Data and program for the paper

A polyhedral norm is a norm N on R n for which the set N (x) 1 is a polytope.This covers the case of the L 1 and L norms.We consider here effective algorithms for determining the Voronoi polytope for such norms with a point set being a lattice.The algorithms, that we propose, use the symmetries effectively in order to compute a decomposition of the space into convex polytopes named V N -spaces.The Voronoi polytopes and other geometrical information are easily obtained from it.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2024-08-31
DOI
https://doi.org/10.1016/j.dam.2014.09.007
Citations
13
Primary Topic
Computational Geometry and Mesh Generation
Type
article
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Data and program for the paper

13 citations
Zenodo (CERN European Organization for Nuclear Research)
Computational Geometry and Mesh Generation
article

Data and program for the paper

article en
13 citations

Abstract

A polyhedral norm is a norm N on R n for which the set N (x) 1 is a polytope.This covers the case of the L 1 and L norms.We consider here effective algorithms for determining the Voronoi polytope for such norms with a point set being a lattice.The algorithms, that we propose, use the symmetries effectively in order to compute a decomposition of the space into convex polytopes named V N -spaces.The Voronoi polytopes and other geometrical information are easily obtained from it.

Zenodo (CERN European Organization for Nuclear Research)
Laboratoire de Géologie de l’École Normale Supérieure (FR)
Sustainable cities and communities
Computational Geometry and Mesh Generation
DOIOpen Access PDFOpenAlex
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Data and program for the paper · Zenodo (CERN European Organization for Nuclear Research) (2024) | TGRS Research Map | TGRS