New geometric methods for fast evaluation of derivatives of polynomial and rational Bézier curves are proposed. They apply an algorithm for evaluating polynomial or rational Bézier curves, which was recently given by the authors. Numerical tests show that the new approach is more efficient than the methods which use the famous de Casteljau algorithm. The algorithms work well even for high-order derivatives of rational Bézier curves of high degrees.

中文翻译：

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贝塞尔曲线导数的快速评估

提出了快速评估多项式和有理贝塞尔曲线导数的新几何方法。他们应用了作者最近给出的评估多项式或有理贝塞尔曲线的算法。数值测试表明，新方法比使用著名的 de Casteljau 算法的方法更有效。即使对于高次有理贝塞尔曲线的高阶导数，该算法也能很好地工作。