2m次Bèzier曲线自适应降次逼近算法

2m-Degree Bézier Plane Parametric Curves 1-Order Reduction Approximation and it's Error Analysis

给出了封闭的2m次Bèzier曲线的降次逼近公式,并讨论了相应的逼近误差。文章工作除了具有传统的端点约束、C1—约束外,还具有以下特点:首先,基于欧几里德范数讨论逼近误差,更加符合人们的认识;其次,对于分段降阶逼近的情形,首先考虑并采用了选择拐点的策略;第三,考虑并采用了选择极大值点的策略。大量数值试验表明:第二、三两条策略的采用可以在很大程度上减少了2m-1次Bèzier曲线段达到逼近2m次Bèzier平面曲线的容差要求。

Presents an algorithm for approximating an n=2m degree Bézier plane parametric curves using(2m-1)th degree Bézier plane parametric curves.Then,the error analysis of the algorithm is discussed.Also gives a formula of computing error in order-reduction of Bézier plane parametric 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 C1-constrained and end-constrained order-reduction of a plane parametric curve,and numerical result is compared visually to that of the best order-reduction method.