{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:54:39Z","timestamp":1753883679544,"version":"3.41.2"},"reference-count":12,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,4,10]],"date-time":"2012-04-10T00:00:00Z","timestamp":1334016000000},"content-version":"vor","delay-in-days":100,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Liaoning Educational Committee","award":["L2010221"],"award-info":[{"award-number":["L2010221"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>This paper is concerned with the nonnegativity preserving interpolation of data on rectangular grids. The function is a kind of bivariate rational interpolation spline with parameters, which is <jats:italic>C<\/jats:italic><jats:sup>1<\/jats:sup> in the whole interpolation region. Sufficient conditions are derived on coefficients in the rational spline to ensure that the surfaces are always nonnegative if the original data are nonnegative. The gradients at the data sites are modified if necessary to ensure that the nonnegativity conditions are fulfilled. Some numerical examples are illustrated in the end of this paper.<\/jats:p>","DOI":"10.1155\/2012\/624978","type":"journal-article","created":{"date-parts":[[2012,4,10]],"date-time":"2012-04-10T21:02:56Z","timestamp":1334091776000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Nonnegativity Preserving Interpolation by <i>C<\/i><sup>1<\/sup> Bivariate Rational Spline Surface"],"prefix":"10.1155","volume":"2012","author":[{"given":"Xingxuan","family":"Peng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhihong","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qian","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2012,4,10]]},"reference":[{"key":"e_1_2_8_1_2","first-page":"379","volume-title":"Wavelets, Images, and Surface Fitting","author":"Mulansky B.","year":"1994"},{"key":"e_1_2_8_2_2","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1016\/0097-8493(95)00036-C","article-title":"Visualization of surface data to preserve positivity and other simple constraints","volume":"19","author":"Brodlie K.","year":"1995","journal-title":"Computers and Graphics"},{"key":"e_1_2_8_3_2","first-page":"253","volume-title":"Scientific Visualization: Overviews, Methodologies and Techniques","author":"Brodlie K.W.","year":"1997"},{"key":"e_1_2_8_4_2","unstructured":"CheangW. H. Positivity preserving surface interpolation thesis 1994 Universiti Sains Malaysia."},{"key":"e_1_2_8_5_2","unstructured":"ChanE. S. KongV. P. andOngB. H. ConstrainedC1interpolation on rectangular grids Proceedings of the International Conference on Computer Graphics Imaging and Visualization 2004 Penang Malaysia."},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.11.094"},{"key":"e_1_2_8_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2007.04.009"},{"key":"e_1_2_8_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2006.04.021"},{"key":"e_1_2_8_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.03.034"},{"key":"e_1_2_8_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2007.05.023"},{"key":"e_1_2_8_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0096-3003(94)00086-J"},{"volume-title":"Curve and Surface Fitting: An Introduction","year":"1986","author":"Lancaster P.","key":"e_1_2_8_12_2"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/624978.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/624978.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/624978","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:09:47Z","timestamp":1718089787000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/624978"}},"subtitle":[],"editor":[{"given":"Kai","family":"Diethelm","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/624978"],"URL":"https:\/\/doi.org\/10.1155\/2012\/624978","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2012-01-07","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-02-08","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-04-10","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"624978"}}