{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T20:41:48Z","timestamp":1760820108081},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2008,12,16]],"date-time":"2008-12-16T00:00:00Z","timestamp":1229385600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Math Model Algor"],"published-print":{"date-parts":[[2009,8]]},"DOI":"10.1007\/s10852-008-9097-6","type":"journal-article","created":{"date-parts":[[2008,12,15]],"date-time":"2008-12-15T05:02:53Z","timestamp":1229317373000},"page":"343-355","source":"Crossref","is-referenced-by-count":13,"title":["A Fast Robust Algorithm for Computing Discrete Voronoi Diagrams"],"prefix":"10.1007","volume":"8","author":[{"given":"Mirko","family":"Veli\u0107","sequence":"first","affiliation":[]},{"given":"Dave","family":"May","sequence":"additional","affiliation":[]},{"given":"Louis","family":"Moresi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,12,16]]},"reference":[{"key":"9097_CR1","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1016\/S0021-9991(02)00031-1","volume":"184","author":"L. Moresi","year":"2003","unstructured":"Moresi, L., Dufour, F., M\u00fchlhaus, H.B.: A lagrangian integration point finite element method for large deformation modeling of viscoelastic geomaterials. J. Comput. Phys. 184, 476\u2013497 (2003)","journal-title":"J. Comput. Phys."},{"key":"9097_CR2","volume-title":"The Finite Element Method: Linear Static and Dynamic Finite Element Analysis","author":"T.J.R. Hughes","year":"1987","unstructured":"Hughes, T.J.R.: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall, Englewood Cliffs (1987)"},{"issue":"2","key":"9097_CR3","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1109\/70.563646","volume":"13","author":"P.G. Tzionas","year":"1997","unstructured":"Tzionas, P.G., Thanailakis, A., Tsalides, P.G.: Collision-free path planning for a diamond-shaped robot using two-dimensional cellular automata. IEEE Trans. Robot. Autom. 13(2), 237\u2013250 (1997)","journal-title":"IEEE Trans. Robot. Autom."},{"issue":"1","key":"9097_CR4","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1006\/jcph.2002.7028","volume":"178","author":"Y. Tsai","year":"2002","unstructured":"Tsai, Y.: Rapid and accurate computation of the distance function using grids. J. Comput. Phys. 178(1), 175\u2013195 (2002). ISSN 0021-9991. doi: 10.1006\/jcph.2002.7028","journal-title":"J. Comput. Phys."},{"key":"9097_CR5","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s00453-001-0114-7","volume":"33","author":"S. Bespamyatnikh","year":"2002","unstructured":"Bespamyatnikh, S., Segal, M.: Fast algorithms for approximating distances. Algorithmica 33, 263\u2013269 (2002)","journal-title":"Algorithmica"},{"key":"9097_CR6","unstructured":"Mauch, S.: A fast algorithm for computing the closest point and distance transform. Technical report, Caltech (2000)"},{"key":"9097_CR7","doi-asserted-by":"crossref","unstructured":"Rong, G., Tan, T.S.: Jump flooding in GPU with applications to Voronoi diagram and distance transform. In: I3D \u201906: Proceedings of the 2006 Symposium on Interactive 3D Graphics and Games, pp. 109\u2013116. ACM, New York (2006). ISBN 1-59593-295-X. doi: 10.1145\/1111411.1111431","DOI":"10.1145\/1111411.1111431"},{"key":"9097_CR8","unstructured":"Rong, G.: Jump flooding algorithm on graphics hardware and it\u2019s applications. Ph.D. thesis, National University of Singapore (2007)"},{"key":"9097_CR9","unstructured":"Sud, A., Govindaraju, N., Manocha, D.: Interactive computation of discrete generalized Voronoi diagrams using range culling. In: Proc. 2nd International Symposium on Voronoi Diagrams in Science and Engineering. Hanyang University, October 2005"},{"issue":"3","key":"9097_CR10","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1145\/285857.285860","volume":"17","author":"B. Mirtich","year":"1998","unstructured":"Mirtich, B.: V-clip: fast and robust polyhedral collision detection. ACM Trans. Graph. 17(3), 177\u2013208, July (1998)","journal-title":"ACM Trans. Graph."},{"issue":"3","key":"9097_CR11","doi-asserted-by":"crossref","first-page":"1144","DOI":"10.1145\/1141911.1142006","volume":"25","author":"A. Sud","year":"2006","unstructured":"Sud, A., Govindaraju, N., Gayle, R., Kabul, I., Manocha, D.: Fast proximity computation among deformable models using discrete Voronoi diagrams. ACM Trans. Graph. 25(3), 1144\u20131153 (2006). ISSN 0730-0301. doi: 10.1145\/1141911.1142006","journal-title":"ACM Trans. Graph."},{"key":"9097_CR12","doi-asserted-by":"crossref","unstructured":"Hu, S.Y., Liao, G.M.: Scalable peer-to-peer networked virtual environment. In: NetGames \u201904: Proceedings of 3rd ACM SIGCOMM Workshop on Network and System Support for Games, pp. 129\u2013133. ACM, New York (2004). ISBN 1-58113-942-X. doi: 10.1145\/1016540.1016552","DOI":"10.1145\/1016540.1016552"},{"issue":"4","key":"9097_CR13","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/0895-7177(96)00003-9","volume":"23","author":"A.I. Adamatzky","year":"1996","unstructured":"Adamatzky, A.I.: Voronoi-like partition of lattice in cellular automata. Math. Comput. Model. 23(4), 51\u201366 (1996)","journal-title":"Math. Comput. Model."},{"issue":"10","key":"9097_CR14","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/S0895-7177(98)00156-3","volume":"28","author":"A.I. Adamatzky","year":"1998","unstructured":"Adamatzky, A.I., Holland, O.: Voronoi-like nondeterministic partition of lattice by collectives of finite automata. Math. Comput. Model. 28(10), 73\u201393 (1998)","journal-title":"Math. Comput. Model."},{"issue":"3","key":"9097_CR15","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1145\/116873.116880","volume":"23","author":"F. Aurenhammer","year":"1991","unstructured":"Aurenhammer, F.: Voronoi diagrams\u2014a survey of a fundamental geometric data structure. ACM Comput. Surv. 23(3), 345\u2013405 (1991). ISSN 0360-0300. doi: 10.1145\/116873.116880","journal-title":"ACM Comput. Surv."},{"key":"9097_CR16","volume-title":"Spatial Tessellations: Concepts and Applications of Voronoi diagrams","author":"A. Okabe","year":"1992","unstructured":"Okabe, A., Boots, B., Sugihara, K.: Spatial Tessellations: Concepts and Applications of Voronoi diagrams. Wiley, New York (1992). ISBN 0-471-93430-5"},{"key":"9097_CR17","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1111\/j.1365-246X.1995.tb06841.x","volume":"122","author":"M.S. Sambridge","year":"1995","unstructured":"Sambridge, M.S., Braun, J., McQueen H.: Geophysical parametrization and interpolation of irregular data using natural neighbours. Geophys. J. Int. 122, 837\u2013857 (1995)","journal-title":"Geophys. J. Int."},{"key":"9097_CR18","unstructured":"May, D.A.: Ph.D. thesis, Monash University (2008)"},{"issue":"2","key":"9097_CR19","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1142\/S0218195998000114","volume":"8","author":"J. Vleugels","year":"1998","unstructured":"Vleugels, J., Overmars, M.: Approximating Voronoi diagrams of convex sites in any dimension. Int. J. Comput. Geom. Appl. 8(2), 201\u2013221 (1998)","journal-title":"Int. J. Comput. Geom. Appl."},{"key":"9097_CR20","doi-asserted-by":"crossref","unstructured":"Kenneth, E., Hoff, I., Keyser, J., Lin, M., Manocha, D., Culver, T.: Fast computation of generalized Voronoi diagrams using graphics hardware. In: SIGGRAPH \u201999: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, pp. 277\u2013286. ACM\/Addison-Wesley, New York (1999). ISBN 0-201-48560-5. doi: 10.1145\/311535.311567","DOI":"10.1145\/311535.311567"}],"container-title":["Journal of Mathematical Modelling and Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10852-008-9097-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10852-008-9097-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10852-008-9097-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T22:26:31Z","timestamp":1559255191000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10852-008-9097-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,12,16]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,8]]}},"alternative-id":["9097"],"URL":"https:\/\/doi.org\/10.1007\/s10852-008-9097-6","relation":{},"ISSN":["1570-1166","1572-9214"],"issn-type":[{"value":"1570-1166","type":"print"},{"value":"1572-9214","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,12,16]]}}}