On Kinetic Line Voronoi Operations and Finite Fields

Author

Mioc, Darka ; Anton, Francois ; Gold, Christopher ; Moulin, Bernard

Author_Institution

Nat. Space Inst., Tech. Univ. of Denmark, Lyngby, Denmark

fYear

2009

fDate

23-26 June 2009

Firstpage

65

Lastpage

70

Abstract

In this paper, we show an isomorphism between the set of complex operations on the kinetic Voronoi diagram of points and open oriented line segments and the sets of numbers of new / deleted Voronoi regions induced by these operations, and its explanation using the finite field of residual classes of integers modulo 5: F₅ = Z/5Z. We show also an isomorphism between the set of complex operations on the kinetic Voronoi diagram of points and open oriented line segments and the set of differences of new and deleted quad-edge edges induced by these operations, and its explanation using the finite field F₁₅ = Z/15Z. We show finally the application of these theoretical results to the logging of a kinetic line Voronoi data structure.

Keywords

computational geometry; finite fields; kinetic Voronoi diagram; kinetic line Voronoi operations; open oriented line segments; Computer science; Data structures; Galois fields; Geodesy; Geographic Information Systems; Gold; Informatics; Kinetic theory; Mathematical model; Software engineering; Kinetic line Voronoi diagram; Quad-Edge; finite field; residual classes;

fLanguage

English

Publisher

ieee

Conference_Titel

Voronoi Diagrams, 2009. ISVD '09. Sixth International Symposium on

Conference_Location

Copenhagen

Print_ISBN

978-1-4244-4769-5

Electronic_ISBN

978-0-7695-3781-8

Type

conf

DOI

10.1109/ISVD.2009.39

Filename

5362413