On explicit basis of bivariate spline space |
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Authors: | Baocai Yin Wen Gao |
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Institution: | (1) Department of Computer Science, Beijing Polytechnic University, 100022 Beijing, PRC;(2) Department of Computer Science, Harbin Institute of Technology, 150001 Harbin, PRC |
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Abstract: | For a subdivision Δ of a region in d-dimensional Euclidean space, we consider computation of dimension and of basis function
in spline space S
k
r
(Δ) consisting of all C piecewise polynomial functions over Δ of degree at most k. A computational scheme is presented for
computing the dimension and bases of spline space S
k
r
(Δ). This scheme based on the Grobner basis algorithm and the smooth co-factor method for computing multivariate spline. For
bivariate splines, explicit basis functions of S
k
r
(Δ) are obtained for any integer k and r when Δ is a cross-cut partition.
The Project is partly supported by the Science and Technology New Star Plan of Beijing and Education Committee of Beijing. |
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Keywords: | |
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