A trivariate Powell-Sabin interpolant
AJ Worsey, B Piper - Computer Aided Geometric Design, 1988 - Elsevier
We consider the problem of producing a piecewise quadratic C 1 interpolant to positional
and gradient information at the vertices of a tessellation in 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 Powell-Sabin element. Since the interpolant is …
and gradient information at the vertices of a tessellation in 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 Powell-Sabin element. Since the interpolant is …
