DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Coexistence of Tricubes in Digital Naive Plane
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Recognizing arithmetic straight lines and planes
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Connectivity of discrete planes
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
On some applications of generalized functionality for arithmetic discrete planes
Image and Vision Computing
On the language of standard discrete planes and surfaces
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Generalized functionality for arithmetic discrete planes
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
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In Vittone and Chassery (Proc. of DGCI'97, Vol. 1347 of Lecture Notes in Computer Sciences, 1997, pp. 87-98) J.-M. Chassery and J. Vittone studied local configurations of (m,n)-cubes in naive planes in function of the parameters of these naive planes. More precisely, they enumerated the bicubes and the tricubes that appear in a naive hyperplane of parameters (a,b,c). A symmetry about the line c=a+b appears clearly in this enumeration. The aim of this paper is to prove that the configurations of (nn)-cubes in the plane of parameters (a,b,c) are in one-to-one relation with those in the plane of parameters (c-b, c-a,c). If we restrict the parameters to the planes such that a+bc, we note a second symmetry about the line c=2b; We also prove this symmetry. We generalize a theorem established by Rveilles and Grard (Grard, Proc. of DGCI'99, Vol. 1568 of Lecture Notes in Computer Sciences, 1999, pp. 65-75, Reveilles, Vision Geometry 4, Vol. 2573 of SPIE 95, San Diego, 1995) and these symmetries to the local configurations of planes of given thickness.