Completeness characterization of Type-I box splines
Completeness characterization of Type-I box splines
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发表时间：
2020-11
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通讯作者：
N. Villamizar;Angelos Mantzaflaris;B. Juttler
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作者：
N. Villamizar;Angelos Mantzaflaris;B. Juttler
基于边接触光滑性质，我们给出了三向三角剖分上的盒样条（也称为I型盒样条空间）的完备性刻画。对于任何给定的I型盒样条，特定的最大程度和秩序的全球光滑，我们的结果允许确定的局部线性子空间的多项式跨越盒样条平移。我们利用箱样条的全局超光滑性质以及在边缘处附加的超光滑条件来刻画由箱样条平移所跨越的样条空间。随后，我们证明了这个空间空间关于盒样条平移所诱导的局部多项式空间的完备性。的完整性属性允许构建的层次空间跨越的转换盒样条的任何多项式次数的多级I型网格。我们提供了一个基础，这些层次盒样条空间下明确的几何条件的域。
We present a completeness characterization of box splines on three-directional triangulations, also called Type-I box spline spaces, based on edge-contact smoothness properties. For any given Type-I box spline, of specific maximum degree and order of global smoothness, our results allow to identify the local linear subspace of polynomials spanned by the box spline translates. We use the global super-smoothness properties of box splines as well as the additional super-smoothness conditions at edges to characterize the spline space spanned by the box spline translates. Subsequently, we prove the completeness of this space space with respect to the local polynomial space induced by the box spline translates. The completeness property allows the construction of hierarchical spaces spanned by the translates of box splines for any polynomial degree on multilevel Type-I grids. We provide a basis for these hierarchical box spline spaces under explicit geometric conditions of the domain.