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The new basis is applied to generate a class of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msup><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>continuous quartic rational Hermite interpolation splines with local tension shape parameters. The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing a<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msup><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>positivity- or monotonicity- preserving interpolation spline. In addition, we extend the quartic rational Said-Ball-like basis to a triangular domain which has three tension shape parameters and includes the cubic triangular Said-Ball basis as a special case. In order to compute the corresponding patch stably and efficiently, a new de Casteljau-type algorithm is developed. Moreover, the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msup><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>continuous conditions are deduced for the joining of two patches.<\/jats:p>","DOI":"10.1155\/2014\/857840","type":"journal-article","created":{"date-parts":[[2014,6,26]],"date-time":"2014-06-26T17:05:46Z","timestamp":1403802346000},"page":"1-18","source":"Crossref","is-referenced-by-count":4,"title":["Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application"],"prefix":"10.1155","volume":"2014","author":[{"given":"Yuanpeng","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuli","family":"Han","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengjun","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(74)90009-8"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(75)90068-8"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(77)90056-2"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1145\/77269.77275"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(91)90037-C"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(95)00047-X"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/s11766-011-2417-z"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(91)90056-3"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02946615"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2007.07.031"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2013.06.043"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/BF02240100"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01932711"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2007.05.023"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.03.034"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1137\/0717021"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/17.2.305"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/S0097-8493(00)00053-4"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/S0097-8493(02)00249-2"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1080\/00207160701595145"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-013-9300-9"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/247120"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/531497"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-013-0071-1"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2008.03.015"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1515\/jnum-2013-0003"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1145\/321607.321609"},{"year":"2011","key":"28"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/857840.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/857840.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/857840.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,29]],"date-time":"2016-07-29T06:16:29Z","timestamp":1469772989000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/857840\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":28,"alternative-id":["857840","857840"],"URL":"https:\/\/doi.org\/10.1155\/2014\/857840","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}