由细层凸镶嵌构造的多项式再生样条空间
Polynomial-reproducing spline spaces from fine zonotopal tilings
摘要：
给定一个点配置A，我们揭示了多项式再生样条空间之间的连接conv（A）的子集和细zonotopal tilings的zonotope Z（V）相关联的相应的向量配置。这种联系直接推广了Delaunay构形上的一个已知结果，并且由于它的组合性质，自然地包含了A中重复点和仿射依赖点的情形。我们证明了这样的空间的一般迭代构造过程的存在性。最后，我们把我们的注意力经常细zonotopal平铺，专门我们以前的结果和利用的邻接图的平铺提出了一套实用的算法，相关的样条函数的建设和评价。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
