c#最小二乘法拟合圆
最小二乘法拟合圆https://blog.csdn.net/u014090257/article/details/108899982
https://www.cnblogs.com/zxtang/p/15519549.html
private void FittingCircle1D(List<System.Drawing.Point> pPointList, out double X_c, out double Y_c, out double R)
{
X_c = 0;
Y_c = 0;
R = 0;
if (pPointList.Count < 3)
{
return; // 最少3个点进行拟合
}
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 (int i = 0; i < pPointList.Count; i++)
{
X1 = X1 + pPointList.X;
Y1 = Y1 + pPointList.Y;
X2 = X2 + pPointList.X * pPointList.X;
Y2 = Y2 + pPointList.Y * pPointList.Y;
X3 = X3 + pPointList.X * pPointList.X * pPointList.X;
Y3 = Y3 + pPointList.Y * pPointList.Y * pPointList.Y;
X1Y1 = X1Y1 + pPointList.X * pPointList.Y;
X1Y2 = X1Y2 + pPointList.X * pPointList.Y * pPointList.Y;
X2Y1 = X2Y1 + pPointList.X * pPointList.X * pPointList.Y;
}
double C, D, E, G, H, N;
double a, b, c;
N = pPointList.Count;
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;
X_c = a / (-2);
Y_c = b / (-2);
R = Math.Sqrt(a * a + b * b - 4 * c) / 2;
}
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