  We classify all possible local linear procedures over triangular meshes
resulting in polynomial $C^1$-spline functions with affinely uniform shape for
the basic functions at the edges, and fitting the 9 value- and gradient data at
the vertices of the mesh members. There is a unique procedure among them with
shape functions and basic polynomials of degree 5 and all other admissible
procedures are its perturbations with higher degree.
