Computing the visibility graph of points within a polygon

Boaz Ben-Moshe, Olaf Hall-Holt, Matthew Katz, Joseph S.B. Mitchell

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

37 Scopus citations

Abstract

We study the problem of computing the visibility graph defined by a set P of n points inside a polygon Q: two points p, q ε P are joined by an edge if the segment pq ⊂ Q. Efficient output-sensitive algorithms are known for the case in which P is the set of all vertices of Q. We examine the general case in which P is an arbitrary set of points, interior or on the boundary of Q and study a variety of algorithmic questions. We give an output-sensitive algorithm, which is nearly optimal, when Q is a simple polygon. We introduce a notion of "fat" or "robust" visibility, and give a nearly optimal algorithm for computing visibility graphs according to it, in polygons Q that may have holes. Other results include an algorithm to detect if there are any visible pairs among P, and algorithms for output-sensitive computation of visibility graphs with distance restrictions, invisibility graphs, and rectangle visibility graphs.

Original languageEnglish GB
Title of host publicationProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
Pages27-35
Number of pages9
DOIs
StatePublished - 1 Jan 2004
EventProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States
Duration: 9 Jun 200411 Jun 2004

Conference

ConferenceProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
Country/TerritoryUnited States
CityBrooklyn, NY
Period9/06/0411/06/04

Keywords

  • Fatness
  • Guarding
  • Illumination
  • Output-sensitive algorithms
  • Polygons
  • Visibility graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

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