四心圆法形成椭圆的误差分析

Error Analysis of Forming Ellipse by Four-Center Method

通过四心圆法绘制长轴为2a和短轴为2b的椭圆,分析四心圆法形成椭圆的绝对误差和相对误差。结果表明:四心圆法形成的椭圆,其绝对误差曲线呈“钩状”并存在两个极值点,正偏差极值点的x轴坐标为([(a^(2)+b^(2)+(a-b)a^(2)+b^(2))2/(4b2)-a^(4)/b^(2)])0.5,负偏差的极值点x轴坐标是x四次方程的根;绝对误差值随着a/b值增大而增加,在长轴端点处达到最大值。

The ellipses with long axis 2a and short axis 2b are drawn by four-center method,and the absolute error and relative error of such formed ellipses analyzed.The results show that the ellipse absolute error curve formed by the four-center method is“hook-shaped”and has two extreme points,the x-axis coordinate of the positive deviation extreme point is([(a^(2)+b^(2)+(a-b)a^(2)+b^(2))2/(4b2)-a^(4)/b^(2)])0.5,and the x-axis coordinate of the negative deviation extreme point is the root of the x-quartic equation.The absolute error value increases with the increase of the a/b value,reaching the maximum value at the end of the long axis.