带形状参数Bézier曲线的G^1连续降阶方法的研究

The Study on Degree Reduction of G^1-continuity of Bézier Curves with Shape Parameter

基于L2范数下的n次带形状参数Bézier曲线,给出了一种在G1连续条件下的一次降多阶逼近方法.求出待降阶曲线和降阶逼近曲线在L2范数下的误差函数,利用共轭梯度迭代法使其最小化,得到新的降阶逼近曲线的控制顶点.并且利用数值实例,与其它降阶方法相比较,说明本文方法更有效.

The Bézier curve with shape parameter of degree n in L2-norm was discussed and a method about the multi-degree reduction of its G1-continuity was presented.The error function in L2-norm between the degree reduced curves and degree reduction of approximation curves was solved and the error was minimized by conjugate gradient iteration method.The new control points were obtained.Compared with other methods by numerical examples,this method is more effective.