Voronoi diagram with respect to criteria on vision information

Tetsuo Asano, Hisao Tamaki, Naoki Katoh, Takeshi Tokuyama

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

6 Citations (Scopus)

Abstract

Voronoi diagram for a set of geometric objects is a partition of the plane (or space in higher dimensions) into disjoint regions each dominated by some given object under a predetermined criterion. In this paper we are interested in various measures associated with criteria on goodness of an input line segment with respect to each point in the plane as the "point of view". These measures basically show how the segment or information displayed on the segment can be seen from the point. Mathematically, the measures are defined in terms of the shape of the triangle determined by the point and the line segment. Given any such measure, we can define a Voronoi diagram for a set of line segments. In this paper we are interested in investigating their common combinatorial and structural properties. We investigate conditions for those measures to de.ne regular Voronoi diagrams and also conditions that local optima on the measures lie only on Voronoi edges, not in the proper interior of Voronoi regions.

Original languageEnglish
Title of host publicationProceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007
Pages25-32
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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