Abstract: The estimation of bounds on the second derivative of rational Bézier curves has important applications in CAGD. Considering the numerator and denominator of the expression of rational Bézier curves as the global respectively, the expression of derivatives of rational Bézier curves is given, according to derivative rule. As derivation to Bernstein basis function  decreasing degree of it, and need of gaining better estimation, it is necessary to elevate degrees of Bernstein basis function, so as to make them equal. By a conclusion of inequality involved, the estimation of bounds on the second derivative of rational Bézier curves is obtained.

Key words: rational Bézier curves, degree elevation, second derivative bound

摘要： 有理Bézier曲线二阶导矢界的估计在CAGD中有重要的应用。把有理Bézier曲线的分子和分母分别看成整体，按照求导法则，得到有理Bézier曲线二阶导矢的表达式。由于求导会降低Bernstein基函数的次数，鉴于获取更好的估计式的需要，对其进行必要的升阶，使Bernstein基函数的阶数一致。利用有关的不等式的结论得出有理Bézier曲线二阶导矢界的估计式。

关键词: 有理Bé, zier曲线, 升阶, 二阶导矢界