{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,8]],"date-time":"2024-09-08T04:17:20Z","timestamp":1725769040460},"publisher-location":"Cham","reference-count":39,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319041254"},{"type":"electronic","value":"9783319041261"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-319-04126-1_5","type":"book-chapter","created":{"date-parts":[[2014,1,8]],"date-time":"2014-01-08T03:16:13Z","timestamp":1389150973000},"page":"49-61","source":"Crossref","is-referenced-by-count":5,"title":["A Digital-Geometric Algorithm for Generating a Complete Spherical Surface in\u00a0\u21243"],"prefix":"10.1007","author":[{"given":"Sahadev","family":"Bera","sequence":"first","affiliation":[]},{"given":"Partha","family":"Bhowmick","sequence":"additional","affiliation":[]},{"given":"Bhargab B.","family":"Bhattacharya","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"5_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"678","DOI":"10.1007\/978-3-540-89639-5_65","volume-title":"Advances in Visual Computing","author":"V.E. Brimkov","year":"2008","unstructured":"Brimkov, V.E., Barneva, R.P., Brimkov, B., de Vieilleville, F.: Offset approach to defining 3D digital lines. In: Bebis, G., et al. (eds.) ISVC 2008, Part I. LNCS, vol.\u00a05358, pp. 678\u2013687. Springer, Heidelberg (2008)"},{"key":"5_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/11907350_3","volume-title":"Discrete Geometry for Computer Imagery","author":"F. Feschet","year":"2006","unstructured":"Feschet, F., Reveill\u00e8s, J.-P.: A Generic Approach for n-Dimensional Digital Lines. In: Kuba, A., Ny\u00fal, L.G., Pal\u00e1gyi, K. (eds.) DGCI 2006. LNCS, vol.\u00a04245, pp. 29\u201340. Springer, Heidelberg (2006)"},{"key":"5_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1007\/978-3-540-79126-3_29","volume-title":"Discrete Geometry for Computer Imagery","author":"Y. Kenmochi","year":"2008","unstructured":"Kenmochi, Y., Buzer, L., Sugimoto, A., Shimizu, I.: Digital planar surface segmentation using local geometric patterns. In: Coeurjolly, D., Sivignon, I., Tougne, L., Dupont, F. (eds.) DGCI 2008. LNCS, vol.\u00a04992, pp. 322\u2013333. Springer, Heidelberg (2008)"},{"key":"5_CR4","doi-asserted-by":"publisher","first-page":"734","DOI":"10.1109\/CISP.2008.746","volume-title":"Proceedings of the 2008 Congress on Image and Signal Processing, CISP 2008","author":"D.M. Woo","year":"2008","unstructured":"Woo, D.M., Han, S.S., Park, D.C., Nguyen, Q.D.: Extraction of 3D Line Segment Using Digital Elevation Data. In: Proceedings of the 2008 Congress on Image and Signal Processing, CISP 2008, vol.\u00a02, pp. 734\u2013738. IEEE Computer Society, Washington, DC (2008)"},{"key":"5_CR5","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1006\/gmip.1995.1043","volume":"57","author":"Y.T. Chan","year":"1995","unstructured":"Chan, Y.T., Thomas, S.M.: Cramer-Rao lower bounds for estimation of a circular arc center and its radius. Graphical Models and Image Processing\u00a057, 527\u2013532 (1995)","journal-title":"Graphical Models and Image Processing"},{"key":"5_CR6","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1016\/0167-8655(88)90068-2","volume":"7","author":"E.R. Davies","year":"1988","unstructured":"Davies, E.R.: A hybrid sequential-parallel approach to accurate circle centre location. Pattern Recognition Letters\u00a07, 279\u2013290 (1988)","journal-title":"Pattern Recognition Letters"},{"key":"5_CR7","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1016\/S0734-189X(84)80015-8","volume":"28","author":"M. Doros","year":"1984","unstructured":"Doros, M.: On some properties of the generation of discrete circular arcs on a square grid. Computer Vision, Graphics, and Image Processing\u00a028, 377\u2013383 (1984)","journal-title":"Computer Vision, Graphics, and Image Processing"},{"key":"5_CR8","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1109\/TSMC.1974.5408463","volume":"4","author":"R.M. Haralick","year":"1974","unstructured":"Haralick, R.M.: A measure for circularity of digital figures. IEEE Trans. Sys., Man & Cybern.\u00a04, 394\u2013396 (1974)","journal-title":"IEEE Trans. Sys., Man & Cybern."},{"key":"5_CR9","doi-asserted-by":"publisher","first-page":"1231","DOI":"10.1016\/j.patrec.2004.04.001","volume":"25","author":"B. Nagy","year":"2004","unstructured":"Nagy, B.: Characterization of digital circles in triangular grid. Pattern Recognition Letters\u00a025, 1231\u20131242 (2004)","journal-title":"Pattern Recognition Letters"},{"key":"5_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10851-011-0270-6","volume":"42","author":"S. Pal","year":"2012","unstructured":"Pal, S., Bhowmick, P.: Determining digital circularity using integer intervals. Journal of Mathematical Imaging and Vision\u00a042, 1\u201324 (2012)","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"5_CR11","doi-asserted-by":"publisher","first-page":"362","DOI":"10.1016\/0734-189X(89)90088-1","volume":"45","author":"S.M. Thomas","year":"1989","unstructured":"Thomas, S.M., Chan, Y.T.: A simple approach for the estimation of circular arc center and its radius. Computer Vision, Graphics, and Image Processing\u00a045, 362\u2013370 (1989)","journal-title":"Computer Vision, Graphics, and Image Processing"},{"key":"5_CR12","doi-asserted-by":"publisher","first-page":"929","DOI":"10.1016\/0167-8655(96)00050-5","volume":"17","author":"P.C. Yuen","year":"1996","unstructured":"Yuen, P.C., Feng, G.C.: A novel method for parameter estimation of digital arc. Pattern Recognition Letters\u00a017, 929\u2013938 (1996)","journal-title":"Pattern Recognition Letters"},{"key":"5_CR13","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1016\/0734-189X(84)90187-7","volume":"26","author":"A. Nakamura","year":"1984","unstructured":"Nakamura, A., Aizawa, K.: Digital circles. Computer Vision, Graphics, and Image Processing\u00a026, 242\u2013255 (1984)","journal-title":"Computer Vision, Graphics, and Image Processing"},{"key":"5_CR14","series-title":"Morgan Kaufmann Series in Computer Graphics and Geometric Modeling","volume-title":"Digital Geometry: Geometric Methods for Digital Picture Analysis","author":"R. Klette","year":"2004","unstructured":"Klette, R., Rosenfeld, A.: Digital Geometry: Geometric Methods for Digital Picture Analysis. Morgan Kaufmann Series in Computer Graphics and Geometric Modeling. Morgan Kaufmann, San Francisco (2004)"},{"key":"5_CR15","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/j.dam.2002.12.001","volume":"139","author":"R. Klette","year":"2004","unstructured":"Klette, R., Rosenfeld, A.: Digital straightness: A review. Discrete Applied Mathematics\u00a0139, 197\u2013230 (2004)","journal-title":"Discrete Applied Mathematics"},{"key":"5_CR16","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/0304-3975(91)90172-X","volume":"82","author":"F. Mignosi","year":"1991","unstructured":"Mignosi, F.: On the number of factors of Sturmian words. Theoretical Computer Science\u00a082, 71\u201384 (1991)","journal-title":"Theoretical Computer Science"},{"key":"5_CR17","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/j.tcs.2008.07.014","volume":"406","author":"V.E. Brimkov","year":"2008","unstructured":"Brimkov, V.E., Barneva, R.P.: On the polyhedral complexity of the integer points in a hyperball. Theoretical Computer Science\u00a0406, 24\u201330 (2008)","journal-title":"Theoretical Computer Science"},{"key":"5_CR18","doi-asserted-by":"crossref","unstructured":"Heath-Brown, D.R.: Lattice points in the sphere. Number theory in progress, vol.\u00a0II, pp. 883\u2013892. Walter de Gruyter, Berlin (1999)","DOI":"10.1515\/9783110285581.883"},{"key":"5_CR19","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1016\/j.jnt.2006.11.010","volume":"126","author":"F. Chamizo","year":"2007","unstructured":"Chamizo, F., Crist\u00f3bal, E., Ubis, A.: Visible lattice points in the sphere. Journal of Number Theory\u00a0126, 200\u2013211 (2007)","journal-title":"Journal of Number Theory"},{"key":"5_CR20","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/s10474-011-0144-9","volume":"135","author":"F. Chamizo","year":"2012","unstructured":"Chamizo, F., Cristobal, E.: The sphere problem and the L-functions. Acta Mathematica Hungarica\u00a0135, 97\u2013115 (2012)","journal-title":"Acta Mathematica Hungarica"},{"key":"5_CR21","doi-asserted-by":"publisher","first-page":"3164","DOI":"10.1023\/A:1015484630940","volume":"110","author":"O. Fomenko","year":"2002","unstructured":"Fomenko, O.: Distribution of lattice points over the four-dimensional sphere. Journal of Mathematical Sciences\u00a0110, 3164\u20133170 (2002)","journal-title":"Journal of Mathematical Sciences"},{"key":"5_CR22","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.jnt.2006.03.006","volume":"122","author":"A. Magyar","year":"2007","unstructured":"Magyar, A.: On the distribution of lattice points on spheres and level surfaces of polynomials. Journal of Number Theory\u00a0122, 69\u201383 (2007)","journal-title":"Journal of Number Theory"},{"key":"5_CR23","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/BF03026771","volume":"22","author":"J.A. Ewell","year":"2000","unstructured":"Ewell, J.A.: Counting lattice points on spheres. The Mathematical Intelligencer\u00a022, 51\u201353 (2000)","journal-title":"The Mathematical Intelligencer"},{"key":"5_CR24","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1112\/S0024609300007505","volume":"32","author":"K.M. Tsang","year":"2000","unstructured":"Tsang, K.M.: Counting lattice points in the sphere. Bulletin of the London Mathematical Society\u00a032, 679\u2013688 (2000)","journal-title":"Bulletin of the London Mathematical Society"},{"key":"5_CR25","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1016\/j.ejc.2009.03.034","volume":"31","author":"H. Maehara","year":"2010","unstructured":"Maehara, H.: On a sphere that passes through n lattice points. European Journal of Combinatorics\u00a031, 617\u2013621 (2010)","journal-title":"European Journal of Combinatorics"},{"key":"5_CR26","unstructured":"Cappell, S.E., Shaneson, J.L.: Some Problems in Number Theory I: The Circle Problem (2007), \n                    \n                      http:\/\/arxiv.org\/abs\/math.NT\/0702613"},{"key":"5_CR27","first-page":"117","volume":"I","author":"R. Honsberger","year":"1973","unstructured":"Honsberger, R.: Circles, Squares, and Lattice Points. Mathematical Gems\u00a0I, 117\u2013127 (1973)","journal-title":"Mathematical Gems"},{"key":"5_CR28","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/BF02940906","volume":"70","author":"M. K\u00fchleitner","year":"2000","unstructured":"K\u00fchleitner, M.: On lattice points in rational ellipsoids: An omega estimate for the error term. Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg\u00a070, 105\u2013111 (2000)","journal-title":"Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg"},{"key":"5_CR29","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/j.jmaa.2008.09.051","volume":"350","author":"F. Chamizo","year":"2009","unstructured":"Chamizo, F., Cristbal, E., Ubis, A.: Lattice points in rational ellipsoids. Journal of Mathematical Analysis and Applications\u00a0350, 283\u2013289 (2009)","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"5_CR30","doi-asserted-by":"crossref","first-page":"265","DOI":"10.4064\/aa-85-3-265-277","volume":"85","author":"F. Chamizo","year":"1998","unstructured":"Chamizo, F.: Lattice points in bodies of revolution. Acta Arithmetica\u00a085, 265\u2013277 (1998)","journal-title":"Acta Arithmetica"},{"key":"5_CR31","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1109\/2945.582354","volume":"3","author":"E. Andres","year":"1997","unstructured":"Andres, E., Jacob, M.: The discrete analytical hyperspheres. IEEE Trans. Visualization and Computer Graphics\u00a03, 75\u201386 (1997)","journal-title":"IEEE Trans. Visualization and Computer Graphics"},{"key":"5_CR32","doi-asserted-by":"crossref","unstructured":"Fiorio, C., Jamet, D., Toutant, J.L.: Discrete circles: an arithmetical approach with non-constant thickness. In: Latecki, L.J., Mount, D.M., Wu, A.Y. (eds.) Vision Geometry XIV, Electronic Imaging, San Jose (CA), USA. SPIE, vol.\u00a06066, p. 60660C (2006)","DOI":"10.1117\/12.642976"},{"key":"5_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/11907350_36","volume-title":"Discrete Geometry for Computer Imagery","author":"C. Fiorio","year":"2006","unstructured":"Fiorio, C., Toutant, J.-L.: Arithmetic discrete hyperspheres and separatingness. In: Kuba, A., Ny\u00fal, L.G., Pal\u00e1gyi, K. (eds.) DGCI 2006. LNCS, vol.\u00a04245, pp. 425\u2013436. Springer, Heidelberg (2006)"},{"key":"5_CR34","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/B978-0-08-050753-8.50070-X","volume-title":"Graphics Gems","author":"C. Montani","year":"1990","unstructured":"Montani, C., Scopigno, R.: Spheres-to-voxels conversion. In: Glassner, A.S. (ed.) Graphics Gems, pp. 327\u2013334. Academic Press Professional, Inc., San Diego (1990)"},{"key":"5_CR35","unstructured":"Stelldinger, P.: Image Digitization and its Influence on Shape Properties in Finite Dimensions. IOS Press (2007)"},{"key":"5_CR36","volume-title":"Computer Graphics \u2014 Principles and Practice","author":"J.D. Foley","year":"1993","unstructured":"Foley, J.D., van Dam, A., Feiner, S.K., Hughes, J.F.: Computer Graphics \u2014 Principles and Practice. Addison-Wesley, Reading (1993)"},{"key":"5_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.tcs.2013.07.036","volume":"506","author":"S. Bera","year":"2013","unstructured":"Bera, S., Bhowmick, P., Stelldinger, P., Bhattacharya, B.B.: On covering a digital disc with concentric circles in \u21242. Theoretical Computer Science\u00a0506, 1\u201316 (2013)","journal-title":"Theoretical Computer Science"},{"key":"5_CR38","doi-asserted-by":"publisher","first-page":"2381","DOI":"10.1016\/j.dam.2007.10.022","volume":"156","author":"P. Bhowmick","year":"2008","unstructured":"Bhowmick, P., Bhattacharya, B.B.: Number theoretic interpretation and construction of a digital circle. Discrete Applied Mathematics\u00a0156, 2381\u20132399 (2008)","journal-title":"Discrete Applied Mathematics"},{"key":"5_CR39","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1504\/IJART.2011.039845","volume":"4","author":"G. Kumar","year":"2011","unstructured":"Kumar, G., Sharma, N., Bhowmick, P.: Wheel-throwing in digital space using number-theoretic approach. International Journal of Arts and Technology\u00a04, 196\u2013215 (2011)","journal-title":"International Journal of Arts and Technology"}],"container-title":["Lecture Notes in Computer Science","Applied Algorithms"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-04126-1_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,1,30]],"date-time":"2019-01-30T23:57:53Z","timestamp":1548892673000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-04126-1_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783319041254","9783319041261"],"references-count":39,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-04126-1_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2014]]}}}