On kinetic line Voronoi operations and finite fields

Darka Mioc, François Anton, Christopher Gold, Bernard Moulin

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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.
Original languageEnglish
Title of host publicationSixth International Symposium on Voronoi Diagrams, 2009. ISVD '09
PublisherIEEE
Publication date2009
Pages65-70
ISBN (Print)978-1-4244-4769-5
DOIs
Publication statusPublished - 2009
Event6th International Symposium on Voronoi Diagrams in Science and Engineering - Technical University of Denmark, Kgs. Lyngby, Denmark
Duration: 23 Jun 200926 Jun 2009
Conference number: 6
http://www2.imm.dtu.dk/projects/ISVD/

Conference

Conference6th International Symposium on Voronoi Diagrams in Science and Engineering
Number6
LocationTechnical University of Denmark
Country/TerritoryDenmark
CityKgs. Lyngby
Period23/06/200926/06/2009
Internet address

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