## 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 language | English |
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Title of host publication | Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) |

Pages | 27-35 |

Number of pages | 9 |

DOIs | |

State | Published - 1 Jan 2004 |

Event | Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States Duration: 9 Jun 2004 → 11 Jun 2004 |

### Conference

Conference | Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) |
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Country/Territory | United States |

City | Brooklyn, NY |

Period | 9/06/04 → 11/06/04 |

## Keywords

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