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

Previous Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Polyhedral Voronoi cells

Ina Voigt and Stephan Weis

Fakultät für Mathematik, Technische Universität Dortmund, Vogelpothsweg 87, D-44227 Dortmund, Germany, E-mail:;
Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Bismarckstraße 1 1/2, D-91054 Erlangen, Germany, E-mail:

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

Full text of the article (for subscribers):

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

© 2010 Heldermann Verlag
© 2010 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition