Abstract
We construct local generators, comprising r functions, for refinable spaces of bivariate Cn-1 spline functions of degree n on meshes comprising all lines through points of the integer lattice in the directions of n + r + 1 pairwise linearly independent vectors with integer components. The generators are characterised by their Fourier transforms. Their shifts are shown to form a Riesz basis if and only if at most r lines in the mesh intersect other than in the integer lattice, which can occur for n ≤ 2r - 1. The symmetry of these generators is studied and examples are given.
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Goodman, T. Multi-Box Splines. Constr Approx 25, 279–301 (2007). https://doi.org/10.1007/s00365-006-0654-3
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DOI: https://doi.org/10.1007/s00365-006-0654-3