Distance trisector of segments and zone diagram of segments in a plane

Jinhi Jiyon, Yuji Okada, Takeshi Tokuyama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

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 C2 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 languageEnglish
Title of host publicationProceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007
Pages66-73
Number of pages8
DOIs
Publication statusPublished - 2007 Dec 1
Event4th International Symposium on Voronoi Diagrams in Science and Engineering 2007, ISVD 2007 - Pontypridd, United Kingdom
Duration: 2007 Jul 92007 Jul 11

Publication series

NameProceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007

Other

Other4th International Symposium on Voronoi Diagrams in Science and Engineering 2007, ISVD 2007
CountryUnited Kingdom
CityPontypridd
Period07/7/907/7/11

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computational Mechanics

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    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