(n, m)-Cubes and Farey Nets for Naive Planes Understanding

A digital naive plane can be represented by repetition of specific elements, called (n,m)-cubes, composed of n × m adjacent voxels. The aim of this paper is to study the class of (n,m)-cubes appearing in a plane in relation with the parametric representation based on the normal vector. Planes are ordered using Farey series coding and we prove the relationship between the segmentation issued from the Farey net and configurations of (n,m)-cubes. This is an original contribution.