论文标题
从精细的扎根砖中的多项式改造的样条空间
Polynomial-reproducing spline spaces from fine zonotopal tilings
论文作者
论文摘要
给定一个点配置a，我们发现了与相应的向量配置相关的Zonotope Z（v）的conv（a）子集的多项式取消样条空间与精细的Zonotopal块之间的连接。该链接直接概括了Delaunay配置的已知结果，并且由于其组合特征，这是A中的重复和依赖点的情况。我们证明了此类空间的一般迭代构建过程。最后，我们将注意力转移到常规的精细质量砖上，专门研究我们先前的结果并利用瓷砖的邻接图，以提出一系列实用算法，以构建和评估相关的样条函数。
Given a point configuration A, we uncover a connection between polynomial-reproducing spline spaces over subsets of conv(A) and fine zonotopal tilings of the zonotope Z(V) associated to the corresponding vector configuration. This link directly generalizes a known result on Delaunay configurations and naturally encompasses, due to its combinatorial character, the case of repeated and affinely dependent points in A. We prove the existence of a general iterative construction process for such spaces. Finally, we turn our attention to regular fine zonotopal tilings, specializing our previous results and exploiting the adjacency graph of the tiling to propose a set of practical algorithms for the construction and evaluation of the associated spline functions.
