### Abstract

Motivated by the work of Asano et al.[1], we consider the distance trisector problem and Zone diagram considering segments in the plane as the input geometric objects. As the most basic case, we first consider the pair of curves (distance trisector curves) trisecting the distance between a point and a line. This is a natural extension of the bisector curve (that is a parabola) of a point and a line. In this paper, we show that these trisector curves C _{1} and C_{2} exist and are unique. We then give a practical algorithm for computing the Zone diagram of a set of segments in a digital plane.

Original language | English |
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Title of host publication | Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007 |

Pages | 66-73 |

Number of pages | 8 |

DOIs | |

Publication status | Published - 2007 Dec 1 |

Event | 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007, ISVD 2007 - Pontypridd, United Kingdom Duration: 2007 Jul 9 → 2007 Jul 11 |

### Publication series

Name | Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007 |
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### Other

Other | 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007, ISVD 2007 |
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Country | United Kingdom |

City | Pontypridd |

Period | 07/7/9 → 07/7/11 |

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computational Mechanics

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## Cite this

Jiyon, J., Okada, Y., & Tokuyama, T. (2007). Distance trisector of segments and zone diagram of segments in a plane. In

*Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007*(pp. 66-73). [4276106] (Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007). https://doi.org/10.1109/ISVD.2007.19