Variational trivariate fitting using Worsey-Piper macro elements on tetrahedral partitions (Q554548)

The authors present a method to construct a trivariate \(C^1\) quadratic spline that approximates a set of Lagrangian data scattered over a subset of \(\mathbb R^3\) in an \(L_2\) sense, and that simultaneously minimizes an energy functional. The method is based on the approach of \textit{A. J. Worsey} and \textit{B. Piper} [Comput. Aided Geom. Des. 5, No.~3, 177--186 (1988; Zbl 0654.65008)] for decomposing the basic domain that contains all data points into a number of tetrahedra and on solving the corresponding local problems on these tetrahedra. The convergence properties of this approach are investigated and some examples are provided.