Invariants of the Dirichlet/Voronoi Tilings of Hyperspheres in Rn and 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 languageEnglish
JournalSiauliai Mathematical Seminar
Volume10
Issue number18
Pages (from-to)123-140
ISSN1822-511X
Publication statusPublished - 2015
Event5th International Conference on Analytic Number Theory and Spatial Tessellations - Kiev, Ukraine
Duration: 16 Sep 201320 Sep 2013

Conference

Conference5th International Conference on Analytic Number Theory and Spatial Tessellations
Country/TerritoryUkraine
CityKiev
Period16/09/201320/09/2013

Keywords

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

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