Tetrahedral $C^m$ Interpolation by Rational Functions

Abstract

A general local $C^m (m \ge 0)$ tetrahedral interpolation scheme by polynomials of degree $4m+1$ plus low order rational functions from the given data is proposed. The scheme can have either $4m+1$ order algebraic precision if $C^{2m}$ data at vertices and $C^m$ data on faces are given or $k+E[k/3]+1$ order algebraic precision if $C^k (k \le 2m)$ data are given at vertices. The resulted interpolant and its partial derivatives of up to order $m$ are polynomials on the boundaries of the tetrahedra.