The structure of C1 spline spaces on freudenthal partitions

We analyze the structure of trivariate C-1 splines on uniform tetrahedral partitions Delta. The Freudenthal partitions Delta are obtained from uniform cube partitions by using three planes with a common line to subdivide every cube into six tetrahedra. This is a natural three-dimensional generalization of the well-known three-directional mesh in the plane. By using Bernstein-Bezier techniques, we construct minimal determining sets for C-1 spline spaces on Delta of arbitrary degree and give explicit formulae for the dimension of the spaces.