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Bivariate C1 Cubic Spline Spaces Over Even Stratified Triangulations |
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| Authors: | Huan-Wen Liu Don Hong |
| Institution: | (1) School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, Australia;(2) Department of Mathematics, East Tennessee, State University, Johnson City, TN, 37614-0663; e-mail;(3) Present address: Department of Mathematics, Guangxi University for Nationalities, Nanning, Guangxi, 530006, P.R. China. e-mail |
| Abstract: | It is well-known that the basic properties of a bivariate spline space such as dimension and approximation order depend on the geometric structure of the partition. The dependence of geometric structure results in the fact that the dimension of a C 1 cubic spline space over an arbitrary triangulation becomes a well-known open problem. In this paper, by employing a new group of smoothness conditions and conformality conditions, we determine the dimension of bivariate C 1 cubic spline spaces over a so-called even stratified triangulation. |
| Keywords: | Bivariate C1 cubic spline smoothness conditions conformality conditions even stratified triangulation dimension |
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