Variational trivariate fitting using Worsey–Piper macro elements on tetrahedral partitions

In this paper we present a method to obtain a trivariate spline constructed over the Worsey–Piper split corresponding to a tetrahedron. Such spline approximates a set of Lagrangian scattered data by minimizing an “energy functional” which also controls the smoothness of the spline. We give a convergence result and we show some graphical examples.