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On explicit basis of bivariate spline space

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Approximation Theory and its Applications

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 rk (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 rk (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 rk (Δ) are obtained for any integer k and r when Δ is a cross-cut partition.

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Authors and Affiliations

  1. Department of Computer Science, Beijing Polytechnic University, 100022, Beijing, PRC

    Baocai Yin

  2. Department of Computer Science, Harbin Institute of Technology, 150001, Harbin, PRC

    Wen Gao

Authors
  1. Baocai Yin
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  2. Wen Gao
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Additional information

The Project is partly supported by the Science and Technology New Star Plan of Beijing and Education Committee of Beijing.

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Yin, B., Gao, W. On explicit basis of bivariate spline space. Approx. Theory & its Appl. 14, 53–65 (1998). https://doi.org/10.1007/BF02856149

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  • DOI: https://doi.org/10.1007/BF02856149

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