conference paper published yes Ranita Biswas author 3C2B033E-F248-11E8-B48F-1D18A9856A870000-0002-5372-7890 Gaëlle Largeteau-Skapin author Rita Zrour author Eric Andres author DGCI: International Conference on Discrete Geometry for Computer Imagery 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. Springer Berlin Heidelberg2019Marne-la-Vallée, France eng 0302-9743 1611-3349 978-3-6624-6446-5 978-3-6624-6447-210.1007/978-3-030-14085-4_3 1141427-37 yes Biswas, R., Largeteau-Skapin, G., Zrour, R., &#38; Andres, E. (2019). Rhombic dodecahedron grid—coordinate system and 3D digital object definitions. In <i>21st IAPR International Conference on Discrete Geometry for Computer Imagery</i> (Vol. 11414, pp. 27–37). Berlin, Heidelberg: Springer Berlin Heidelberg. <a href="https://doi.org/10.1007/978-3-030-14085-4_3">https://doi.org/10.1007/978-3-030-14085-4_3</a> R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, in:, 21st IAPR International Conference on Discrete Geometry for Computer Imagery, Springer Berlin Heidelberg, Berlin, Heidelberg, 2019, 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, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Rhombic Dodecahedron Grid—Coordinate System and 3D Digital Object Definitions.” In <i>21st IAPR International Conference on Discrete Geometry for Computer Imagery</i>, 11414:27–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 2019. <a href="https://doi.org/10.1007/978-3-030-14085-4_3">https://doi.org/10.1007/978-3-030-14085-4_3</a>. R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Rhombic dodecahedron grid—coordinate system and 3D digital object definitions,” in <i>21st IAPR International Conference on Discrete Geometry for Computer Imagery</i>, Marne-la-Vallée, France, 2019, vol. 11414, pp. 27–37. Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Rhombic dodecahedron grid—coordinate system and 3D digital object definitions. In: <i>21st IAPR International Conference on Discrete Geometry for Computer Imagery</i>. Vol 11414. Berlin, Heidelberg: Springer Berlin Heidelberg; 2019:27-37. doi:<a href="https://doi.org/10.1007/978-3-030-14085-4_3">10.1007/978-3-030-14085-4_3</a> Biswas, Ranita, et al. “Rhombic Dodecahedron Grid—Coordinate System and 3D Digital Object Definitions.” <i>21st IAPR International Conference on Discrete Geometry for Computer Imagery</i>, vol. 11414, Springer Berlin Heidelberg, 2019, pp. 27–37, doi:<a href="https://doi.org/10.1007/978-3-030-14085-4_3">10.1007/978-3-030-14085-4_3</a>. 61632019-03-21T12:12:19Z2022-01-27T14:25:17Z