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Dynamically maintaining the visibility graph

  • Gert Vegter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 519)

Abstract

An algorithm is presented to maintain the visibility graph of a set of N line segments in the plane in O(log2N+K log N) time, where K is the total number of arcs of the visibility graph that are destroyed or created upon insertion or deletion of a line segment. The line segments should be disjoint, except possibly at their end-points. The algorithm maintains the visibility diagram, a 2-dimensional cell complex whose 0-dimensional cells correspond to arcs of the visibility graph.

The method can also be applied to determine the visibility polygon of a query point, and also to plan the motion of a rod amidst a dynamically changing set of obstacles. The time complexity of both applications meets the optimal time bounds for their static counterparts.

Keywords

Line Segment Query Point Active Face Visibility Graph Dual Image 
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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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Gert Vegter
    • 1
  1. 1.Dept. of Math. and Comp. ScUniversity of GroningenGroningenThe Netherlands

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