---
_id: '6163'
abstract:
- lang: eng
  text: 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.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Ranita
  full_name: Biswas, Ranita
  id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
  last_name: Biswas
  orcid: 0000-0002-5372-7890
- first_name: Gaëlle
  full_name: Largeteau-Skapin, Gaëlle
  last_name: Largeteau-Skapin
- first_name: Rita
  full_name: Zrour, Rita
  last_name: Zrour
- first_name: Eric
  full_name: Andres, Eric
  last_name: Andres
citation:
  ama: '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>'
  apa: '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>'
  chicago: '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>.'
  ieee: 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.
  ista: '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.'
  mla: 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>.
  short: 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.
conference:
  end_date: 2019-03-28
  location: Marne-la-Vallée, France
  name: 'DGCI: International Conference on Discrete Geometry for Computer Imagery'
  start_date: 2019-03-26
date_created: 2019-03-21T12:12:19Z
date_published: 2019-02-23T00:00:00Z
date_updated: 2022-01-27T14:25:17Z
day: '23'
doi: 10.1007/978-3-030-14085-4_3
extern: '1'
intvolume: '     11414'
language:
- iso: eng
month: '02'
oa_version: None
page: 27-37
place: Berlin, Heidelberg
publication: 21st IAPR International Conference on Discrete Geometry for Computer
  Imagery
publication_identifier:
  isbn:
  - 978-3-6624-6446-5
  - 978-3-6624-6447-2
  issn:
  - 0302-9743
  - 1611-3349
publication_status: published
publisher: Springer Berlin Heidelberg
quality_controlled: '1'
status: public
title: Rhombic dodecahedron grid—coordinate system and 3D digital object definitions
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 11414
year: '2019'
...