最小二乘法拟合圆

/**

* 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;

}