Invariants of the Dirichlet/Voronoi Tilings of Hyperspheres in Rn and their Dual Delone/Delaunay Graphs

Francesc/François Antón Castro

Invariants of the Dirichlet/Voronoi Tilings of Hyperspheres in Rⁿand their Dual Delone/Delaunay Graphs

Francesc/François Antón Castro

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Abstract

In this paper, we are addressing the geometric and topological invariants that arise in the exact computation of the Delone (Delaunay) graph and the Dirichlet/Voronoi tiling of N-dimensional hyperspheres using Ritt-Wu's algorithm. Our main contribution is a methodology for automated derivation of geometric and topological invariants of the Dirichlet tiling of N + 1-dimenional hyperspheres and its dual Delone graph from the invariants of the Dirichlet tiling of N-dimensional hyperspheres and its dual Delone graph (starting from N = 3).

Original language	English
Journal	Siauliai Mathematical Seminar
Volume	10
Issue number	18
Pages (from-to)	123-140
ISSN	1822-511X
Publication status	Published - 2015
Event	5th International Conference on Analytic Number Theory and Spatial Tessellations - Kiev, Ukraine Duration: 16 Sept 2013 → 20 Sept 2013

Conference

Conference	5th International Conference on Analytic Number Theory and Spatial Tessellations
Country/Territory	Ukraine
City	Kiev
Period	16/09/2013 → 20/09/2013

Keywords

Delaunay graph of hyperspheres
Geometric invariants
Ritt-Wu characteristic set method
Voronoi diagram of hyperspheres
Topological invariants

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title = "Invariants of the Dirichlet/Voronoi Tilings of Hyperspheres in Rn and their Dual Delone/Delaunay Graphs",

abstract = "In this paper, we are addressing the geometric and topological invariants that arise in the exact computation of the Delone (Delaunay) graph and the Dirichlet/Voronoi tiling of N-dimensional hyperspheres using Ritt-Wu's algorithm. Our main contribution is a methodology for automated derivation of geometric and topological invariants of the Dirichlet tiling of N + 1-dimenional hyperspheres and its dual Delone graph from the invariants of the Dirichlet tiling of N-dimensional hyperspheres and its dual Delone graph (starting from N = 3).",

keywords = "Delaunay graph of hyperspheres, Geometric invariants, Ritt-Wu characteristic set method, Voronoi diagram of hyperspheres, Topological invariants",

author = "{Ant{\'o}n Castro}, Francesc/Fran{\c c}ois",

year = "2015",

language = "English",

volume = "10",

pages = "123--140",

journal = "Siauliai Mathematical Seminar",

issn = "1822-511X",

publisher = "Siauliu Universiteto Leidykla",

number = "18",

note = "5th International Conference on Analytic Number Theory and Spatial Tessellations ; Conference date: 16-09-2013 Through 20-09-2013",

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T1 - Invariants of the Dirichlet/Voronoi Tilings of Hyperspheres in Rn and their Dual Delone/Delaunay Graphs

AU - Antón Castro, Francesc/François

PY - 2015

Y1 - 2015

N2 - In this paper, we are addressing the geometric and topological invariants that arise in the exact computation of the Delone (Delaunay) graph and the Dirichlet/Voronoi tiling of N-dimensional hyperspheres using Ritt-Wu's algorithm. Our main contribution is a methodology for automated derivation of geometric and topological invariants of the Dirichlet tiling of N + 1-dimenional hyperspheres and its dual Delone graph from the invariants of the Dirichlet tiling of N-dimensional hyperspheres and its dual Delone graph (starting from N = 3).

AB - In this paper, we are addressing the geometric and topological invariants that arise in the exact computation of the Delone (Delaunay) graph and the Dirichlet/Voronoi tiling of N-dimensional hyperspheres using Ritt-Wu's algorithm. Our main contribution is a methodology for automated derivation of geometric and topological invariants of the Dirichlet tiling of N + 1-dimenional hyperspheres and its dual Delone graph from the invariants of the Dirichlet tiling of N-dimensional hyperspheres and its dual Delone graph (starting from N = 3).

KW - Delaunay graph of hyperspheres

KW - Geometric invariants

KW - Ritt-Wu characteristic set method

KW - Voronoi diagram of hyperspheres

KW - Topological invariants

M3 - Conference article

SN - 1822-511X

VL - 10

SP - 123

EP - 140

JO - Siauliai Mathematical Seminar

JF - Siauliai Mathematical Seminar

IS - 18

T2 - 5th International Conference on Analytic Number Theory and Spatial Tessellations

Y2 - 16 September 2013 through 20 September 2013

ER -