Bézier曲线的单侧降阶逼近

Approximation of Bézier curve with unilateral degree reduction

为解决曲线局部包络问题,提出Bézier曲线的n-1单侧降阶逼近的方法.这种方法的主要步骤是先根据已知Bézier曲线的具体特点利用切比雪夫多项式构造出它的最佳阶一致逼近曲线.然后根据其顶点偏移向量得到误差曲线,再使用Legendre最佳平方逼近多项式方法构造出所要求的n-1次最佳逼近多项式曲线.这种方法可以给出处于原曲线的一侧或在一定范围内处于原曲线的一侧的曲线以满足某些曲线设计的要求.

In this paper, the method for approximation of Bézier curve with unilateral degree reduction has been developed in order to resolving the local envelope problem of curves. The technique of offset approximation is used here to generate a curve which locates at one side of the original curve or partly locates at one side of the original curve. The method can meet requirements in the design of some curves.