---
_id: '9249'
abstract:
- lang: eng
  text: 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.
acknowledgement: "This work has been partially supported by the European Research
  Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation
  programme, grant no. 788183, and the DFG Collaborative Research Center TRR 109,
  ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no.
  I 02979-N35. "
article_processing_charge: No
article_type: original
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. Digital objects in rhombic
    dodecahedron grid. <i>Mathematical Morphology - Theory and Applications</i>. 2020;4(1):143-158.
    doi:<a href="https://doi.org/10.1515/mathm-2020-0106">10.1515/mathm-2020-0106</a>
  apa: Biswas, R., Largeteau-Skapin, G., Zrour, R., &#38; Andres, E. (2020). Digital
    objects in rhombic dodecahedron grid. <i>Mathematical Morphology - Theory and
    Applications</i>. De Gruyter. <a href="https://doi.org/10.1515/mathm-2020-0106">https://doi.org/10.1515/mathm-2020-0106</a>
  chicago: Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Digital
    Objects in Rhombic Dodecahedron Grid.” <i>Mathematical Morphology - Theory and
    Applications</i>. De Gruyter, 2020. <a href="https://doi.org/10.1515/mathm-2020-0106">https://doi.org/10.1515/mathm-2020-0106</a>.
  ieee: R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Digital objects
    in rhombic dodecahedron grid,” <i>Mathematical Morphology - Theory and Applications</i>,
    vol. 4, no. 1. De Gruyter, pp. 143–158, 2020.
  ista: Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2020. Digital objects in
    rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications.
    4(1), 143–158.
  mla: Biswas, Ranita, et al. “Digital Objects in Rhombic Dodecahedron Grid.” <i>Mathematical
    Morphology - Theory and Applications</i>, vol. 4, no. 1, De Gruyter, 2020, pp.
    143–58, doi:<a href="https://doi.org/10.1515/mathm-2020-0106">10.1515/mathm-2020-0106</a>.
  short: R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology
    - Theory and Applications 4 (2020) 143–158.
date_created: 2021-03-16T08:55:19Z
date_published: 2020-11-17T00:00:00Z
date_updated: 2021-03-22T09:01:50Z
day: '17'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/mathm-2020-0106
ec_funded: 1
file:
- access_level: open_access
  checksum: 4a1043fa0548a725d464017fe2483ce0
  content_type: application/pdf
  creator: dernst
  date_created: 2021-03-22T08:56:37Z
  date_updated: 2021-03-22T08:56:37Z
  file_id: '9272'
  file_name: 2020_MathMorpholTheoryAppl_Biswas.pdf
  file_size: 3668725
  relation: main_file
  success: 1
file_date_updated: 2021-03-22T08:56:37Z
has_accepted_license: '1'
intvolume: '         4'
issue: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '11'
oa: 1
oa_version: Published Version
page: 143-158
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '788183'
  name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I02979-N35
  name: Persistence and stability of geometric complexes
publication: Mathematical Morphology - Theory and Applications
publication_identifier:
  issn:
  - 2353-3390
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
status: public
title: Digital objects in rhombic dodecahedron grid
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 4
year: '2020'
...