Minimal arithmetic thickness connecting discrete planes Original Research Article

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 three-dimensional case, that is on arithmetic discrete planes. Thanks to arithmetic reductions on a vector image, we provide algorithms either to determine whether a given arithmetic discrete plane with image as normal vector is connected, or to compute the minimal thickness for which an arithmetic discrete plane with normal vector image is connected.