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(nlog2r) deterministic time, where r is the number of reflex vertices of \(\ensuremath{\mathcal{P}}\).

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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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