摘要
本文给出了矩形域上Bernstein-Bezier多项式的一般升阶公式,并证明了它的升阶系数的极限逼近性质。在此基础上,得到了多项式为正和(强)凸的充分必要条件。
The degree elevation formula for the Bernstein-Bezier polynomial over rectangles is presented, and the limit approximating property of the coefficients (Farin Theorem) is proved. Based on the formula, this paper obtains the conditions (necessary and sufficient) for the positivity and (strong) convexity of the Bernstein-Bezier polynomial over rectangles.
基金
The projet supported by NNSF of China and SF of Chinese Educational Committee
关键词
BEZIER
多项式
正性
凸性
伯恩斯坦
degree elevation, the Bernstein-Bezier polynomial, positivity, convexity
