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Volume 5, Issue 4
On the Structure of Bézier Nets

Jia-Chang Sun & Kang Zhao

J. Comp. Math., 5 (1987), pp. 376-382.

Published online: 1987-05

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  • 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 $C^{\infty}$.

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@Article{JCM-5-376, author = {Jia-Chang Sun and Kang Zhao}, title = {On the Structure of Bézier Nets}, journal = {Journal of Computational Mathematics}, year = {1987}, volume = {5}, number = {4}, pages = {376--382}, 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 $C^{\infty}$.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9561.html} }
TY - JOUR T1 - On the Structure of Bézier Nets AU - Jia-Chang Sun & Kang Zhao JO - Journal of Computational Mathematics VL - 4 SP - 376 EP - 382 PY - 1987 DA - 1987/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9561.html KW - AB -

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 $C^{\infty}$.

Jia-Chang Sun and Kang Zhao. (1987). On the Structure of Bézier Nets. Journal of Computational Mathematics. 5 (4). 376-382. doi:
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