{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:15Z","timestamp":1740134535683,"version":"3.37.3"},"reference-count":28,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["60970097","11271376","CX2012B111"],"award-info":[{"award-number":["60970097","11271376","CX2012B111"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["60970097","11271376","CX2012B111"],"award-info":[{"award-number":["60970097","11271376","CX2012B111"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Graduate Students Scientific Research Innovation Project of Hunan Province","award":["60970097","11271376","CX2012B111"],"award-info":[{"award-number":["60970097","11271376","CX2012B111"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Within the general framework of Quasi Extended Chebyshev space, we prove that the cubic trigonometric B\u00e9zier basis with two shape parameters<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>\u03bb<\/mml:mi><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>\u03bc<\/mml:mi><\/mml:mrow><\/mml:math>given in Han et al. (2009) forms an optimal normalized totally positive basis for<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>\u03bb,<\/mml:mi><mml:mi>\u03bc<\/mml:mi><mml:mo>\u2208(-<\/mml:mo><mml:mn mathvariant=\"normal\">2,1<\/mml:mn><mml:mo stretchy=\"false\">]<\/mml:mo><\/mml:math>. Moreover, we show that for<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mi>\u03bb<\/mml:mi><mml:mo>=-<\/mml:mo><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:math>or<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mi>\u03bc<\/mml:mi><mml:mo>=-<\/mml:mo><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:math>the basis is not suited for curve design from the blossom point of view. In order to compute the corresponding cubic trigonometric B\u00e9zier curves stably and efficiently, we also develop a new corner cutting algorithm.<\/jats:p>","DOI":"10.1155\/2014\/198745","type":"journal-article","created":{"date-parts":[[2014,3,17]],"date-time":"2014-03-17T17:01:16Z","timestamp":1395075676000},"page":"1-5","source":"Crossref","is-referenced-by-count":3,"title":["Total Positivity of the Cubic Trigonometric B\u00e9zier Basis"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7708-6971","authenticated-orcid":true,"given":"Xuli","family":"Han","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanpeng","family":"Zhu","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\/0021-9045(79)90017-0"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02510180"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(96)00061-1"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(95)00022-4"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(96)00019-2"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2005.04.009"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(02)00089-4"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(02)00126-7"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-03-01530-8"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2004.10.008"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2005.02.013"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2004.03.001"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2008.03.015"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.07.065"},{"issue":"3","key":"15","first-page":"441","volume":"10","year":"2013","journal-title":"International Journal of Computer Science"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/247120"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/531497"},{"issue":"3","key":"18","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.eij.2013.09.002","volume":"14","year":"2013","journal-title":"Egyptian Informatics Journal"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-013-0071-1"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(01)00031-0"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-007-0133-7"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-008-0164-8"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-011-9461-x"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-010-0312-9"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-002-0530-1"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1007\/BF02071384"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(99)00035-7"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511618994"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/198745.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/198745.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/198745.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T05:44:54Z","timestamp":1498110294000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/198745\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":28,"alternative-id":["198745","198745"],"URL":"https:\/\/doi.org\/10.1155\/2014\/198745","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}