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.
|Number of pages||23|
|Publication status||Published - 2007|