Trivariate $C^1$-continuous macro-elements based on splits of a tetrahedron

Using Bernstein-Bézier techniques, we discuss construction of several trivariate $C^1$ macro-elements based on different splits of a single tetrahedron: Alfeld split, Clough-Tocher split, Powell-Sabin split and their modifications. The construction includes the associate spline space and its dimension, local Bernstein-Bézier basis, data, approximation order and geometric constraints if applicable.