{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,20]],"date-time":"2025-07-20T04:20:37Z","timestamp":1752985237111,"version":"3.37.3"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2021,10,17]],"date-time":"2021-10-17T00:00:00Z","timestamp":1634428800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,10,17]],"date-time":"2021-10-17T00:00:00Z","timestamp":1634428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61802129"],"award-info":[{"award-number":["61802129"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2018A030310381"],"award-info":[{"award-number":["2018A030310381"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Doctoral Research Project of Chongqing Technology and Business University","award":["1956003"],"award-info":[{"award-number":["1956003"]}]},{"name":"Chongqing Social Science Plan Project","award":["2020YBTJ102"],"award-info":[{"award-number":["2020YBTJ102"]}]},{"name":"Open Project from Chongqing Key Laboratory of Social Economy and the Applied Statistics","award":["KFJJ2018066"],"award-info":[{"award-number":["KFJJ2018066"]}]},{"name":"Mathematic and Statistics Team from Chongqing Technology and Business University","award":["ZDPTTD201906"],"award-info":[{"award-number":["ZDPTTD201906"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s40314-021-01664-7","type":"journal-article","created":{"date-parts":[[2021,10,17]],"date-time":"2021-10-17T10:29:13Z","timestamp":1634466553000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["$$C^1$$ interpolation splines over type-1 triangulations with shape parameters"],"prefix":"10.1007","volume":"40","author":[{"given":"Xiangbin","family":"Qin","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8682-6089","authenticated-orcid":false,"given":"Yuanpeng","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,17]]},"reference":[{"key":"1664_CR1","doi-asserted-by":"publisher","first-page":"1188","DOI":"10.1016\/j.cam.2009.07.035","volume":"234","author":"D Barrera","year":"2010","unstructured":"Barrera D, Guessab A, Ib\u00e1\u00f1ez MJ, Nouisser O (2010) Optimal bivariate $$C^1$$ cubic quasi-interpolation on a type-2 triangulation. J Comput Appl Math 234:1188\u20131199","journal-title":"J Comput Appl Math"},{"key":"1664_CR2","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/j.cam.2018.08.005","volume":"349","author":"D Barrera","year":"2019","unstructured":"Barrera D, Dagnino C, Ib\u00e1\u00f1ez MJ, Remogna S (2019) Quasi-interpolation by $$C^1$$ quartic splines on type-1 triangulations. J Comput Appl Math 349:225\u2013238","journal-title":"J Comput Appl Math"},{"key":"1664_CR3","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/0895-7177(91)90053-A","volume":"15","author":"CV Camp","year":"1991","unstructured":"Camp CV, Gipson GS (1991) Overhauser elements in boundary element analysis. Math Comput Modell 15:59\u201369","journal-title":"Math Comput Modell"},{"key":"1664_CR4","doi-asserted-by":"publisher","first-page":"352","DOI":"10.1080\/10020070612331343269","volume":"17","author":"J Cao","year":"2007","unstructured":"Cao J, Wang GZ (2007) An extension of Bernstein-B\u00e9zier surface over the triangular domain. Prog Nat. Sci. 17:352\u2013357","journal-title":"Prog Nat. Sci."},{"key":"1664_CR5","unstructured":"Clough RW, Tocher JL (1965) Finite element stiffness matrices for analysis of plates in bending. In: Proceedings of the Conference on Matrix Methods in Structural Mechanics, Wright-Patterson A. F. B., OH"},{"key":"1664_CR6","doi-asserted-by":"publisher","first-page":"4183","DOI":"10.1002\/(SICI)1097-0207(19961230)39:24<4183::AID-NME38>3.0.CO;2-9","volume":"39","author":"JF Durodola","year":"1996","unstructured":"Durodola JF, Fenner RT (1996) Overhauser triangular elements for three-dimensional potential problems using boundary element method. Int J Numer Methods Eng 39:4183\u20134198","journal-title":"Int J Numer Methods Eng"},{"key":"1664_CR7","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/0167-8396(86)90016-6","volume":"3","author":"G Farin","year":"1986","unstructured":"Farin G (1986) Triangular Bernstein-B\u00e9zier patches. Comput Aided Geom Des 3:83\u2013127","journal-title":"Comput Aided Geom Des"},{"key":"1664_CR8","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1016\/j.cam.2018.04.061","volume":"343","author":"J Gro\u0161elj","year":"2018","unstructured":"Gro\u0161elj J, Knez M (2018) A B-spline basis for $$C^1$$ quadratic splines on triangulations with a 10-split. J Comput Appl Math 343:413\u2013427","journal-title":"J Comput Appl Math"},{"key":"1664_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cagd.2017.05.003","volume":"57","author":"J Gro\u0161elj","year":"2017","unstructured":"Gro\u0161elj J, Speleers H (2017) Construction and analysis of cubic Powell-Sabin B-splines. Comput Aided Geom Des 57:1\u201322","journal-title":"Comput Aided Geom Des"},{"key":"1664_CR10","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/S0895-7177(00)00057-1","volume":"31","author":"H Hadavinia","year":"2000","unstructured":"Hadavinia H, Travis RP, Fenner RT (2000) $$C^1$$-continuous generalised parabolic blending elements in boundary element method. Math Comput Model 31:17\u201334","journal-title":"Math Comput Model"},{"key":"1664_CR11","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/0895-7177(96)00012-X","volume":"23","author":"PR Johnston","year":"1995","unstructured":"Johnston PR (1995) Second order overhauser elements for boundary element analysis. Math Comput Modell 23:61\u201374","journal-title":"Math Comput Modell"},{"key":"1664_CR12","doi-asserted-by":"publisher","first-page":"2087","DOI":"10.1002\/(SICI)1097-0207(19970615)40:11<2087::AID-NME162>3.0.CO;2-5","volume":"40","author":"PR Johnston","year":"1997","unstructured":"Johnston PR (1997) $$C^2$$-continuous elements for boundary element analysis. Int J Numer Methods Eng 40:2087\u20132108","journal-title":"Int J Numer Methods Eng"},{"key":"1664_CR13","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1016\/j.cam.2013.12.034","volume":"263","author":"I Juh\u00e1sz","year":"2014","unstructured":"Juh\u00e1sz I, R\u00f3th \u00c1 (2014) A scheme for interpolation with trigonometric spline curves. J Comput Appl Math 263:246\u2013261","journal-title":"J Comput Appl Math"},{"key":"1664_CR14","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511721588","volume-title":"Spline functions on triangulations","author":"MJ Lai","year":"2007","unstructured":"Lai MJ, Schumaker LL (2007) Spline functions on triangulations. Cambridge University Press, Cambridge"},{"key":"1664_CR15","unstructured":"Overhauser AW (1968) Analytic definition of curves and surfaces by parabolic blending. Technical Report No. SL68-40, Ford Motor Company Scientific Laboratory"},{"key":"1664_CR16","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1016\/0010-4485(91)90059-6","volume":"23","author":"AP Pobegailo","year":"1991","unstructured":"Pobegailo AP (1991) Local interpolation with weight functions for variable smoothness curve design. Comput Aided Des 23:579\u2013582","journal-title":"Comput Aided Des"},{"key":"1664_CR17","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1145\/355759.355761","volume":"3","author":"MJD Powell","year":"1977","unstructured":"Powell MJD, Sabin MA (1977) Piecewise quadratic approximation on triangles. ACM Trans Math Softw 3:316\u2013325","journal-title":"ACM Trans Math Softw"},{"key":"1664_CR18","doi-asserted-by":"publisher","first-page":"1155","DOI":"10.1016\/0898-1221(86)90019-2","volume":"12","author":"W Schneider","year":"1986","unstructured":"Schneider W (1986) A simple technique for adding tension to parabolic blending interpolation. Comput Math Appl 12:1155\u20131160","journal-title":"Comput Math Appl"},{"key":"1664_CR19","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/j.cagd.2015.05.002","volume":"37","author":"H Speleers","year":"2015","unstructured":"Speleers H (2015) A new B-spline representation for cubic splines over Powell-Sabin triangulations. Comput Aided Geom Des 37:42\u201356","journal-title":"Comput Aided Geom Des"},{"key":"1664_CR20","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1016\/j.cag.2003.08.003","volume":"27","author":"A Wiltsche","year":"2003","unstructured":"Wiltsche A (2003) $$C^1$$- and $$C^2$$-continuous spline-interpolation of a regular triangular net of points. Comput Graph 27:917\u2013930","journal-title":"Comput Graph"},{"key":"1664_CR21","first-page":"67","volume":"9","author":"A Wiltsche","year":"2005","unstructured":"Wiltsche A (2005) Blending curves. J Geom Graph 9:67\u201375","journal-title":"J Geom Graph"},{"key":"1664_CR22","first-page":"2607","volume":"17","author":"HY Wu","year":"2005","unstructured":"Wu HY, Xia CY (2005) Extensions of B\u00e9zier curves and surfaces with multiple shape parameters. J Comput Aided Des Comput Graph 17:2607\u20132612","journal-title":"J Comput Aided Des Comput Graph"},{"key":"1664_CR23","first-page":"2863","volume":"218","author":"LL Yan","year":"2011","unstructured":"Yan LL, Liang JF (2011) An extension of the B\u00e9zier model. Appl Math Comput 218:2863\u20132879","journal-title":"Appl Math Comput"},{"key":"1664_CR24","doi-asserted-by":"publisher","first-page":"1253","DOI":"10.1080\/00207160701821715","volume":"86","author":"LQ Yang","year":"2009","unstructured":"Yang LQ, Zeng XM (2009) B\u00e9zier curves and surfaces with shape parameters. Int J Comput Math 86:1253\u20131263","journal-title":"Int J Comput Math"},{"key":"1664_CR25","doi-asserted-by":"publisher","first-page":"1374","DOI":"10.1145\/1095878.1095885","volume":"24","author":"A Yvart","year":"2005","unstructured":"Yvart A, Hahmann S, Bonneau GP (2005) Hierarchical triangular splines. ACM Trans Graph 24:1374\u20131391","journal-title":"ACM Trans Graph"},{"key":"1664_CR26","first-page":"181","volume":"250","author":"YP Zhu","year":"2015","unstructured":"Zhu YP, Han XL (2015) Quasi-Bernstein-B\u00e9zier polynomials over triangular domain with multiple shape parameters. Appl Math Comput 250:181\u2013192","journal-title":"Appl Math Comput"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01664-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-021-01664-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01664-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,3]],"date-time":"2021-12-03T13:16:35Z","timestamp":1638537395000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-021-01664-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,17]]},"references-count":26,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["1664"],"URL":"https:\/\/doi.org\/10.1007\/s40314-021-01664-7","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2021,10,17]]},"assertion":[{"value":"17 April 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 August 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 September 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 October 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"275"}}