Bézier曲线的几何生成法及其有效性分析

Analysis of Three Geometry Methods to Generate Bézier Curve

基于对Bézier曲线的三种几何生成法:简单割角法、升阶法、de Casteljau方法的讨论,找出最佳的Bézier曲线几何作图法.对三个算法的时间复杂度和生成曲线误差进行分析、比较.de Casteljau算法是最佳的Bézier曲线几何作图法.简单割角法在实现的过程中使用了递归,增大了空间复杂度;升阶法在逼近过程中会产生一定的误差,虽然这个误差可以随升阶次数增大而变小,但这样却大大影响了计算机的运算速度;而de Casteljau算法简单,稳定,可靠,直观实用,易于编程实现,且速度也相当的快,同时具有几何直观性.

Bézier curve is always used in designing the shape of aircraft,ships or automobiles. Because of its many good characteristics,Bézier curve has been studied and used as one of the basic model methods in CAGD. In this paper, the geometry methods to generate Bézier curve with corner cutting, elevation and de Casteljau algorithm are discussed in order to give the best method to form Bézier curve. The time complexity and the error of these three algorithms are analyzed and compared esch other. Corner cutting algorithm is implemented by recursion,which increases the space complexity. The error brought by the elevation algorithm decreases the speed of computing, de Casteljau algorithm the best because it is simple, stable, reliable and easy to realized. Furthermore, it has high speed and geometric intuition.