基于拐点分割高阶奇次贝济埃曲线降一阶逼近

Higher odd degree Bézier curves 1degree reduction approximation based on inflect subdivision

给出了2m+1(m≥2)次贝济埃曲线降一阶逼近方法。该方法除了具有传统的端点约束和C1—约束外,还具有以下特点:基于欧几里德范数讨论逼近误差,更加符合人们的直观认识;对于分段降阶逼近的情形,不考虑尖点情形;首先考虑并采用了选择拐点的策略;考虑并采用了选择二重点(自交点、结点)等奇点的策略;考虑并采用了选择曲率局部极大值点的策略。数值试验表明:这几条策略的采用可以在很大程度上减少2m次贝济埃曲线段,而达到逼近2m+1次贝济埃平面曲线的容差要求。

An algorithm for approximating an n=2m+1 degree Bézier curves is presented by using 2mth degree Bézier curves. Then, the error analysis of the algorithm was discussed. A formula of computing error was given in degree reduction of Bézier curves and original curves. The representations in closed form for the coefficients and the error bound are very useful to user of Computer Graphics, CAGD or CAD/CAM systems. Using the error bound in the closed form, a simple subdivision scheme for C k -constrained and end-con- strained order-reduction of a curve, and numerical result were compared visually to that of the best order-reduction method.