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Alok Aggarwal
    • 1
  • Shlomo Moran
    • 2
  • Peter W. Shor
    • 3
  • Subhash Suri
    • 4
  1. 1.IBM T. J. Watson CenterYorktown Heights
  2. 2.Department of Computer Science, TechnionHaifaIsrael
  3. 3.AT & T Bell LabsMurray Hill
  4. 4.Bell Communications ResearchMorristown

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