{"issue":"1","date_published":"2020-11-17T00:00:00Z","publication_status":"published","abstract":[{"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.","lang":"eng"}],"department":[{"_id":"HeEd"}],"day":"17","type":"journal_article","file":[{"date_updated":"2021-03-22T08:56:37Z","file_size":3668725,"date_created":"2021-03-22T08:56:37Z","file_id":"9272","success":1,"relation":"main_file","checksum":"4a1043fa0548a725d464017fe2483ce0","file_name":"2020_MathMorpholTheoryAppl_Biswas.pdf","access_level":"open_access","creator":"dernst","content_type":"application/pdf"}],"date_updated":"2021-03-22T09:01:50Z","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"article_processing_charge":"No","month":"11","status":"public","quality_controlled":"1","title":"Digital objects in rhombic dodecahedron grid","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2021-03-16T08:55:19Z","oa_version":"Published Version","oa":1,"publisher":"De Gruyter","article_type":"original","citation":{"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.","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.","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>.","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>","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.","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>"},"ec_funded":1,"_id":"9249","language":[{"iso":"eng"}],"author":[{"full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","first_name":"Ranita","orcid":"0000-0002-5372-7890"},{"full_name":"Largeteau-Skapin, Gaëlle","last_name":"Largeteau-Skapin","first_name":"Gaëlle"},{"last_name":"Zrour","first_name":"Rita","full_name":"Zrour, Rita"},{"first_name":"Eric","last_name":"Andres","full_name":"Andres, Eric"}],"publication":"Mathematical Morphology - Theory and Applications","has_accepted_license":"1","doi":"10.1515/mathm-2020-0106","page":"143-158","publication_identifier":{"issn":["2353-3390"]},"file_date_updated":"2021-03-22T08:56:37Z","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. ","project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020"},{"call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"ddc":["510"],"volume":4,"intvolume":"         4","year":"2020"}