%0 Journal Article
%T Refinability of splines derived from regular tessellations
%A J£¿rg Peters
%J Mathematics
%D 2012
%I arXiv
%X Splines can be constructed by convolving the indicator function of a cell whose shifts tessellate $\R^k$. This paper presents simple, non-algebraic criteria that imply that, for regular shift-invariant tessellations, only a small subset of such spline families yield nested spaces: primarily the well-known tensor-product and box splines. Among the many non-refinable constructions are hex-splines and their generalization to the Voronoi cells of non-Cartesian root lattices.
%U http://arxiv.org/abs/1210.5532v2