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Given a grid in R d , consisting of d bi-infinite sequences of hyperplanes (possibly with multiplici-ties) 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… (More)

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 (Mokriš et al., 2014). While the first mechanism ensures the partition of unity property, which is essential for geometric modeling applications, the… (More)

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