(untitled) (Journal of Computational Mathematics, 2021)
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^∞.