On the completeness of hierarchical tensor-product B-splines
نویسندگان
چکیده
منابع مشابه
On the completeness of hierarchical tensor-product B-splines
Given a grid in R, consisting of d bi-infinite sequences of hyperplanes (possibly with multiplicities) orthogonal to the d axes of the coordinate system, we consider the spaces of tensor-product spline functions of a given degree on a multi-cell domain. Such a domain consists of finite set of cells which are defined by the grid. A piecewise polynomial function belongs to the spline space if its...
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We construct a uniformly stable family of bases for tensor product spline approximation on domains in Rd. These bases are derived from the standard B-spline basis by normalization with respect to the L p-norm and a selection process relying on refined estimates for the de Boor-Fix functionals.
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We prove that the dimension of bivariate tensor–product spline spaces of bi– degree (d, d) with maximum order of smoothness on a multi–cell domain (more precisely, on a set of cells from a tensor–product grid) is equal to the number of tensor–product B–spline basis functions, defined by only single knots in both directions, acting on the considered domain. A certain reasonable assumption on the...
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We prove that the dimension of trivariate tensor-product spline space of tri-degree (m,m,m) with maximal order of smoothness over a threedimensional 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 certain assumption about the configurati...
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We introduce a novel basis for multivariate hierarchical tensor-product spline spaces. Our construction combines the truncation mechanism (Giannelli et al., 2012) with the idea of decoupling basis functions (Mokrǐs et al., 2014). While the first mechanism ensures the partition of unity property, which is essential for geometric modeling applications, the idea of decoupling allows us to obtain a...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2014
ISSN: 0377-0427
DOI: 10.1016/j.cam.2014.04.001