Digital Objects in Rhombic Dodecahedron Grid

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 d...

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Bibliographic Details
Published inMathematical Morphology - Theory and Applications Vol. 4; no. 1; pp. 143 - 158
Main Authors Biswas, Ranita, Largeteau-Skapin, Gaëlle, Zrour, Rita, Andres, Eric
Format Journal Article
LanguageEnglish
Published De Gruyter Open 01.01.2020
De Gruyter
Subjects
3D coordinate system
3D digital line
52C
Computer Science
Computer Vision and Pattern Recognition
digital plane
digital sphere
face-centered cubic (FCC) grid
Modeling and Simulation
rhombic dodecahedron
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Summary: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.
ISSN:2353-3390
2353-3390
DOI:10.1515/mathm-2020-0106