We describe a new de Casteljau–type algorithm for complex rational Bézier curves. After proving that these curves exhibit the maximal possible circularity, we construct their points via a de Casteljau–type algorithm over complex numbers. Consequently, the line segments that correspond to convex linear combinations in affine spaces are replaced by circular arcs. In difference to the algorithm of Sánchez-Reyes (2009), the construction of all the points is governed by (generically complex) roots of the denominator, using one of them for each level. Moreover, one of the bi-polar coordinates is fixed at each level, independently of the parameter value. A rational curve of the complex degree n admits generically n! distinct de Casteljau–type algorithms, corresponding to the different orderings of the denominator's roots.

我们描述了一种新的 de Casteljau 型复杂有理贝塞尔曲线算法。在证明这些曲线表现出最大可能的圆度后，我们通过复数上的 de Casteljau 型算法构造它们的点。因此，仿射空间中对应于凸线性组合的线段被圆弧代替。与Sánchez-Reyes (2009)的算法不同，所有点的构造均由分母的（一般复数）根控制，每个级别使用其中一个根。此外，其中一个双极坐标在每一级都是固定的，与参数值无关。复数为n的有理曲线一般承认n ! 不同的 de Casteljau 类型算法，对应于分母根的不同排序。