# 最小二乘法拟合圆公式推导及vc实现[r

VC实现的代码：
void CViewActionImageTool::LeastSquaresFitting()
{

if (m_nNum<3)

{

return;
}

int i=0;

double X1=0;

double Y1=0;

double X2=0;

double Y2=0;

double X3=0;

double Y3=0;

double X1Y1=0;

double X1Y2=0;

double X2Y1=0;

for (i=0;i<m_nNum;i++)

{
X1
= X1 + m_points[i].x;
Y1
= Y1 + m_points[i].y;
X2
= X2 + m_points[i].x*m_points[i].x;
Y2
= Y2 + m_points[i].y*m_points[i].y;
X3
= X3 + m_points[i].x*m_points[i].x*m_points[i].x;
Y3
= Y3 + m_points[i].y*m_points[i].y*m_points[i].y;
X1Y1
= X1Y1 + m_points[i].x*m_points[i].y;
X1Y2
= X1Y2 + m_points[i].x*m_points[i].y*m_points[i].y;
X2Y1
= X2Y1 + m_points[i].x*m_points[i].x*m_points[i].y;
}

double C,D,E,G,H,N;

double a,b,c;
N
= m_nNum;
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;

double A,B,R;
A
= a/(-2);
B
= b/(-2);
R
= sqrt(a*a+b*b-4*c)/2;

m_fCenterX
= A;
m_fCenterY
= B;
= R;

return;
}

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