New geometric methods for fast evaluation of derivatives of polynomial and rational B\'{e}zier curves are proposed. They apply an algorithm for evaluating polynomial or rational B\'{e}zier 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 B\'{e}zier curves of high degrees.

翻译：本文提出了多项式与有理Bézier曲线导数快速求值的新几何方法。这些方法应用了作者近期提出的多项式或有理Bézier曲线求值算法。数值实验表明，新方法比使用著名的de Casteljau算法的方法效率更高。即使对于高次有理Bézier曲线的高阶导数，该算法也能良好运行。