直线拟合算法 qt 源码

#include "hellodialog.h" #include "ui_hellodialog.h" #include <QDebug> float pY[25] = { 10.98, 11.13, 12.51, 8.40, 9.27, 8.73, 6.36, 8.50, 7.82, 9.14, 8.24, 12.19, 11.88, 9.57, 10.94, 9.58, 10.09, 8.11, 6.83, 8.88, 7.68, 8.47, 8.86, 10.38, 11.08 }; float pX[25] = { 35.3, 29.7, 30.8, 58.8, 61.4, 71.3, 74.4, 76.6, 70.7, 57.5, 46.4, 28.9, 28.1, 39.1, 46.8, 48.5, 59.3, 70.0, 70.0, 74.5, 72.1, 58.1, 44.6, 33.4, 28.6 }; float spY[25] = { 1,2,3,4,5,6,7,8,9,10, 11,12,13,14,15,16,17,18,19,20, 21,22,23,24,25 }; float spX[25] = { 1,2,3,4,5,6,7,8,9,10, 11,12,13,14,15,16,17,18,19,20, 21,22,23,24,25 }; float a; float b; void LineFitLeastSquares(float *data_x, float *data_y, int data_n, float &a, float &b) { float A = 0.0; float B = 0.0; float C = 0.0; float D = 0.0; float E = 0.0; float F = 0.0; for (int i=0; i<data_n; i++) { A += data_x[i] * data_x[i]; B += data_x[i]; C += data_x[i] * data_y[i]; D += data_y[i]; } // 计算斜率a和截距b float temp = 0; if( temp = (data_n*A - B*B) )// 判断分母不为0 { a = (data_n*C - B*D) / temp; b = (A*D - B*C) / temp; } else { a = 1; b = 0; } // 计算相关系数r float Xmean, Ymean; Xmean = B / data_n; Ymean = D / data_n; float tempSumXX = 0.0, tempSumYY = 0.0; for (int i=0; i<data_n; i++) { tempSumXX += (data_x[i] - Xmean) * (data_x[i] - Xmean); tempSumYY += (data_y[i] - Ymean) * (data_y[i] - Ymean); E += (data_x[i] - Xmean) * (data_y[i] - Ymean); } F = sqrt(tempSumXX) * sqrt(tempSumYY); float r; r = E / F; qDebug()<<"Send filepage len a= "<<a<<"."; qDebug()<<"Send filepage len b= "<<b<<"."; qDebug()<<"Send filepage len r*r= "<<r*r<<"."; // vResult.push_back(a); // vResult.push_back(b); // vResult.push_back(r*r); } typedef struct { float x; float y; }point; point points[25]; float c; float fabs(float data) { if(data < 0) return (-data); return data; } bool lineFit( float &a, float &b, float &c) { int size = 25; int i; float x_mean = 0; float y_mean = 0; for(int i = 0; i < size; i++) { points[i].x = pX[i]; points[i].y = pY[i]; } for(int i = 0; i < size; i++) { x_mean += points[i].x; y_mean += points[i].y; } x_mean /= size; y_mean /= size; //至此，计算出了 x y 的均值 float Dxx = 0, Dxy = 0, Dyy = 0; for(int i = 0; i < size; i++) { Dxx += (points[i].x - x_mean) * (points[i].x - x_mean); Dxy += (points[i].x - x_mean) * (points[i].y - y_mean); Dyy += (points[i].y - y_mean) * (points[i].y - y_mean); } float lambda = ( (Dxx + Dyy) - sqrt( (Dxx - Dyy) * (Dxx - Dyy) + 4 * Dxy * Dxy) ) / 2.0; float den = sqrt( Dxy * Dxy + (lambda - Dxx) * (lambda - Dxx) ); if(fabs(den) < 1e-5) //针对 den=0做特殊处理 { if( fabs(Dxx / Dyy - 1) < 1e-5) //这时没有一个特殊的直线方向，无法拟合 1e-5 == 0.00001 { return false; } else { a = 1; b = 0; c = - x_mean; } } else { a = Dxy / den; b = (lambda - Dxx) / den; c = - a * x_mean - b * y_mean; } qDebug()<<"Send filepage len a= "<<a<<"."; qDebug()<<"Send filepage len b= "<<b<<"."; qDebug()<<"Send filepage lenc= "<<c<<"."; qDebug()<<"Send filepage fabs(Dxx / Dyy - 1)= "<<fabs(Dxx / Dyy - 1)<<"."; return true; } HelloDialog::HelloDialog(QWidget *parent) : QDialog(parent), ui(new Ui::HelloDialog) { ui->setupUi(this); LineFitLeastSquares(pX, pY, 25, a, b); // LineFitLeastSquares(spX, spY, 25, a, b); // lineFit( a, b, c); } HelloDialog::~HelloDialog() { delete ui; }