1.  方式1(直接基于最小二乘的数学解析解)

bool circle_LS(const vector<POINT>& points, double& center_x, double& center_y, double& radius)
{center_x = 0.0;center_y = 0.0;radius = 0.0;if (points.size() < 3){return false;}double sum_x = 0.0, sum_y = 0.0;double sum_x2 = 0.0, sum_y2 = 0.0;double sum_x3 = 0.0, sum_y3 = 0.0;double sum_xy = 0.0, sum_x1y2 = 0.0, sum_x2y1 = 0.0;int N = points.size();for (int i = 0; i < N; i++){double x = points[i].x;double y = points[i].y;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