对于网上常用的拟合圆代码(经过修改， 因为除数可能为0)
/*
* 参考: http://blog.csdn.net/liyuanbhu/article/details/50889951
* 通过最小二乘法来拟合圆的信息
* pts: 所有点坐标
* center: 得到的圆心坐标
* radius: 圆的半径
*/
static bool CircleInfo2(std::vector<cv::Point2d>& pts, cv::Point2d& center, double& radius)
{
center = cv::Point2d(0, 0);
radius = 0.0;
if (pts.size() < 3) return false;;
double sumX = 0.0;
double sumY = 0.0;
double sumX2 = 0.0;
double sumY2 = 0.0;
double sumX3 = 0.0;
double sumY3 = 0.0;
double sumXY = 0.0;
double sumX1Y2 = 0.0;
double sumX2Y1 = 0.0;
const double N = (double)pts.size();
for (int i = 0; i < pts.size(); ++i)
{
double x = pts.at(i).x;
double y = pts.at(i).y;
double x2 = x * x;
double y2 = y * y;
double x3 = x2 *x;
double y3 = y2 *y;
double xy = x * y;
double x1y2 = x * y2;
double x2y1 = x2 * y;
sumX += x;
sumY += y;
sumX2 += x2;
sumY2 += y2;
sumX3 += x3;
sumY3 += y3;
sumXY += xy;
sumX1Y2 += x1y2;
sumX2Y1 += x2y1;
}
double C = N * sumX2 - sumX * sumX;
double D = N * sumXY - sumX * sumY;
double E = N * sumX3 + N * sumX1Y2 - (sumX2 + sumY2) * sumX;
double G = N * sumY2 - sumY * sumY;
double H = N * sumX2Y1 + N * sumY3 - (sumX2 + sumY2) * sumY;
double denominator = C * G - D * D;
if (std::abs(denominator) < DBL_EPSILON) return false;
double a = (H * D - E * G) / (denominator);
denominator = D * D - G * C;
if (std::abs(denominator) < DBL_EPSILON) return false;
double b = (H * C - E * D) / (denominator);
double c = -(a * sumX + b * sumY + sumX2 + sumY2) / N;
center.x = a / (-2);
center.y = b / (-2);
radius = std::sqrt(a * a + b * b - 4 * c) / 2;
return true;
}
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本文来自 wfh2015 的CSDN 博客 ，全文地址请点击：https://blog.csdn.net/wfh2015/article/details/79626581?utm_source=copy 然而，很多人对这部分代码表示有疑问，所以我根据网上的资料另外写了一个部分，但是速度差很多，仅仅用于学习代码公式是按照这个博客来的。个人认为，这份博客的大部分是正确的，比如求圆的圆心是正确的。但是最后面的计算圆的半径博客公式可能有问题，我根据下面网友评论修改了一下，得到正确的结果。下面是我写的代码
#include <iostream>
#include <string>
#include "opencv2/opencv.hpp"
/////////////////////////////////////根据公式编写代码//////////////////////////////////////////
/**
计算所有点的X坐标均值
pts: 点坐标
return: 均值
*/
static double meanX(std::vector<cv::Point2d>& pts)
{
if (pts.size() <= 0) return 0.0;
const double N = (double)pts.size();
double sum = 0.0;
for (int i = 0; i < pts.size(); ++i)
{
cv::Point2d pt = pts.at(i);
sum += (pt.x);
}
double avg = sum / N;
return avg;
}
/**
计算所有点的Y坐标均值
pts: 点坐标
return: 均值
*/
static double meanY(std::vector<cv::Point2d>& pts)
{
if (pts.size() <= 0) return 0.0;
const double N = (double)pts.size();
double sum = 0.0;
for (int i = 0; i < pts.size(); ++i)
{
cv::Point2d pt = pts.at(i);
sum += (pt.y);
}
double avg = sum / N;
return avg;
}
static double Ui(std::vector<cv::Point2d>& pts, int index, double meanXValue)
{
double xi = pts.at(index).x;
return xi - meanXValue;
}
static double Vi(std::vector<cv::Point2d>& pts, int index, double meanYValue)
{
double yi = pts.at(index).y;
return yi - meanYValue;
}
static double Suvv(std::vector<cv::Point2d>& pts, double mean_x, double mean_y)
{
double sum = 0.0;
for (int i = 0; i < pts.size(); ++i)
{
double u = Ui(pts, i, mean_x);
double v = Vi(pts, i, mean_y);
double cur = u * v *v;
sum += cur;
}
return sum;
}
static double Suuv(std::vector<cv::Point2d>& pts, double mean_x, double mean_y)
{
double sum = 0.0;
for (int i = 0; i < pts.size(); ++i)
{
double u = Ui(pts, i, mean_x);
double v = Vi(pts, i, mean_y);
double cur = u * u * v;
sum += cur;
}
return sum;
}
static double Suv(std::vector<cv::Point2d>& pts, double mean_x, double mean_y)
{
double sum = 0.0;
for (int i = 0; i < pts.size(); ++i)
{
double u = Ui(pts, i, mean_x);
double v = Vi(pts, i, mean_y);
double cur = u * v;
sum += cur;
}
return sum;
}
static double Svv(std::vector<cv::Point2d>& pts, double mean_y)
{
double sum = 0.0;
for (int i = 0; i < pts.size(); ++i)
{
double value = Vi(pts, i, mean_y);
double cur = value * value;
sum += cur;
}
return sum;
}
static double Suu(std::vector<cv::Point2d>& pts, double mean_x)
{
double sum = 0;
for (int i = 0; i < pts.size(); ++i)
{
double value = Ui(pts, i, mean_x);
double cur = value * value;
sum += cur;
}
return sum;
}
static double Svvv(std::vector<cv::Point2d>& pts, double mean_y)
{
double sum = 0.0;
for (int i = 0; i < pts.size(); ++i)
{
double v = Vi(pts, i, mean_y);
double cur = v * v * v;
sum += cur;
}
return sum;
}
static double Suuu(std::vector<cv::Point2d>& pts, double mean_x)
{
double sum = 0.0;
for (int i = 0; i < pts.size(); ++i)
{
double u = Ui(pts, i, mean_x);
double cur = u * u * u;
sum += cur;
}
return sum;
}
static double Uc(double A, double B, double C, double D, double E, double F, double G)
{
double numerator = A * B - C * D - E * D + B * F;
double denominator = 2 * (B * B - G * D);
double result = numerator / denominator;
return result;
}
static double Vc(double A, double B, double C, double D, double E, double F, double G)
{
double numerator = -1 * G * A + C * B + B * E - G * F;
double denominator = 2 * (B * B - G * D);
double result = numerator / denominator;
return result;
}
static double GetRadius(std::vector<cv::Point2d>& pts, cv::Point2d center)
{
double sum = 0.0;
for (int i = 0; i < pts.size(); ++i)
{
double p1 = pts.at(i).x - center.x;
double p2 = pts.at(i).y - center.y;
double cur = p1*p1 + p2*p2;
sum += cur;
}
double radius = std::sqrt(sum / (pts.size()));
return radius;
}
static void CircleInfo(std::vector<cv::Point2d>& pts, cv::Point2d& center, double& radius)
{
double mean_x = meanX(pts);
double mean_y = meanY(pts);
double A = Suuv(pts, mean_x, mean_y);
double B = Suv(pts, mean_x, mean_y);
double C = Suuu(pts, mean_x);
double D = Svv(pts, mean_y);
double E = Suvv(pts, mean_x, mean_y);
double F = Svvv(pts, mean_y);
double G = Suu(pts, mean_x);
double uc = Uc(A, B, C, D, E, F, G);
double vc = Vc(A, B, C, D, E, F, G);
center.x = uc + mean_x;
center.y = vc + mean_y;
radius = GetRadius(pts, center);
}
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本文来自 wfh2015 的CSDN 博客 ，全文地址请点击：https://blog.csdn.net/wfh2015/article/details/79626581?utm_source=copy 另外，附上所有的测试代码下载。
最后，感谢我参考的博客作者的公式推导。谢谢！