基于单位圆弧段逼近的Bézier曲线等距线生成算法

Bézier Curve Offset Based on Circular Arc Approximation

提出一种用四次Bézier曲线逼近单位圆弧段(Unit Circular Arcs)的方法及其详细误差函数分析。使用这种方法,给出一种使用同阶Bézier曲线逼近给定Bézier曲线等距线的算法。在Matlab7.0上实现了该算法,试验表明,新算法比Lee和Ahn所提出的算法有更高的精度和计算效率。由于B样条和NURBS曲线可以认为由多段Bézier曲线组成,因此,新算法为B样条和NURBS曲线等距线的求解提供了一种新的途径。

An approximation method and detail error function analysis for circular arcs by quartic Bezier curves is proposed. Using this method, a new approximation algorithm of the offset curve of given plane Bezier curve by Bezier curve of the same degree is presented. The new algorithm has been implemented in software of Matlab 7.0 and the experiments show that new algorithm can achieve more precision and high efficiency than Lee or Ahn algorithm. Because B-spline and NURBS curve can be considered to be composed by piecewise Bezier curves, so the algorithm provides a new way of achieving offset curve of B-spline and NURBS.