Arithmetic Discrete Hyperspheres and Separatingness

Abstract : In the framework of the arithmetic discrete geometry, a discrete object is provided with its own analytical definition corresponding to a discretization scheme. It can thus be considered as the equivalent, in a discrete space, of a Euclidean object. Linear objects, namely lines and hyperplanes, have been widely studied under this assumption and are now deeply understood. This is not the case for discrete circles and hyperspheres for which no satisfactory definition exists. In the present paper, we try to fill this gap. Our main results are a general definition of discrete hyperspheres and the characterization of the k-minimal ones thanks to an arithmetic definition based on a non-constant thickness function. To reach such topological properties, we link adjacency and separatingness with norms.
Type de document :
Communication dans un congrès
Attila Kuba. DGCI'06: 13th International Conference on Discrete Geometry for Computer Imagery, Oct 2006, Szeged, Hungary, France. Springer-Verlag, pp.425-436, 2006, LNCS. 〈10.1007/11907350_36〉
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Contributeur : Christophe Fiorio <>
Soumis le : mercredi 31 janvier 2007 - 15:15:55
Dernière modification le : jeudi 24 mai 2018 - 15:59:20
Document(s) archivé(s) le : mardi 6 avril 2010 - 22:56:09

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Christophe Fiorio, Jean-Luc Toutant. Arithmetic Discrete Hyperspheres and Separatingness. Attila Kuba. DGCI'06: 13th International Conference on Discrete Geometry for Computer Imagery, Oct 2006, Szeged, Hungary, France. Springer-Verlag, pp.425-436, 2006, LNCS. 〈10.1007/11907350_36〉. 〈lirmm-00128277〉

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