一种端点插值的Bézier曲线降阶的方法  

A method of multidegree reduction of Bézier curves with endpoint interpolations

作　　者：梁秀霞[1] 张彩明[1] 

机构地区：[1]山东大学计算机科学与技术学院,山东济南250100

出　　处：《山东大学学报（理学版）》2004年第1期68-72,共5页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金 ( 6 0 1 730 5 2 );山东省重点自然科学基金 (Z2 0 0 1G0 1 )资助项目

摘　　要：提出了一种端点插值的B啨ｚｉｅｒ曲线降阶的新方法 .利用B啨ｚｉｅｒ曲线升阶公式产生端点插值降阶的约束条件 .新的B啨ｚｉｅｒ曲线通过极小化降阶前和降阶后两曲线的一阶导矢之差的平方的积分产生 ,从而把新旧控制点之间应满足的关系归结为一个导致线性方程组的目标函数 ,通过求解线性方程组求出降阶曲线的控制点 ,实现了一次降多阶逼近 .本文还通过实例对新方法和已有方法的逼近精度进行了比较 .A new method is presented for reducing the degree of Bézier curve, which preserves arbitrary degree interpolation conditions at the two endpoints of the curve. The elevation property of Bézier curves is used to develop the constraints of endpoints continuity. New curve is obtained by minimizing the integrated square of the difference between the first derivatives of the new and old curve. So the relations which should be satisfied by the new and the old control points is formulized as an objective function that results in a linear equations. The new control points are obtained by solving a linear equation and multidegree reduction at one time is realized. Examples for comparing the new method with the existing ones are included.

关 键 词：BÉZIER曲线 升阶 降多阶 逼近 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]