Computing the Visibility Polygon Using Few Variables

  • Luis Barba
  • Matias Korman
  • Stefan Langerman
  • Rodrigo I. Silveira
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

Abstract

We present several algorithms for computing the visibility polygon of a simple polygon \(\ensuremath{\mathcal{P}}\) from a viewpoint inside the polygon, when the polygon resides in read-only memory and only few working variables can be used. The first algorithm uses a constant number of variables, and outputs the vertices of the visibility polygon in \(O(n\ensuremath{\bar{r}})\) time, where \(\ensuremath{\bar{r}}\) denotes the number of reflex vertices of \(\ensuremath{\mathcal{P}}\) that are part of the output. The next two algorithms use O(logr) variables, and output the visibility polygon in O(nlogr) randomized expected time or O(nlog2 r) deterministic time, where r is the number of reflex vertices of \(\ensuremath{\mathcal{P}}\).

Keywords

Voronoi Diagram Delaunay Triangulation Simple Polygon Visible Point Recursion Tree 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Luis Barba
    • 1
  • Matias Korman
    • 2
  • Stefan Langerman
    • 2
  • Rodrigo I. Silveira
    • 3
  1. 1.Universidad Nacional Autónoma de México (UNAM)Mexico D.F.Mexico
  2. 2.Université Libre de Bruxelles (ULB)BrusselsBelgium
  3. 3.Universitat Politècnica de Catalunya (UPC)BarcelonaSpain

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