基于牛顿迭代法的椭圆近似画法误差分析

四心圆法是用四段圆弧拼接成近似椭圆。由于其对称性，取图形的1/4 为研究对象，利用二分法求解方程组，得出两段圆弧拼接点坐标值；分别用两段圆弧的极径和实际椭圆中相应的极径进行长度误差分析，列出两段圆弧与椭圆极坐标方程，使用牛顿迭代法，求出圆弧与实际椭圆的极径长度最大误差值；计算出近似椭圆与实际椭圆面积，求出面积误差值。在编程软件中，根据所得数学模型编制计算器，计算结果列表对比分析，得出四心圆法作近似椭圆的误差结论。

Error Analysis of Ellipse Based on Newton Iteration Method

The four-arcs method uses four arcs joining together similarly into an ellipse. Due to itssymmetry, we take a quater graphics as the researching object and solve the equations by usingdichotomy. Then we get the splicing point coordinates of the two pieces of circular arc. Then do erroranalysis with the actual ellipse in the two pieces of circular arc, and list the mathematical equations ofthe two pieces of circular arc and the ellipse polar. Then solve the actual maximum error value of theellipse and the two pieces of circular arc with Newton iterative method. After that, figure out theapproximate and actual ellipse areas, so as to work out the area error values. With the mathematicalmodel, the calculator software is developed. It is concluded that the error of the approximated ellipse issolved through comparing the analysis list of calculating results.