Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 51, No. 2, pp. 587-598 (2010)

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Polyhedral Voronoi cells

Ina Voigt and Stephan Weis

Fakultät für Mathematik, Technische Universität Dortmund, Vogelpothsweg 87, D-44227 Dortmund, Germany, E-mail: ina.voigt@tu-dortmund.de;
Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Bismarckstraße 1 1/2, D-91054 Erlangen, Germany, E-mail: weis@mi.uni-erlangen.de

Abstract: Voronoi cells of a discrete set in Euclidean space are known as generalized polyhedra. We identify polyhedral cells of a discrete set through a direction cone. For an arbitrary set we distinguish polyhedral from non-polyhedral cells using inversion at a sphere and a theorem of semi-infinite linear programming.

Keywords: Voronoi cell, polyhedron, discrete point set

Classification (MSC2000): 52C22, 51M20

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Electronic version published on: 24 Jun 2010. This page was last modified: 8 Sep 2010.

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