{"scopus_import":"1","intvolume":"       142","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"status":"public","date_updated":"2023-10-10T07:37:16Z","article_number":"109693","publication_status":"published","volume":142,"type":"journal_article","article_processing_charge":"No","date_published":"2023-10-01T00:00:00Z","title":"Discrete analytical objects in the body-centered cubic grid","quality_controlled":"1","acknowledgement":"The first author has been partially supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia through the project no. 451-03-47/2023-01/200156. The fourth author is funded by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35.","doi":"10.1016/j.patcog.2023.109693","_id":"13134","publisher":"Elsevier","external_id":{"isi":["001013526000001"]},"date_created":"2023-06-18T22:00:45Z","department":[{"_id":"HeEd"}],"project":[{"grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Discretization in Geometry and Dynamics","grant_number":"I4887"}],"month":"10","day":"01","article_type":"original","year":"2023","author":[{"last_name":"Čomić","full_name":"Čomić, Lidija","first_name":"Lidija"},{"first_name":"Gaëlle","full_name":"Largeteau-Skapin, Gaëlle","last_name":"Largeteau-Skapin"},{"first_name":"Rita","last_name":"Zrour","full_name":"Zrour, Rita"},{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","first_name":"Ranita"},{"last_name":"Andres","full_name":"Andres, Eric","first_name":"Eric"}],"language":[{"iso":"eng"}],"issue":"10","publication_identifier":{"issn":["0031-3203"]},"publication":"Pattern Recognition","oa_version":"None","abstract":[{"text":"We propose a characterization of discrete analytical spheres, planes and lines in the body-centered cubic (BCC) grid, both in the Cartesian and in the recently proposed alternative compact coordinate system, in which each integer triplet addresses some voxel in the grid. We define spheres and planes through double Diophantine inequalities and investigate their relevant topological features, such as functionality or the interrelation between the thickness of the objects and their connectivity and separation properties. We define lines as the intersection of planes. The number of the planes (up to six) is equal to the number of the pairs of faces of a BCC voxel that are parallel to the line.","lang":"eng"}],"citation":{"mla":"Čomić, Lidija, et al. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” <i>Pattern Recognition</i>, vol. 142, no. 10, 109693, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.patcog.2023.109693\">10.1016/j.patcog.2023.109693</a>.","ieee":"L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, and E. Andres, “Discrete analytical objects in the body-centered cubic grid,” <i>Pattern Recognition</i>, vol. 142, no. 10. Elsevier, 2023.","apa":"Čomić, L., Largeteau-Skapin, G., Zrour, R., Biswas, R., &#38; Andres, E. (2023). Discrete analytical objects in the body-centered cubic grid. <i>Pattern Recognition</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.patcog.2023.109693\">https://doi.org/10.1016/j.patcog.2023.109693</a>","short":"L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition 142 (2023).","chicago":"Čomić, Lidija, Gaëlle Largeteau-Skapin, Rita Zrour, Ranita Biswas, and Eric Andres. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” <i>Pattern Recognition</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.patcog.2023.109693\">https://doi.org/10.1016/j.patcog.2023.109693</a>.","ista":"Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. 2023. Discrete analytical objects in the body-centered cubic grid. Pattern Recognition. 142(10), 109693.","ama":"Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. Discrete analytical objects in the body-centered cubic grid. <i>Pattern Recognition</i>. 2023;142(10). doi:<a href=\"https://doi.org/10.1016/j.patcog.2023.109693\">10.1016/j.patcog.2023.109693</a>"}}