Rhombic dodecahedron grid—coordinate system and 3D digital object definitions
Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2019. Rhombic dodecahedron grid—coordinate system and 3D digital object definitions. 21st IAPR International Conference on Discrete Geometry for Computer Imagery. DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS, vol. 11414, 27–37.
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Conference Paper
| Published
| English
Author
Biswas, RanitaISTA 
;
Largeteau-Skapin, Gaëlle;
Zrour, Rita;
Andres, Eric
;
Largeteau-Skapin, Gaëlle;
Zrour, Rita;
Andres, EricSeries Title
LNCS
Abstract
We propose a new non-orthogonal basis to express the 3D Euclidean space in terms of a regular grid. Every grid point, each represented by integer 3-coordinates, corresponds to rhombic dodecahedron centroid. 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 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. A characterization of a 3D digital sphere with relevant topological features is proposed as well with the help of a 48 symmetry that comes with the new coordinate system.
Publishing Year
Date Published
2019-02-23
Proceedings Title
21st IAPR International Conference on Discrete Geometry for Computer Imagery
Publisher
Springer Berlin Heidelberg
Volume
11414
Page
27-37
Conference
DGCI: International Conference on Discrete Geometry for Computer Imagery
Conference Location
Marne-la-Vallée, France
Conference Date
2019-03-26 – 2019-03-28
IST-REx-ID
Cite this
Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Rhombic dodecahedron grid—coordinate system and 3D digital object definitions. In: 21st IAPR International Conference on Discrete Geometry for Computer Imagery. Vol 11414. Berlin, Heidelberg: Springer Berlin Heidelberg; 2019:27-37. doi:10.1007/978-3-030-14085-4_3
Biswas, R., Largeteau-Skapin, G., Zrour, R., & Andres, E. (2019). Rhombic dodecahedron grid—coordinate system and 3D digital object definitions. In 21st IAPR International Conference on Discrete Geometry for Computer Imagery (Vol. 11414, pp. 27–37). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-030-14085-4_3
Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Rhombic Dodecahedron Grid—Coordinate System and 3D Digital Object Definitions.” In 21st IAPR International Conference on Discrete Geometry for Computer Imagery, 11414:27–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 2019. https://doi.org/10.1007/978-3-030-14085-4_3.
R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Rhombic dodecahedron grid—coordinate system and 3D digital object definitions,” in 21st IAPR International Conference on Discrete Geometry for Computer Imagery, Marne-la-Vallée, France, 2019, vol. 11414, pp. 27–37.
Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2019. Rhombic dodecahedron grid—coordinate system and 3D digital object definitions. 21st IAPR International Conference on Discrete Geometry for Computer Imagery. DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS, vol. 11414, 27–37.
Biswas, Ranita, et al. “Rhombic Dodecahedron Grid—Coordinate System and 3D Digital Object Definitions.” 21st IAPR International Conference on Discrete Geometry for Computer Imagery, vol. 11414, Springer Berlin Heidelberg, 2019, pp. 27–37, doi:10.1007/978-3-030-14085-4_3.
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