### Abstract

We consider a generalization of notions of external visibility of simple polygons, namely weak external visibility, weak external visibility from a line and monotonicity, that we call sector visibility. Informally, sector visibility addresses the question of external visibility along rays (or sight lines) whose angles are restricted to a sector (wedge) of specified width u. This provides an interesting measure of the degree of external visibility of a polygon. Our framework also permits a unification and extension of a number of previously unrelated results. Finally, our results uncover a curious complexity discontinuity in this family of problems; algorithms are θ(n) when γ < φ or γ = 2φr, but require ω(n log n) time (at least), when φ < u < 2φ.

Original language | English (US) |
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Title of host publication | Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989 |

Publisher | Association for Computing Machinery |

Pages | 247-254 |

Number of pages | 8 |

Volume | Part F130124 |

ISBN (Electronic) | 0897913183 |

DOIs | |

State | Published - Jun 5 1989 |

Event | 5th Annual Symposium on Computational Geometry, SCG 1989 - Saarbruchen, Germany Duration: Jun 5 1989 → Jun 7 1989 |

### Other

Other | 5th Annual Symposium on Computational Geometry, SCG 1989 |
---|---|

Country | Germany |

City | Saarbruchen |

Period | 6/5/89 → 6/7/89 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

### Cite this

*Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989*(Vol. Part F130124, pp. 247-254). Association for Computing Machinery. https://doi.org/10.1145/73833.73860

**Determining sector visibility of a polygon.** / Bhattacharya, B.; Kirkpatrick, D. G.; Toussaint, Godfried.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989.*vol. Part F130124, Association for Computing Machinery, pp. 247-254, 5th Annual Symposium on Computational Geometry, SCG 1989, Saarbruchen, Germany, 6/5/89. https://doi.org/10.1145/73833.73860

}

TY - GEN

T1 - Determining sector visibility of a polygon

AU - Bhattacharya, B.

AU - Kirkpatrick, D. G.

AU - Toussaint, Godfried

PY - 1989/6/5

Y1 - 1989/6/5

N2 - We consider a generalization of notions of external visibility of simple polygons, namely weak external visibility, weak external visibility from a line and monotonicity, that we call sector visibility. Informally, sector visibility addresses the question of external visibility along rays (or sight lines) whose angles are restricted to a sector (wedge) of specified width u. This provides an interesting measure of the degree of external visibility of a polygon. Our framework also permits a unification and extension of a number of previously unrelated results. Finally, our results uncover a curious complexity discontinuity in this family of problems; algorithms are θ(n) when γ < φ or γ = 2φr, but require ω(n log n) time (at least), when φ < u < 2φ.

AB - We consider a generalization of notions of external visibility of simple polygons, namely weak external visibility, weak external visibility from a line and monotonicity, that we call sector visibility. Informally, sector visibility addresses the question of external visibility along rays (or sight lines) whose angles are restricted to a sector (wedge) of specified width u. This provides an interesting measure of the degree of external visibility of a polygon. Our framework also permits a unification and extension of a number of previously unrelated results. Finally, our results uncover a curious complexity discontinuity in this family of problems; algorithms are θ(n) when γ < φ or γ = 2φr, but require ω(n log n) time (at least), when φ < u < 2φ.

UR - http://www.scopus.com/inward/record.url?scp=0346928759&partnerID=8YFLogxK

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U2 - 10.1145/73833.73860

DO - 10.1145/73833.73860

M3 - Conference contribution

VL - Part F130124

SP - 247

EP - 254

BT - Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989

PB - Association for Computing Machinery

ER -