一种用多项式曲线逼近有理曲线的新方法  

A new method for approximation of rational curves by parametric polynomial curves

作　　者：杨连喜[1] 徐晨东[1] 

机构地区：[1]宁波大学理学院,浙江宁波315211

出　　处：《浙江大学学报（理学版）》2015年第1期21-27,共7页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11101230;11371209);浙江省自然科学基金资助项目(LY13A010013);宁波大学学科项目资助(XKL11D2051)

摘　　要：研究了用多项式曲线逼近有理曲线的新方法,利用结式将有理曲线参数方程转化为隐式代数方程,然后将逼近问题转化为一个以多项式为目标函数的优化问题,求解该问题得到待定参数的值,从而确定多项式曲线.数值算例表明,该方法计算简便,具有较好的逼近效果,且使得利用Hausdorff距离定义的曲线间逼近误差较小.A new method for approximation of rational curves by polynomial curves is proposed. The parametric equation of the rational curve can be transformed into an implicit algebraic equation through the resultant method. Then the approximation problem is transformed into an optimization problem with polynomial objective function. Solve this problem to get the parameters so that the polynomial curve is determined. Numerical examples show that our method is simpler in calculating and have better approximation results. Additionally, We obtain smaller error between the curves defined by Hausdorff distance.

关 键 词：有理曲线 BÉZIER曲线 结式 HAUSDORFF距离 

分 类 号：O241.5[理学—计算数学] TP391[理学—数学]