On the Structure of Bézier Nets

Abstract

The distance between two neighbouring multivariate Bézier nets is proved to be $O(m^{-2})$ in this paper. As a consequence, the sequence of Bézier nets is uniformly convergent with the optimal approximation order $O(m^{-1})$. Furthermore, the structures of Bézier nets are explored by investigating how the piecewise linear surface tends to the Bézier surface of $C^{\infty}$.