Dimensions and bases of hierarchical tensor-product splines
Abstract
We prove that the dimension of trivariate tensor-product spline space of tri-degree (m,m,m) with maximal order of smoothness over a three- dimensional domain coincides with the number of tensor-product B-spline basis functions acting effectively on the domain considered. A domain is required to belong to a certain class. This enables us to show that, for a cer- tain assumption about the configuration of a hierarchical mesh, hierarchical B-splines span the spline space. This paper presents an extension to three-dimensional hierarchical meshes of results proposed recently by Giannelli and Ju ̈ttler for two-dimensional hierarchical meshes.
Domains
Algebraic Geometry [math.AG]
Origin : Files produced by the author(s)
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