//-----------------------------------【头文件包含部分】---------------------------------------
//       描述：包含程序所依赖的头文件
//----------------------------------------------------------------------------------------------
#include"opencv2/highgui/highgui.hpp"
#include"opencv2/imgproc/imgproc.hpp"
#include <iostream>//-----------------------------------【命名空间声明部分】--------------------------------------
//    描述：包含程序所使用的命名空间
//-----------------------------------------------------------------------------------------------
using namespace cv;bool polynomial_curve_fit(std::vector<cv::Point>& key_point, int n, cv::Mat& A)
{//Number of key pointsint N = key_point.size();//构造矩阵Xcv::Mat X = cv::Mat::zeros(n + 1, n + 1, CV_64FC1);for (int i = 0; i < n + 1; i++){for (int j = 0; j < n + 1; j++){for (int k = 0; k < N; k++){X.at<double>(i, j) = X.at<double>(i, j) +std::pow(key_point[k].x, i + j);}}}//构造矩阵Ycv::Mat Y = cv::Mat::zeros(n + 1, 1, CV_64FC1);for (int i = 0; i < n + 1; i++){for (int k = 0; k < N; k++){Y.at<double>(i, 0) = Y.at<double>(i, 0) +std::pow(key_point[k].x, i) * key_point[k].y;}}A = cv::Mat::zeros(n + 1, 1, CV_64FC1);//求解矩阵Acv::solve(X, Y, A, cv::DECOMP_LU);return true;
}int main()
{//创建用于绘制的深蓝色背景图像cv::Mat image = cv::Mat::zeros(480, 640, CV_8UC3);image.setTo(cv::Scalar(0, 0, 100));//输入拟合点std::vector<cv::Point> points;points.push_back(cv::Point(100., 58.));points.push_back(cv::Point(150., 70.));points.push_back(cv::Point(200., 90.));points.push_back(cv::Point(252., 140.));points.push_back(cv::Point(300., 220.));points.push_back(cv::Point(350., 400.));//将拟合点绘制到空白图上for (int i = 0; i < points.size(); i++){cv::circle(image, points[i], 5, cv::Scalar(0, 0, 255), 2, 8, 0);}//绘制折线cv::polylines(image, points, false, cv::Scalar(0, 255, 255), 1, 8, 0);cv::Mat A;polynomial_curve_fit(points, 3, A);std::cout << "A = " << A << std::endl;std::vector<cv::Point> points_fitted;for (int x = 0; x < 400; x++){double y = A.at<double>(0, 0) + A.at<double>(1, 0) * x +A.at<double>(2, 0)*std::pow(x, 2) + A.at<double>(3, 0)*std::pow(x, 3);points_fitted.push_back(cv::Point(x, y));}cv::polylines(image, points_fitted, false, cv::Scalar(255, 255, 255), 1, 8, 0);cv::imshow("image", image);cv::waitKey(0);return 0;
}