### 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) |
---|---|

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 |

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 |

### Publication series

Name | Proceedings of the Annual Symposium on Computational Geometry |
---|---|

Volume | Part F130124 |

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