Dimension ofC1-splines on type-6 tetrahedral partitions

Abstract

We consider a linear space of piecewise polynomials in three variables which are globally smooth, i.e. trivariate C 1 -splines of arbitrary polynomial degree. The splines are defined on type-6 tetrahedral partitions, which are natural generalizations of the four-directional mesh. By using Bernstein-Bézier techniques, we analyze the structure of the spaces and establish formulae for the dimension of the smooth splines on such uniform type partitions.