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Volume 18, Issue 2
The Blossom Approach to the Dimension of the Bivariate Spline Space

Zhi-Bin Chen, Yu-Yu Feng & Jernej Kozak

J. Comp. Math., 18 (2000), pp. 183-198.

Published online: 2000-04

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  • Abstract

The dimension of the bivariate spline space $S^r_nΔ$ may depend on geometric properties of triangulation Δ, in particular if $n$ is not much bigger than $r$. In the paper, the blossom approach to the dimension count is outlined. It leads to the symbolic algorithm that gives the answer whether a triangulation is singular or not. The approach is demonstrated on the case of Morgan-Scott partition and twice differentiable splines.  

  • Keywords

Bivariate spline space Blossom Dimension

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COPYRIGHT: © Global Science Press

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@Article{JCM-18-183, author = {Chen , Zhi-BinFeng , Yu-Yu and Kozak , Jernej}, title = {The Blossom Approach to the Dimension of the Bivariate Spline Space}, journal = {Journal of Computational Mathematics}, year = {2000}, volume = {18}, number = {2}, pages = {183--198}, abstract = {

The dimension of the bivariate spline space $S^r_nΔ$ may depend on geometric properties of triangulation Δ, in particular if $n$ is not much bigger than $r$. In the paper, the blossom approach to the dimension count is outlined. It leads to the symbolic algorithm that gives the answer whether a triangulation is singular or not. The approach is demonstrated on the case of Morgan-Scott partition and twice differentiable splines.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9034.html} }
TY - JOUR T1 - The Blossom Approach to the Dimension of the Bivariate Spline Space AU - Chen , Zhi-Bin AU - Feng , Yu-Yu AU - Kozak , Jernej JO - Journal of Computational Mathematics VL - 2 SP - 183 EP - 198 PY - 2000 DA - 2000/04 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9034.html KW - Bivariate spline space KW - Blossom KW - Dimension AB -

The dimension of the bivariate spline space $S^r_nΔ$ may depend on geometric properties of triangulation Δ, in particular if $n$ is not much bigger than $r$. In the paper, the blossom approach to the dimension count is outlined. It leads to the symbolic algorithm that gives the answer whether a triangulation is singular or not. The approach is demonstrated on the case of Morgan-Scott partition and twice differentiable splines.  

Chen , Zhi-BinFeng , Yu-Yu and Kozak , Jernej. (2000). The Blossom Approach to the Dimension of the Bivariate Spline Space. Journal of Computational Mathematics. 18 (2). 183-198. doi:
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