Invariants of the Dirichlet/Voronoi tilings of hyperspheres in \mathbb{R}^{N} and their dual Delone/Delaunay graphs

Author:

Francesc~Ant{\'o}n~Castro

2010 Mathematics Subject Classification:

14Q15, 65D18, 51M15, 86A30.

Keywords:

Delaunay graph of hyperspheres, geometric invariants, Ritt-Wu characteristic set method, Voronoi diagram of hyperspheres, topological invariants.

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-dimensional 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).

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Vol. 10 (18), 2015