On the Connectedness of Rational Arithmetic Discrete Hyperplanes

Damien Jamet (1) , Jean-Luc Toutant (2)

1 ADAGIO - Applying Discrete Algorithms to Genomics and Imagery
2 LLAIC1 - Laboratoire de Logique, Algorithmique et Informatique

While connected arithmetic discrete lines are entirely char- acterized by their arithmetic thickness, only partial results exist for arith- metic discrete hyperplanes in any dimension. In the present paper, we focus on 0-connected rational arithmetic discrete planes in Z3. Thanks to an arithmetic reduction on a given integer vector n, we provide an al- gorithm which computes the thickness of the thinnest 0-connected arith- metic plane with normal vector n.

Mots clés: Discrete Geometry; Connectedness; Hyperplane

Domaines: Mathématique discrète [cs.DM]

Damien Jamet, Jean-Luc Toutant. On the Connectedness of Rational Arithmetic Discrete Hyperplanes. DGCI - Discrete Geometry for Computer Imagery, Oct 2006, Szeged, Hungary, Hungary. pp.223-234. ⟨lirmm-00135621v2⟩