### Abstract

Let X be a given set of n circular and straight line segments in the plane where two segments may interest only at their endpoints. We introduce a new technique that computes the Voronoi diagram of X in O(n log n) time. This result improves on several previous algorithms for special cases of the problem. The new algorithm is relatively simple, an important factor for the numerous practical applications of the Voronoi diagram.

Original language | English (US) |
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Pages (from-to) | 365-393 |

Number of pages | 29 |

Journal | Discrete and Computational Geometry |

Volume | 2 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1987 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

### Cite this

**An O(n log n) algorithm for the voronoi diagram of a set of simple curve segments.** / Yap, Chee.

Research output: Contribution to journal › Article

*Discrete and Computational Geometry*, vol. 2, no. 1, pp. 365-393. https://doi.org/10.1007/BF02187890

}

TY - JOUR

T1 - An O(n log n) algorithm for the voronoi diagram of a set of simple curve segments

AU - Yap, Chee

PY - 1987/12

Y1 - 1987/12

N2 - Let X be a given set of n circular and straight line segments in the plane where two segments may interest only at their endpoints. We introduce a new technique that computes the Voronoi diagram of X in O(n log n) time. This result improves on several previous algorithms for special cases of the problem. The new algorithm is relatively simple, an important factor for the numerous practical applications of the Voronoi diagram.

AB - Let X be a given set of n circular and straight line segments in the plane where two segments may interest only at their endpoints. We introduce a new technique that computes the Voronoi diagram of X in O(n log n) time. This result improves on several previous algorithms for special cases of the problem. The new algorithm is relatively simple, an important factor for the numerous practical applications of the Voronoi diagram.

UR - http://www.scopus.com/inward/record.url?scp=0346755279&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346755279&partnerID=8YFLogxK

U2 - 10.1007/BF02187890

DO - 10.1007/BF02187890

M3 - Article

VL - 2

SP - 365

EP - 393

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 1

ER -