{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T06:44:36Z","timestamp":1773816276262,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":19,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540486268","type":"print"},{"value":"9783540486275","type":"electronic"}],"license":[{"start":{"date-parts":[[2006,1,1]],"date-time":"2006-01-01T00:00:00Z","timestamp":1136073600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1007\/11919629_20","type":"book-chapter","created":{"date-parts":[[2007,1,11]],"date-time":"2007-01-11T14:22:12Z","timestamp":1168525332000},"page":"186-195","source":"Crossref","is-referenced-by-count":2,"title":["Issues and Implementation of C 1 and C 2 Natural Neighbor Interpolation"],"prefix":"10.1007","author":[{"given":"T.","family":"Bobach","sequence":"first","affiliation":[]},{"given":"M.","family":"Bertram","sequence":"additional","affiliation":[]},{"given":"G.","family":"Umlauf","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"20_CR1","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1017\/S0305004100056589","volume":"87","author":"R. Sibson","year":"1980","unstructured":"Sibson, R.: A vector identity for the Dirichlet tessellation. Mathematical Proceedings of Cambridge Philosophical Society\u00a087, 151\u2013155 (1980)","journal-title":"Mathematical Proceedings of Cambridge Philosophical Society"},{"issue":"3","key":"20_CR2","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1016\/0550-3213(82)90124-9","volume":"210","author":"N.H. Christ","year":"1982","unstructured":"Christ, N.H., Friedberg, R., Lee, T.D.: Weights of links and plaquettes in a random lattice. Nuclear Physics B\u00a0210(3), 337\u2013346 (1982)","journal-title":"Nuclear Physics B"},{"key":"20_CR3","first-page":"9","volume":"37","author":"V. Belikov","year":"1997","unstructured":"Belikov, V., Ivanov, V., Kontorovich, V., Korytnik, S., Semenov, A.: The non-Sibsonian interpolation: A new method of interpolation of the values of a function on an arbitrary set of points. Comp. Math. and Math. Physics\u00a037, 9\u201315 (1997)","journal-title":"Comp. Math. and Math. Physics"},{"key":"20_CR4","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/S0010-4485(98)00079-7","volume":"13","author":"K. Sugihara","year":"1999","unstructured":"Sugihara, K.: Surface interpolation based on new local coordinates. Computer Aided Design\u00a013, 51\u201358 (1999)","journal-title":"Computer Aided Design"},{"key":"20_CR5","doi-asserted-by":"crossref","unstructured":"Hiyoshi, H., Sugihara, K.: Voronoi-based interpolation with higher continuity. In: Symposium on Computational Geometry, pp. 242\u2013250 (2000)","DOI":"10.1145\/336154.336210"},{"key":"20_CR6","unstructured":"Hiyoshi, H.: Stable computation of natural neighbor interpolation. In: Proc. of the 2nd Int. Sym. on Voronoi Diagrams in Science and Engineering, pp. 325\u2013333 (2005)"},{"key":"20_CR7","unstructured":"Sibson, R.: A brief description of natural neighbor interpolation. Interpreting Multivariate Data, 21\u201336 (1981)"},{"key":"20_CR8","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1016\/0167-8396(90)90036-Q","volume":"7","author":"G. Farin","year":"1990","unstructured":"Farin, G.: Surfaces over Dirichlet tessellations. Computer Aided Geometric Design\u00a07, 281\u2013292 (1990)","journal-title":"Computer Aided Geometric Design"},{"key":"20_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/978-3-540-24767-8_8","volume-title":"Computational Science and Its Applications \u2013 ICCSA 2004","author":"H. Hiyoshi","year":"2004","unstructured":"Hiyoshi, H., Sugihara, K.: Improving the global continuity of the natural neighbor interpolation. In: Lagan\u00e1, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds.) ICCSA 2004. LNCS, vol.\u00a03045, pp. 71\u201380. Springer, Heidelberg (2004)"},{"key":"20_CR10","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/S0166-218X(99)00004-9","volume":"93","author":"L. Gross","year":"1999","unstructured":"Gross, L., Farin, G.E.: A transfinite form of Sibson\u2019s interpolant. Discrete Applied Mathematics\u00a093, 33\u201350 (1999)","journal-title":"Discrete Applied Mathematics"},{"key":"20_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/978-3-540-46515-7_10","volume-title":"Discrete and Computational Geometry","author":"H. Hiyoshi","year":"2000","unstructured":"Hiyoshi, H., Sugihara, K.: An interpolant based on line segment voronoi diagrams. In: Akiyama, J., Kano, M., Urabe, M. (eds.) JCDCG 1998. LNCS, vol.\u00a01763, pp. 119\u2013128. Springer, Heidelberg (2000)"},{"key":"20_CR12","unstructured":"Anton, F., Mioc, D., Gold, C.: Line Voronoi diagram based interpolation and application to digital terrain modelling. In: ISPRS - XXth Congress, vol.\u00a02. International Society for Photogrammetry and Remote Sensing (2004)"},{"key":"20_CR13","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/S0010-4485(03)00059-9","volume":"36","author":"J.D. Boissonat","year":"2004","unstructured":"Boissonat, J.D., Fl\u00f6totto, J.: A coordinate system associated with points scattered on a surface. Computer-Aided Design\u00a036, 161\u2013174 (2004)","journal-title":"Computer-Aided Design"},{"key":"20_CR14","unstructured":"Fan, Q., Efrat, A., Koltun, V., Krishnan, S., Venkatasubramanian, S.: Hardware-assisted natural neighbor interpolation. In: Proc. 7th Workshop on Algorithm Engineering and Experiments (ALENEX) (2005)"},{"key":"20_CR15","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1109\/TVCG.2006.27","volume":"2","author":"S. Park","year":"2006","unstructured":"Park, S., Linsen, L., Kreylos, O., Owens, J., Hamann, B.: Discrete sibson interpolation. IEEE Trans. on Vis. and Comp. Graphics 12\u00a02, 243\u2013253 (2006)","journal-title":"IEEE Trans. on Vis. and Comp. Graphics 12"},{"key":"20_CR16","first-page":"182","volume-title":"Proc. of Dagstuhl Conf. on Sci. Vis.","author":"S.K. Lodha","year":"1999","unstructured":"Lodha, S.K., Franke, R.: Scattered data techniques for surfaces. In: Proc. of Dagstuhl Conf. on Sci. Vis., pp. 182\u2013222. IEEE Comp. Soc. Press, Los Alamitos (1999)"},{"key":"20_CR17","series-title":"Cambridge Monographs on Appl. and Comp. Math.","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511617539","volume-title":"Scattered Data Approximation","author":"H. Wendland","year":"2004","unstructured":"Wendland, H.: Scattered Data Approximation. Cambridge Monographs on Appl. and Comp. Math., vol.\u00a017. Cambridge University Press, Cambridge (2004)"},{"key":"20_CR18","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1145\/116873.116880","volume":"23","author":"F. Aurenhammer","year":"1991","unstructured":"Aurenhammer, F.: Voronoi diagrams - a survey of a fundamental geometric data structure. ACM Computing surveys\u00a023, 345\u2013405 (1991)","journal-title":"ACM Computing surveys"},{"key":"20_CR19","series-title":"Wiley series in probability and statistics","doi-asserted-by":"crossref","DOI":"10.1002\/9780470317013","volume-title":"Spatial Tessellations: Concepts and applications of Voronoi diagrams","author":"A. Okabe","year":"2000","unstructured":"Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations: Concepts and applications of Voronoi diagrams. Wiley series in probability and statistics. John Wiley & Sons Ltd., Chichester (2000)"}],"container-title":["Lecture Notes in Computer Science","Advances in Visual Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11919629_20","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,19]],"date-time":"2019-05-19T17:04:54Z","timestamp":1558285494000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11919629_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9783540486268","9783540486275"],"references-count":19,"URL":"https:\/\/doi.org\/10.1007\/11919629_20","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006]]}}}