复杂曲线逼近是CAGD中的基本问题,传统deCasteljau算法通常固定细分参数为0.5.本文考虑平面Bézier曲线的凸包最小和扁平度最小两种情况,分别给出凸包最优和扁平度最优的细分参数的定义和计算方法,使每次细分后得到的新控制多边形更好地逼近原曲线.通过分析不同类型曲线的最优参数发现,对于较小的曲线段,细分参数选为0.5具有一定的合理性.比较扁平最小方法与deCasteljau定参数方法发现:对于形状复杂的曲线,前者细分效率提高50%以上;对于简单曲线,二者相当.

Complex curve approximation is a basic problem in CAGD, and the traditional de Casteljau algorithm is commonly used with the fixed parameter value of 0.5. To achieve better subdivided curves in approximation, we consider two different choices of the subdivision parameters for the planar Bézier curves. The two choices of the parameter are associated with convex hull area minimization and convex hull flat minimization. The definitions and algorithms of the parameters are proposed in both cases. By analyzing the parameters for different types of curves, we find that the optimal parameter volues are close to 0.5 when the curve segments are short enough. This fact indicates that it is reasonable to select the parameter value of 0.5 for the small curve segments. For some complex curves the least flat method improves the efficiency of the subdivision by more than 50%, compared to the traditional de Casteljau method. For other curves, the two methods have similar efficiency.