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 LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier

While connected arithmetic discrete lines are entirely characterized, only partial results exist for arithmetic discrete hyperplanes in any dimension. In the present paper, we focus on $0$-connected rational arithmetic discrete planes in $\Z^3$. Thanks to an arithmetic reduction on the parameters of a given integer vector $\vect{n}$, we provide an algorithm which computes the thickness of the thinnest $0$-connected arithmetic plane with normal vector $\vect{n}$.

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'06: Discrete Geometry for Computer Imagery, Oct 2006, Szeged, Hongrie, pp.223-234, ⟨10.1007/11907350_19⟩. ⟨lirmm-00135621v1⟩