Computing the visibility graph of points within a polygon

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

Research output: Contribution to conferencePaperpeer-review

41 Scopus citations


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
Number of pages9
StatePublished - 2004
Externally publishedYes
EventProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States
Duration: 9 Jun 200411 Jun 2004


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


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


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