Abstract
The discrete plane β (a,b,c,μ,ω) is the set of integer points (x,y,z)∈ ℤ satisfying 0 ≤ ax+by+cz + μ < ω. In the case ω=max(|a|,|b|,|c|),the discrete plane is said naive and is well-known to be functional on one of the coordinate planes, that is, for any point of P of this coordinate plane, there exists a unique point in the discrete plane obtained by adding to P a third coordinate. Naive planes have been widely studied, see for instance [Rev91, DRR94, DR95, AAS97, VC97, Col02, BB02].
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Berthé, V., Fiorio, C., Jamet, D. (2005). Generalized Functionality for Arithmetic Discrete Planes. In: Andres, E., Damiand, G., Lienhardt, P. (eds) Discrete Geometry for Computer Imagery. DGCI 2005. Lecture Notes in Computer Science, vol 3429. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31965-8_26
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