Splines can be constructed by convolving the indicator function of a cell whose shifts tessellate R n . This paper presents simple, geometric 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. 
Refinability of splines derived from regular tessellations