Minimal arithmetic thickness connecting discrete planes

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

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

While connected arithmetic discrete lines are entirely characterized, only partial results exist for the more general case of arithmetic discrete hyperplanes. In the present paper, we focus on the $3$-dimensional case, that is on arithmetic discrete planes. Thanks to arithmetic reductions on a vector $\vect{n}$, we provide algorithms either to determine whether a given arithmetic discrete plane with $\vect{n}$ as normal vector is connected, or to compute the minimal thickness for which an arithmetic discrete plane with normal vector $\vect{n}$ is connected.

Mots clés: Discrete geometry; arithmetic discrete planes; connectedness

Domaines: Mathématique discrète [cs.DM]

Damien Jamet, Jean-Luc Toutant. Minimal arithmetic thickness connecting discrete planes. Discrete Applied Mathematics, 2009, 157 (3), pp.500-509. ⟨10.1016/j.dam.2008.05.027⟩. ⟨hal-00579872⟩