C#使用最小二乘法对多个离散点进行圆拟合
/// <summary> /// 最小二乘法拟合圆,计算拟合圆半径和拟合圆圆心 /// </summary> /// <param name="points">拟合点</param> /// <returns>返回拟合圆的计算结果</returns> public double[] FittingCircleByLeastSquare(List<Point> points) { //最小二乘法拟合圆 ///https://blog.csdn.net/qq_31253399/article/details/107306569 double U_i = 0, V_i = 0, U_c = 0, V_c = 0; double X = points.Average(p => p.X), Y = points.Average(p => p.Y); double S_uuu = 0, S_vvv = 0, S_uvv = 0, S_uuv = 0; double S_uu = 0, S_vv = 0, S_uv = 0; for (int i = 0; i < points.Count; i++) { U_i = points[i].X - X; V_i = points[i].Y - Y; S_uuu += Math.Pow(U_i, 3); S_uuv += Math.Pow(U_i, 2) * V_i; S_uuu += Math.Pow(U_i, 3); S_uvv += Math.Pow(V_i, 2) * U_i; S_uu += Math.Pow(U_i, 2); S_vv += Math.Pow(V_i, 2); S_uv += U_i * V_i; } U_c = (S_uuv * S_uv - S_uuu * S_vv - S_uvv * S_vv + S_uv * S_vvv) / 2 * (S_uv * S_uv - S_uu * S_vv); V_c = (S_uuu * S_uv - S_uuv * S_uu - S_uu * S_vvv + S_uv * S_uvv) / 2 * (S_uv * S_uv - S_uu * S_vv); //计算拟合圆圆心坐标 double X_c = U_c + X; double Y_c = V_c + Y; //计算R double R = points.Sum(p => ((p.X - X_c) * (p.X - X_c) + (p.Y - X_c) * (p.Y - Y_c))); return new double[3] { X_c, Y_c, R }; }
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