{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:40:01Z","timestamp":1759063201472,"version":"3.44.0"},"reference-count":46,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2021,1,10]],"date-time":"2021-01-10T00:00:00Z","timestamp":1610236800000},"content-version":"vor","delay-in-days":1470,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Discrete Applied Mathematics"],"published-print":{"date-parts":[[2017,1]]},"DOI":"10.1016\/j.dam.2015.11.017","type":"journal-article","created":{"date-parts":[[2015,12,22]],"date-time":"2015-12-22T17:30:28Z","timestamp":1450805428000},"page":"362-375","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":3,"special_numbering":"P2","title":["On the polyhedra of graceful spheres and circular geodesics"],"prefix":"10.1016","volume":"216","author":[{"given":"Ranita","family":"Biswas","sequence":"first","affiliation":[]},{"given":"Partha","family":"Bhowmick","sequence":"additional","affiliation":[]},{"given":"Valentin E.","family":"Brimkov","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"5","key":"10.1016\/j.dam.2015.11.017_br000005","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1016\/0097-8493(94)90164-3","article-title":"Discrete circles, rings and spheres","volume":"18","author":"Andres","year":"1994","journal-title":"Comput. Graph."},{"issue":"5","key":"10.1016\/j.dam.2015.11.017_br000010","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1006\/gmip.1997.0427","article-title":"Discrete analytical hyperplanes","volume":"59","author":"Andres","year":"1997","journal-title":"Graph. Models Image Process."},{"issue":"1","key":"10.1016\/j.dam.2015.11.017_br000015","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1109\/2945.582354","article-title":"The discrete analytical hyperspheres","volume":"3","author":"Andres","year":"1997","journal-title":"IEEE Trans. Vis. Comput. Graphics"},{"issue":"1","key":"10.1016\/j.dam.2015.11.017_br000020","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1109\/2945.582354","article-title":"The discrete analytical hyperspheres","volume":"3","author":"Andres","year":"1997","journal-title":"IEEE Trans. Vis. Comput. Graphics"},{"key":"10.1016\/j.dam.2015.11.017_br000025","doi-asserted-by":"crossref","unstructured":"A. Balog, I. B\u00e1r\u00e1ny, On the convex hull of the integer points in a disc, in: Proc. 7th Annual Symposium on Computational Geometry, SoCG\u00a01991, 1991, pp. 162\u2013165.","DOI":"10.1145\/109648.109666"},{"key":"10.1016\/j.dam.2015.11.017_br000030","doi-asserted-by":"crossref","unstructured":"R. Biswas, P. Bhowmick, On finding spherical geodesic paths and circles in Z3, in: Proceedings of the 18th International Conference on Discrete Geometry for Computer Imagery, 2014, pp. 396\u2013409.","DOI":"10.1007\/978-3-319-09955-2_33"},{"key":"10.1016\/j.dam.2015.11.017_br000035","series-title":"Discrete Geometry for Computer Imagery","first-page":"53","article-title":"Graceful planes and thin tunnel-free meshes","volume":"vol. 1568","author":"Brimkov","year":"1999"},{"issue":"1","key":"10.1016\/j.dam.2015.11.017_br000040","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/S0304-3975(01)00061-5","article-title":"Graceful planes and lines","volume":"283","author":"Brimkov","year":"2002","journal-title":"Theoret. Comput. Sci."},{"issue":"1\u20133","key":"10.1016\/j.dam.2015.11.017_br000045","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.tcs.2004.02.015","article-title":"Connectivity of discrete planes","volume":"319","author":"Brimkov","year":"2004","journal-title":"Theoret. Comput. Sci."},{"issue":"2\u20133","key":"10.1016\/j.dam.2015.11.017_br000050","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.dam.2004.09.010","article-title":"Plane digitization and related combinatorial problems","volume":"147","author":"Brimkov","year":"2005","journal-title":"Discrete Appl. Math."},{"issue":"1\u20132","key":"10.1016\/j.dam.2015.11.017_br000055","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.tcs.2008.07.014","article-title":"On the polyhedral complexity of the integer points in a hyperball","volume":"406","author":"Brimkov","year":"2008","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/j.dam.2015.11.017_br000060","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.gmod.2011.06.002","article-title":"Connected distance-based rasterization of objects in arbitrary dimension","volume":"73","author":"Brimkov","year":"2011","journal-title":"Graph. Models"},{"issue":"4","key":"10.1016\/j.dam.2015.11.017_br000065","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1016\/j.dam.2006.08.004","article-title":"Digital planarity\u2014A review","volume":"155","author":"Brimkov","year":"2007","journal-title":"Discrete Appl. Math."},{"issue":"1\u20132","key":"10.1016\/j.dam.2015.11.017_br000070","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s10474-011-0144-9","article-title":"The sphere problem and the L-functions","volume":"135","author":"Chamizo","year":"2012","journal-title":"Acta Math. Hungar."},{"issue":"2","key":"10.1016\/j.dam.2015.11.017_br000075","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.jnt.2006.11.010","article-title":"Visible lattice points in the sphere","volume":"126","author":"Chamizo","year":"2007","journal-title":"J. Number Theory"},{"issue":"2","key":"10.1016\/j.dam.2015.11.017_br000080","doi-asserted-by":"crossref","first-page":"417","DOI":"10.4171\/rmi\/178","article-title":"On the sphere problem","volume":"11","author":"Chamizo","year":"1995","journal-title":"Rev. Mat. Iberoam."},{"issue":"6","key":"10.1016\/j.dam.2015.11.017_br000085","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1109\/38.469516","article-title":"Voxel-based modeling for layered manufacturing","volume":"15","author":"Chandru","year":"1995","journal-title":"IEEE Comput. Graph. Appl."},{"issue":"5","key":"10.1016\/j.dam.2015.11.017_br000090","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/S1359-0286(98)80010-7","article-title":"Ceramic hollow spheres and their applications","volume":"3","author":"Cochran","year":"1998","journal-title":"Curr. Opin. Solid State Mater. Sci."},{"issue":"6","key":"10.1016\/j.dam.2015.11.017_br000095","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1006\/gmip.1995.1039","article-title":"Fundamentals of surface voxelization","volume":"57","author":"Cohen-Or","year":"1995","journal-title":"Graph. Models Image Process."},{"year":"1973","series-title":"Regular Polytopes","author":"Coxeter","key":"10.1016\/j.dam.2015.11.017_br000100"},{"issue":"4","key":"10.1016\/j.dam.2015.11.017_br000105","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/BF03026771","article-title":"Counting lattice points on spheres","volume":"22","author":"Ewell","year":"2000","journal-title":"Math. Intell."},{"key":"10.1016\/j.dam.2015.11.017_br000110","doi-asserted-by":"crossref","unstructured":"C. Fiorio, D. Jamet, J.-L. Toutant, Discrete circles: An arithmetical approach with non-constant thickness, in: A.Y.W. Longin Jean\u00a0Latecki, David M.\u00a0Mount, (Eds.), Vision Geometry XIV, Electronic Imaging, SPIE, vol. 6066, San Jose (CA), USA, 2006, p. 60660C.","DOI":"10.1117\/12.642976"},{"issue":"6","key":"10.1016\/j.dam.2015.11.017_br000115","doi-asserted-by":"crossref","first-page":"3164","DOI":"10.1023\/A:1015484630940","article-title":"Distribution of lattice points over the four-dimensional sphere","volume":"110","author":"Fomenko","year":"2002","journal-title":"J. Math. Sci."},{"key":"10.1016\/j.dam.2015.11.017_br000120","series-title":"Discrete Geometry for Computer Imagery","first-page":"1","article-title":"On recent trends in discrete geometry in computer science","volume":"vol. 1176","author":"Fran\u00e7on","year":"1996"},{"key":"10.1016\/j.dam.2015.11.017_br000125","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.apradiso.2013.12.009","article-title":"Production and quality control of radioactive yttrium microspheres for medical applications","volume":"85","author":"Ghahramani","year":"2014","journal-title":"Appl. Radiat. Isot."},{"issue":"13\u201314","key":"10.1016\/j.dam.2015.11.017_br000130","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1016\/j.matlet.2009.01.064","article-title":"Morphology and dispersivity modulation of hollow microporous spheres synthesized by a hard template route","volume":"63","author":"Guo","year":"2009","journal-title":"Mater. Lett."},{"key":"10.1016\/j.dam.2015.11.017_br000135","doi-asserted-by":"crossref","unstructured":"D.R. Heath-Brown, Lattice points in the sphere, in: Number theory in progress, Walter de Gruyter, Berlin, II:883\u2013892, 1999.","DOI":"10.1515\/9783110285581.883"},{"issue":"2","key":"10.1016\/j.dam.2015.11.017_br000140","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1108\/13552540910943441","article-title":"Design and analysis of digital materials for physical 3D voxel printing","volume":"15","author":"Hiller","year":"2009","journal-title":"Rapid Prototyp. J."},{"issue":"4","key":"10.1016\/j.dam.2015.11.017_br000145","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1108\/13552541011049252","article-title":"Tunable digital material properties for 3D voxel printers","volume":"16","author":"Hiller","year":"2010","journal-title":"Rapid Prototyp. J."},{"issue":"17","key":"10.1016\/j.dam.2015.11.017_br000150","doi-asserted-by":"crossref","first-page":"2955","DOI":"10.1016\/S0142-9612(03)00094-2","article-title":"Preparation of ceramic microspheres for in situ radiotherapy of deep-seated cancer","volume":"24","author":"Kawashita","year":"2003","journal-title":"Biomaterials"},{"issue":"7","key":"10.1016\/j.dam.2015.11.017_br000155","doi-asserted-by":"crossref","first-page":"3839","DOI":"10.1109\/TAP.2014.2317489","article-title":"Rapid prototyping of electrically small spherical wire antennas","volume":"62","author":"Kim","year":"2014","journal-title":"IEEE Trans. Antennas and Propagation"},{"year":"2004","series-title":"Digital Geometry: Geometric Methods for Digital Picture Analysis","author":"Klette","key":"10.1016\/j.dam.2015.11.017_br000160"},{"key":"10.1016\/j.dam.2015.11.017_br000165","doi-asserted-by":"crossref","first-page":"974","DOI":"10.1038\/35023115","article-title":"Automatic design and manufacture of robotic lifeforms","volume":"406","author":"Lipson","year":"2000","journal-title":"Nature"},{"issue":"2","key":"10.1016\/j.dam.2015.11.017_br000170","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1016\/j.ejc.2009.03.034","article-title":"On a sphere that passes through n lattice points","volume":"31","author":"Maehara","year":"2010","journal-title":"European J. Combin."},{"issue":"1","key":"10.1016\/j.dam.2015.11.017_br000175","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.jnt.2006.03.006","article-title":"On the distribution of lattice points on spheres and level surfaces of polynomials","volume":"122","author":"Magyar","year":"2007","journal-title":"J. Number Theory"},{"key":"10.1016\/j.dam.2015.11.017_br000180","series-title":"Graphics gems (Chapter: Spheres-to-voxels conversion)","first-page":"327","author":"Montani","year":"1990"},{"key":"10.1016\/j.dam.2015.11.017_br000185","series-title":"Proc. 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI~2007","first-page":"209","article-title":"Statistical shape analysis of brain structures using spherical wavelets","author":"Nain","year":"2007"},{"issue":"3","key":"10.1016\/j.dam.2015.11.017_br000190","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1299\/jamdsm.7.362","article-title":"Reconstruction of complete 3D models by voxel integration","volume":"7","author":"Nanya","year":"2013","journal-title":"J. Adv. Mech. Des. Syst. Manuf."},{"key":"10.1016\/j.dam.2015.11.017_br000195","unstructured":"B. Roget, J. Sitaraman, Wall distance search algorithm using voxelized marching spheres, in: 7th International Conference on Computational Fluid Dynamics. ICCFD7, 2012, pp. 1\u201323."},{"key":"10.1016\/j.dam.2015.11.017_br000200","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.jcp.2013.01.035","article-title":"Wall distance search algorithm using voxelized marching spheres","volume":"241","author":"Roget","year":"2013","journal-title":"J. Comput. Phys."},{"issue":"42\u201344","key":"10.1016\/j.dam.2015.11.017_br000205","doi-asserted-by":"crossref","first-page":"4887","DOI":"10.1016\/j.jnoncrysol.2008.04.041","article-title":"Synthesis and characterization of phosphate glass microspheres for radiotherapy applications","volume":"354","author":"Sene","year":"2008","journal-title":"J. Non-Cryst. Solids"},{"issue":"16\u201317","key":"10.1016\/j.dam.2015.11.017_br000210","doi-asserted-by":"crossref","first-page":"2662","DOI":"10.1016\/j.dam.2013.06.001","article-title":"Digital circles, spheres and hyperspheres: From morphological models to analytical characterizations and topological properties","volume":"161","author":"Toutant","year":"2013","journal-title":"Discrete Appl. Math."},{"key":"10.1016\/j.dam.2015.11.017_br000215","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1112\/S0024609300007505","article-title":"Counting lattice points in the sphere","volume":"32","author":"Tsang","year":"2000","journal-title":"Bull. Lond. Math. Soc."},{"key":"10.1016\/j.dam.2015.11.017_br000220","series-title":"Medical Image Computing and Computer-Assisted Intervention, MICCAI~2007","first-page":"842","article-title":"A new method for spherical object detection and its application to computer aided detection of pulmonary nodules in CT images","author":"Zhang","year":"2007"},{"issue":"24","key":"10.1016\/j.dam.2015.11.017_br000225","doi-asserted-by":"crossref","first-page":"2991","DOI":"10.1016\/j.matlet.2006.02.030","article-title":"Preparation of oxide hollow spheres by colloidal carbon spheres","volume":"60","author":"Zheng","year":"2006","journal-title":"Mater. Lett."},{"issue":"8","key":"10.1016\/j.dam.2015.11.017_br000230","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1364\/AO.49.001267","article-title":"Validity criteria of the discrete dipole approximation","volume":"49","author":"Zubko","year":"2010","journal-title":"Appl. Opt."}],"container-title":["Discrete Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0166218X15005727?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0166218X15005727?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:00:26Z","timestamp":1759060826000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0166218X15005727"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":46,"alternative-id":["S0166218X15005727"],"URL":"https:\/\/doi.org\/10.1016\/j.dam.2015.11.017","relation":{},"ISSN":["0166-218X"],"issn-type":[{"type":"print","value":"0166-218X"}],"subject":[],"published":{"date-parts":[[2017,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"On the polyhedra of graceful spheres and circular geodesics","name":"articletitle","label":"Article Title"},{"value":"Discrete Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.dam.2015.11.017","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2015 Elsevier B.V.","name":"copyright","label":"Copyright"}]}}