/**
* 最小二乘法拟合圆
* 拟合出的圆以圆心坐标和半径的形式表示
* 此代码改编自 newsmth.net 的 jingxing 在 Graphics 版贴出的代码。
* 版权归 jingxing， 我只是搬运工外加一些简单的修改工作。
*/typedef complex POINT;bool circleLeastFit(const std::vector &points, double ¢er_x, double ¢er_y, double &radius)
{
center_x = 0.0f;
center_y = 0.0f;
radius = 0.0f;
if (points.size() < 3)
{
return false;
}
double sum_x = 0.0f, sum_y = 0.0f;
double sum_x2 = 0.0f, sum_y2 = 0.0f;
double sum_x3 = 0.0f, sum_y3 = 0.0f;
double sum_xy = 0.0f, sum_x1y2 = 0.0f, sum_x2y1 = 0.0f;
int N = points.size();
for (int i = 0; i < N; i++)
{
double x = points[i].real();
double y = points[i].imag();
double x2 = x * x;
double y2 = y * y;
sum_x += x;
sum_y += y;
sum_x2 += x2;
sum_y2 += y2;
sum_x3 += x2 * x;
sum_y3 += y2 * y;
sum_xy += x * y;
sum_x1y2 += x * y2;
sum_x2y1 += x2 * y;
}
double C, D, E, G, H;
double a, b, c;
C = N * sum_x2 - sum_x * sum_x;
D = N * sum_xy - sum_x * sum_y;
E = N * sum_x3 + N * sum_x1y2 - (sum_x2 + sum_y2) * sum_x;
G = N * sum_y2 - sum_y * sum_y;
H = N * sum_x2y1 + N * sum_y3 - (sum_x2 + sum_y2) * sum_y;
a = (H * D - E * G) / (C * G - D * D);
b = (H * C - E * D) / (D * D - G * C);
c = -(a * sum_x + b * sum_y + sum_x2 + sum_y2) / N;
center_x = a / (-2);
center_y = b / (-2);
radius = sqrt(a * a + b * b - 4 * c) / 2;
return true;
}
