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 Sept 201320 Sept 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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