A plane-sweep algorithm for finding a closest pair among convex planar objects

  • Frank Bartling
  • Klaus Hinrichs
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 577)


Given a set of geometric objects a closest pair is a pair of objects whose mutual distance is smallest. We present a plane-sweep algorithm which finds a closest pair with respect to any LP -metric, 1≤p≤∞, for planar configurations consisting of n (possibly intersecting) compact convex objects such as line segments, circular discs and convex polygons. For configurations of line segments or discs the algorithm runs in asymptotically optimal time O(n log n). For a configuration of n convex m-gons given in a suitable representation it finds a closest pair with respect to the Euclidean metric L2 in time O(n log(n·m)).

Key words

computational geometry plane-sweep algorithm closest-pair problem 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Frank Bartling
    • 1
  • Klaus Hinrichs
    • 2
  1. 1.FB 12, InformatikUniversität-GH-SiegenSiegenGermany
  2. 2.FB 15, InformatikWestfälische Wilhelms-UniversitätMünsterGermany

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