Generalized Functionality for Arithmetic Discrete Planes

Naive discrete planes are well known to be functional on a coordinate plane. The aim of our paper is to extend the functionality concept to a larger family of arithmetic discrete planes, by introducing suitable projection directions (a1,a2,a3) satisfying a1v1 + a2v2 + a3v3 = w. Several applications are considered. We first study certain local configurations, that is, the (m,n)-cubes introduced in Ref. [J. Vittone, J.-M. Chassery, (n,m)-cubes and Farey Nets for Naive Planes Understanding, in: DGCI, 8th International Conference, Lecture Notes in Computer Science, vol. 1568, Springer-Verlag, 1999, pp. 76–87.]. We compute their number for a given (m,n) and study their statistical behaviour. We then apply functionality to formulate an algorithm for generating arithmetic discrete planes, inspired by Debled-Renesson [I. Debled-Renesson, Reconnaissance des Droites et Plans Discrets, The`se de doctorat, Universite´ Louis Pasteur, Strasbourg, France, 1995.]. We also prove that an arithmeti...

• Type: Conference
• Year: 2005
• Where: DGCI
• Authors: Valérie Berthé, Christophe Fiorio, Damien Jamet
• Keywords: Arithmetic Discrete Plane, DGCI 2005, Discrete Planes, Naive Discrete Planes