{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T20:53:45Z","timestamp":1761512025918},"reference-count":0,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2003,3,21]],"date-time":"2003-03-21T00:00:00Z","timestamp":1048204800000},"content-version":"vor","delay-in-days":4250,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Computer Graphics Forum"],"published-print":{"date-parts":[[1991,8]]},"abstract":"<jats:p>This paper describes first results of a test implementation that implements the new multivariate B\u2010splines as recently developed by Dahmen et al. 10for quadratics and cubics. The surface scheme is based on blending functions and control points and allows the modelling of <jats:styled-content><jats:italic>C<\/jats:italic><jats:sup><jats:italic>k<\/jats:italic>\u2212 1<\/jats:sup><\/jats:styled-content> \u2010continuous piecewise polynomial surfaces of degree <jats:italic>k<\/jats:italic> over arbitrary triangulations of the parameter plane. The surface scheme exhibits both affine invariance and the convex hull property, and the control points can be used to manipulate the shape of the surface locally. Additional degrees of freedom in the underlying knot net allow for the modelling of discontinuities. Explicit formulas are given for the representation of polynomials and piecewise polynomials as linear combinations of B\u2010splines.<\/jats:p>","DOI":"10.1111\/1467-8659.1040309","type":"journal-article","created":{"date-parts":[[2004,12,21]],"date-time":"2004-12-21T12:44:59Z","timestamp":1103633099000},"page":"309-317","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Control Points for Multivariate B\u2010Spline Surfaces over Arbitrary Triangulations"],"prefix":"10.1111","volume":"10","author":[{"given":"Philip","family":"Fong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hans\u2010Peter","family":"Seidel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2003,3,21]]},"container-title":["Computer Graphics Forum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2F1467-8659.1040309","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/1467-8659.1040309","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T00:09:56Z","timestamp":1698019796000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/1467-8659.1040309"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,8]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1991,8]]}},"alternative-id":["10.1111\/1467-8659.1040309"],"URL":"https:\/\/doi.org\/10.1111\/1467-8659.1040309","archive":["Portico"],"relation":{},"ISSN":["0167-7055","1467-8659"],"issn-type":[{"value":"0167-7055","type":"print"},{"value":"1467-8659","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,8]]},"assertion":[{"value":"2003-03-21","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}