On kinetic line Voronoi operations and finite fields

Darka Mioc; François Anton; Christopher Gold; Bernard Moulin

doi:10.1109/ISVD.2009.39

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 language	English
Title of host publication	Sixth International Symposium on Voronoi Diagrams, 2009. ISVD '09
Publisher	IEEE
Publication date	2009
Pages	65-70
ISBN (Print)	978-1-4244-4769-5
DOIs	https://doi.org/10.1109/ISVD.2009.39
Publication status	Published - 2009
Event	6th International Symposium on Voronoi Diagrams in Science and Engineering - Technical University of Denmark, Kgs. Lyngby, Denmark Duration: 23 Jun 2009 → 26 Jun 2009 Conference number: 6 http://www2.imm.dtu.dk/projects/ISVD/

Conference

Conference	6th International Symposium on Voronoi Diagrams in Science and Engineering
Number	6
Location	Technical University of Denmark
Country/Territory	Denmark
City	Kgs. Lyngby
Period	23/06/2009 → 26/06/2009
Internet address	http://www2.imm.dtu.dk/projects/ISVD/

Bibliographical note

Copyright 2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

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title = "On kinetic line Voronoi operations and finite fields",

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.",

author = "Darka Mioc and Fran{\c c}ois Anton and Christopher Gold and Bernard Moulin",

note = "Copyright 2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.; 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009 ; Conference date: 23-06-2009 Through 26-06-2009",

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AU - Anton, François

AU - Gold, Christopher

AU - Moulin, Bernard

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N2 - 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.

AB - 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.

U2 - 10.1109/ISVD.2009.39

DO - 10.1109/ISVD.2009.39

M3 - Article in proceedings

SN - 978-1-4244-4769-5

SP - 65

EP - 70

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

PB - IEEE

T2 - 6th International Symposium on Voronoi Diagrams in Science and Engineering

Y2 - 23 June 2009 through 26 June 2009

ER -

On kinetic line Voronoi operations and finite fields

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