The Blossom Approach to the Dimension of the Bivariate Spline Space

Abstract

The dimension of the bivariate spline space $S^r_n\u0394$ may depend on geometric properties of triangulation \u0394, in particular if $n$ is not much bigger than $r$. In the paper, the blossom approach to the dimension count is outlined. It leads to the symbolic algorithm that gives the answer whether a triangulation is singular or not. The approach is demonstrated on the case of Morgan-Scott partition and twice differentiable splines. \u00a0