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Article Dans Une Revue Mathematical Morphology - Theory and Applications Année : 2020

Digital Objects in Rhombic Dodecahedron Grid

Résumé

Abstract Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system.

Dates et versions

hal-04504629 , version 1 (14-03-2024)

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Citer

Ranita Biswas, Gaëlle Largeteau-Skapin, Rita Zrour, Eric Andres. Digital Objects in Rhombic Dodecahedron Grid. Mathematical Morphology - Theory and Applications, 2020, 4 (1), pp.143-158. ⟨10.1515/mathm-2020-0106⟩. ⟨hal-04504629⟩
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