用双圆弧逼近两条相容圆锥曲线的卷积曲线

Approximating the Convolution Curve of Two Compatible Conics Using Biarc Curves

基于2条相容圆锥曲线的卷积曲线并不一定能够被有理曲线表示,给出了一种新的逼近该卷积曲线的方法——圆弧逼近方法.先用分段标准圆弧来逼近原来的2条相容的圆锥曲线,再把得到的分段圆弧作卷积运算.该方法不仅能够使得逼近曲线是有理2次,而且能够先验地确定逼近的误差上界.数值例子结果表明,文中方法在数控加工和数控绘图中比较有效.

Because the convolution curve of two compatible conics can not always be represented by rational curves,a new method for approximating the convolution curve is presented,which is called biarc approximation method.Firstly,approximate the two given compatible conics by biarc curves,and then,take the convolution curve of the biarc curves as the approximate curve.This method can not only make the approximate curve represented by rational quadratic Bézier curves,but also obtain the upper bound of the error in advance.Numerical examples show that the method in this paper is much effective in CNC machining and CNC drawing.