本文主要验证了博客上的最小二乘法拟合平面的。与 用matlab拟合出来的平面计算的点到直线的距离是一样的，而且系数也是一样的。说明了本方法的可行性。
matlab中公式为z = c + ax +by
oepncv中公式为Ax+By+Cz=D 将opencv中公式换算成matlab的公式，系数是一样的。
平面公式为：Ax+By+Cz=D
//对应的方程：Ax+By+Cz=D 其中 A = plane12[0], B = plane12[1], C = plane12[2], D = plane12[3],这是要注意的方程的表示
//float plane12[4] = { 0 };//定义用来储存平面参数的数组，分别对应ABCD
拟合平面
1 void cvFitPlane(vector<float>dx, vector<float>dy, vector<float>dz, float* plane) {
2
3 //直线方程为：
4 //构建点集cvmat
5 CvMat* points = cvCreateMat(dx.size(), 3, CV_32FC1);
6 int nnum = 96;
7 for (int i = 0; i < dx.size(); ++i)
8 {
9 points->data.fl[i * 3 + 0] = dx[i];//矩阵的值进行初始化 X的坐标值
10 points->data.fl[i * 3 + 1] = dy[i];// Y的坐标值
11 points->data.fl[i * 3 + 2] = dz[i]; // Z的坐标值
12
13 }
14
15 Estimate geometric centroid.
16 int nrows = points->rows;
17 int ncols = points->cols;
18 int type = points->type;
19 CvMat* centroid = cvCreateMat(1, ncols, type);
20 cvSet(centroid, cvScalar(0));
21 for (int c = 0; c < ncols; c++) {
22 for (int r = 0; r < nrows; r++)
23 {
24 centroid->data.fl[c] += points->data.fl[ncols*r + c];
25 }
26 centroid->data.fl[c] /= nrows;
27 }
28 // Subtract geometric centroid from each point.
29 CvMat* points2 = cvCreateMat(nrows, ncols, type);
30 for (int r = 0; r < nrows; r++)
31 for (int c = 0; c < ncols; c++)
32 points2->data.fl[ncols*r + c] = points->data.fl[ncols*r + c] - centroid->data.fl[c];
33 // Evaluate SVD of covariance matrix.
34 CvMat* A = cvCreateMat(ncols, ncols, type);
35 CvMat* W = cvCreateMat(ncols, ncols, type);
36 CvMat* V = cvCreateMat(ncols, ncols, type);
37
38 cvGEMM(points2, points, 1, NULL, 0, A, CV_GEMM_A_T);
39 cvSVD(A, W, NULL, V, CV_SVD_V_T);
40
41 // Assign plane coefficients by singular vector corresponding to smallest singular value.
42 plane[ncols] = 0;
43 for (int c = 0; c < ncols; c++) {
44 plane[c] = V->data.fl[ncols*(ncols - 1) + c];
45 plane[ncols] += plane[c] * centroid->data.fl[c];
46 }
47 // Release allocated resources.
48 cvReleaseMat(&points);
49 cvReleaseMat(¢roid);
50 cvReleaseMat(&points2);
51 cvReleaseMat(&A);
52 cvReleaseMat(&W);
53 cvReleaseMat(&V);
54 }
计算点到平面的距离
1 //计算点到平面的距离
2 //Ax+By+Cz=D
3 //|点（a,b,c） 到平面bai Ax+By+Cz=D的距离du
4
5 //= | A * a + B * b + C * c - D| /√(A ^ 2 + B ^ 2 + C ^ 2)
6 void calculateDist(vector<float>dx, vector<float>dy, vector<float>dz, float* plane, vector<float> &dist)
7 {
8 for (int i = 0; i < dx.size(); i++)
9 {
10 float ds = fabs(plane[0] * dx[i] + plane[1] * dy[i] + plane[2] * dz[i] - plane[3]);
11 float dfen = sqrt(plane[0] * plane[0] + plane[1] * plane[1] + plane[2] * plane[2]);
12 if (!(dfen > -0.00001 && dfen < -0.00001))
13 {
14 float ddist = ds / dfen;
15 dist.push_back(ddist);
16 }
17 }
18 }
测试流程
从文件中读取数据，然后计算拟合平面，计算点到平面的距离，并输出到csv文件中
数据格式为：
一行中代表xyz
1 -53.883533,55.133049,895.801941
2 -40.928612,32.402653,897.237793
3 -21.391739,50.161041,899.748901
4 2.107507,62.850151,902.479065
5 3.594930,37.490810,902.427490
具体代码为：
1 fstream fs;
2 fs.open("E:\\wokspace\\PROJECT\\ThirdTrailInspection\\matlab\\dResult.txt");
3 if (!fs.is_open())
4 {
5 return;
6 }
7 vector<float> dx;
8 vector<float> dy;
9 vector<float> dz;
10 int i = 0;
11 string buff;
12 while (getline(fs, buff))//是否到文件结bai尾
13 {
14 int nfist = buff.find_first_of(',');
15 int nLast = buff.find_last_of(',');
16 string st1 = buff.substr(0, nfist);
17 string st2 = buff.substr(nfist + 1, nLast - nfist - 1);
18 string st3 =(buff.substr(nLast + 1));
19 dx.push_back(stof(buff.substr(0, nfist)));
20 dy.push_back(stof(buff.substr(nfist + 1, nLast - nfist - 1)));
21 dz.push_back(stof(buff.substr(nLast + 1)));
22 }
23 fs.close();
24
25
26 //代入最小二乘算法中
27 float plane[4] = { 0 };
28 vector<float> dx1;
29 vector<float> dy1;
30 vector<float> dz1;
31 dx1.assign(dx.begin(), dx.begin() + 96);
32 dy1.assign(dy.begin(), dy.begin() + 96);
33 dz1.assign(dz.begin(), dz.begin() + 96);
34 cvFitPlane(dx1, dy1, dz1, plane);
35 vector<float> dist;
36 calculateDist(dx, dy, dz, plane, dist);
37 fstream fws("e://de.csv", fstream::in | fstream::out | fstream::trunc);
38 for (int i = 0; i < dist.size(); i++)
39 {
40 fws << dist[i] <<"\r";
41 }
42 fws.close();
对应的matlab代码
1 clc;
2 close all;
3 clear all;
4 %https://www.ilovematlab.cn/thread-220252-1-1.html
5
6 data = importdata('E:\wokspace\PROJECT\ThirdTrailInspection\matlab\dResult.txt');
7 x = data(1:96, 1);
8 y = data(1:96, 2);
9 z = data(1:96, 3);
10 % x = data(113:192, 1);
11 % y = data(113:192, 2);
12 % z = data(113:192, 3);
13 scatter3(x, y,z, 'r');%画点 散点图
14 hold on;
15 X = [ones(length(x),1) x y];
16 [b,bint,r,rint,stats] = regress(z,X,95);
17
18 % 图形绘制
19 xfit = min(x):0.1:max(x);
20 yfit = min(y):0.1:max(y);
21 [XFIT,YFIT]= meshgrid (xfit,yfit);%用于生成网格采样点
22 ZFIT = b(1) + b(2) * XFIT + b(3) * YFIT;
23 mesh(XFIT,YFIT,ZFIT);
24
25 %%测试结果
26 %data = importdata('C:\Users\apr_z\Desktop\dResult.txt');
27 xx = data(:, 1);
28 yy = data(:, 2);
29 zz = data(:, 3);
30 [row, col] = size(xx);%求矩阵的行数和列数
31 dist = ones(row, 1);
32 for i = 1: row
33 dist(i) = abs(b(2) * xx(i) + b(3) * yy(i) - zz(i) + b(1)) / sqrt(b(2)* b(2) + b(3)*b(3) + 1 );
34 end
35 xlswrite('C:\Users\apr_z\Desktop\AnalyzeResult.xlsx', dist);
小结：
vector 复制某一些数据时： dx1.assign(dx.begin(), dx.begin() + 96);
vector容器 追加其他容器的内容，使用insert
pt3DList.insert(pt3DList.end(), vc.begin(), vc.end());
用此平面拟合的计算 点到直线的距离 与 用matlab计算出来的点到直线的距离是一模一样的。