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

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.