Decomposition of Rational Discrete Planes - Archive ouverte HAL
Communication Dans Un Congrès Année : 2024

Decomposition of Rational Discrete Planes

Tristan Roussillon
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Sébastien Labbé

Résumé

This paper is a contribution to the study of rational discrete planes, i.e., sets of points with integer coordinates lying between two parallel planes. Up to translation and symmetry, they are completely determined by a normal vector a ∈ N 3 . Excepted for a few well-identifed cases, it is shown that there are two approximations b, c ∈ N 3 of a, satisfying a = b + c, such that the discrete plane of normal a can be partitioned into two sets having respectively the combinatorial structure of discrete planes of normal b and c. Christoffel graphs are used to compactly encode the structure of discrete planes. This result may have practical interest in discrete geometry for the analysis of planar features.

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Dates et versions

hal-04715762 , version 1 (01-10-2024)

Identifiants

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Tristan Roussillon, Sébastien Labbé. Decomposition of Rational Discrete Planes. Third International Joint Conference on Discrete Geometry and Mathematical Morphology, Sara Brunetti and Andrea Frosini and Simone Rinaldi, Apr 2024, Florence (IT), Italy. pp.54-66, ⟨10.1007/978-3-031-57793-2_5⟩. ⟨hal-04715762⟩
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