matlab 2009-01-17 |||| 最小二乘法拟合圆公式推导及 matlab 2009-01-17 2009-01-17 matlab 2009-01-17 matlab 实现 最小二乘法(least squares analysis)是一种数学优化技术，它通过 最小化误差的平方和找到一组数据的最佳函数匹配。最小二乘法是用最 简的方法求得一些绝对不可知的真值，而令误差平方之和为最小。 最 小二乘法通常用于曲线拟合 (least squares fitting) 。 这里有拟合圆曲线 的公式推导过程和 vc 实现。 





matlabmatlab matlab matlab 实现： function [R,A,B]=circ(x,y,N) x1 = 0; x2 = 0; x3 = 0; y1 = 0; y2 = 0; y3 = 0; x1y1 = 0; x1y2 = 0; x2y1 = 0; for i = 1 : N x1 = x1 + x(i); x2 = x2 + x(i)*x(i); x3 = x3 + x(i)*x(i)*x(i); y1 = y1 + y(i); 

y2 = y2 + y(i)*y(i); y3 = y3 + y(i)*y(i)*y(i); x1y1 = x1y1 + x(i)*y(i); x1y2 = x1y2 + x(i)*y(i)*y(i); x2y1 = x2y1 + x(i)*x(i)*y(i); end C = N * x2 - x1 * x1; D = N * x1y1 - x1 * y1; E = N * x3 + N * x1y2 - (x2 + y2) * x1; G = N * y2 - y1 * y1; H = N * x2y1 + N * y3 - (x2 + y2) * y1; a = (H * D - E * G)/(C * G - D * D); b = (H * C - E * D)/(D * D - G * C); c = -(a * x1 + b * y1 + x2 + y2)/N; A = a/(-2); B = b/(-2); R = sqrt(a * a + b * b - 4 * c)/2; %x 坐标 %y 坐标