On the dimension of spline spaces on planar T-meshes
On the dimension of spline spaces on planar T-meshes
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DOI：
10.1090/s0025-5718-2013-02738-x
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发表时间：
2010-11
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影响因子：
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通讯作者：
B. Mourrain
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文献类型：
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作者：
B. Mourrain
我们分析了平面t网格沿内边缘的二元函数空间，这些二元函数是二次<= (m, m')和光滑度r的分段多项式。利用同调技术给出了该空间维数的新的组合下界和上界。我们将这个维度与t网格的最大内部段的权重联系起来，为这些最大内部段的排序定义。我们表明，对于足够高的度或对于足够规则的分层t网格，下界和上界重合。我们给出了一个细分规则来构造这些下界和上界重合的分层t网格。最后，我们通过分析小度和光滑的样条空间来说明这些结果。
We analyze the space of bivariate functions that are piecewise polynomial of bi-degree <= (m, m') and of smoothness r along the interior edges of a planar T-mesh. We give new combinatorial lower and upper bounds for the dimension of this space by exploiting homological techniques. We relate this dimension to the weight of the maximal interior segments of the T-mesh, defined for an ordering of these maximal interior segments. We show that the lower and upper bounds coincide, for high enough degrees or for hierarchical T-meshes which are enough regular. We give a rule of subdivision to construct hierarchical T-meshes for which these lower and upper bounds coincide. Finally, we illustrate these results by analyzing spline spaces of small degrees and smoothness.