A trivariate Powell-Sabin interpolant
We consider the problem of producing a piecewise quadratic C 1 interpolant to positional and gradient information at the vertices of a tessellation in \({\mathbb{R}}^ 3 \)of tetrahedra. By splitting each tetrahedron in an appropriate way we show how the problem may be solved. The solution does rely upon the fact that certain geometric constraints must be satisfied. We consider these, and examine how they might be met through a splitting process which is a generalization of that for the bivariate element studied by \textit{M. J. Powell} and \textit{M. A. Sabin} [ACM Trans. Math. Software 3, 316-325 (1977; Zbl 0375.41010)]. Since the interpolant is piecewise quadratic, it can be contured easily.
scientific article; zbMATH DE number 4068144