论文标题
I型盒子花纹的完整性表征
Completeness characterization of Type-I box splines
论文作者
论文摘要
我们基于边缘接触平滑度属性，在三个方向三角形（也称为I型盒子样条空间）上呈现盒子花纹的完整性表征。对于任何给定的类型I框样条，具有特定的最大程度和全局平滑度的顺序，我们的结果允许识别由盒子样条跨度转换的多项式的局部线性子空间。我们使用盒子花纹的全局超平滑度属性以及边缘的其他超平滑度条件来表征由盒子样条跨度翻译的样条空间。随后，我们证明了该空间空间相对于盒子样条诱导的局部多项式空间的完整性。完整性属性允许构建由盒子花纹的翻译跨越的层次空间，该框架花纹在多项式I型网格上的任何多项式学位。我们在域的明确几何条件下为这些层次框样条空间提供了基础。
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.
