### Abstract

Given a simple polygon with n sides in the plane and a set of k point "sites" in its interior or on the boundary, compute the Voronoi diagram of the set of sites using the internal "geodesic" distance inside the polygon as the metric. We describe an O ((n+k )log^{2}(n+k)) time algorithm for solving this problem and sketch a faster 0((n+t)log(n+k)) algorithm for the case when the set of sites includes all reflex vertices of the polygon in question.

Original language | English (US) |
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Title of host publication | Proceedings of the 3rd Annual Symposium on Computational Geometry, SCG 1987 |

Publisher | Association for Computing Machinery, Inc |

Pages | 39-49 |

Number of pages | 11 |

ISBN (Electronic) | 0897912314, 9780897912310 |

DOIs | |

State | Published - Oct 1 1987 |

Event | 3rd Annual Symposium on Computational Geometry, SCG 1987 - Waterloo, Canada Duration: Jun 8 1987 → Jun 10 1987 |

### Other

Other | 3rd Annual Symposium on Computational Geometry, SCG 1987 |
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Country | Canada |

City | Waterloo |

Period | 6/8/87 → 6/10/87 |

### Fingerprint

### ASJC Scopus subject areas

- Geometry and Topology
- Computational Mathematics

### Cite this

*Proceedings of the 3rd Annual Symposium on Computational Geometry, SCG 1987*(pp. 39-49). Association for Computing Machinery, Inc. https://doi.org/10.1145/41958.41963

**On the geodesic Voronoi diagram of point sites in a simple polygon.** / Aronov, Boris.

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

*Proceedings of the 3rd Annual Symposium on Computational Geometry, SCG 1987.*Association for Computing Machinery, Inc, pp. 39-49, 3rd Annual Symposium on Computational Geometry, SCG 1987, Waterloo, Canada, 6/8/87. https://doi.org/10.1145/41958.41963

}

TY - GEN

T1 - On the geodesic Voronoi diagram of point sites in a simple polygon

AU - Aronov, Boris

PY - 1987/10/1

Y1 - 1987/10/1

N2 - Given a simple polygon with n sides in the plane and a set of k point "sites" in its interior or on the boundary, compute the Voronoi diagram of the set of sites using the internal "geodesic" distance inside the polygon as the metric. We describe an O ((n+k )log2(n+k)) time algorithm for solving this problem and sketch a faster 0((n+t)log(n+k)) algorithm for the case when the set of sites includes all reflex vertices of the polygon in question.

AB - Given a simple polygon with n sides in the plane and a set of k point "sites" in its interior or on the boundary, compute the Voronoi diagram of the set of sites using the internal "geodesic" distance inside the polygon as the metric. We describe an O ((n+k )log2(n+k)) time algorithm for solving this problem and sketch a faster 0((n+t)log(n+k)) algorithm for the case when the set of sites includes all reflex vertices of the polygon in question.

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U2 - 10.1145/41958.41963

DO - 10.1145/41958.41963

M3 - Conference contribution

SP - 39

EP - 49

BT - Proceedings of the 3rd Annual Symposium on Computational Geometry, SCG 1987

PB - Association for Computing Machinery, Inc

ER -