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
代码：
来自于：https://blog.csdn.net/laobai1015/article/details/73603327?utm_source=blogxgwz4

//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

void cvFitPlane(vector<float>dx, vector<float>dy, vector<float>dz, float* plane) {

	//直线方程为：
	//构建点集cvmat
	CvMat* points = cvCreateMat(dx.size(), 3, CV_32FC1);
	int nnum = 96;
	for (int i = 0; i < dx.size(); ++i)
	{
		points->data.fl[i * 3 + 0] = dx[i];//矩阵的值进行初始化   X的坐标值  
		points->data.fl[i * 3 + 1] = dy[i];//  Y的坐标值  
		points->data.fl[i * 3 + 2] = dz[i]; //  Z的坐标值

	}

	 Estimate geometric centroid.  
	int nrows = points->rows;
	int ncols = points->cols;	
	int type = points->type;
	CvMat* centroid = cvCreateMat(1, ncols, type);
	cvSet(centroid, cvScalar(0));
	for (int c = 0; c < ncols; c++) {
		for (int r = 0; r < nrows; r++)
		{
			centroid->data.fl[c] += points->data.fl[ncols*r + c];
		}
		centroid->data.fl[c] /= nrows;
	}
	// Subtract geometric centroid from each point.  
	CvMat* points2 = cvCreateMat(nrows, ncols, type);
	for (int r = 0; r < nrows; r++)
		for (int c = 0; c < ncols; c++)
			points2->data.fl[ncols*r + c] = points->data.fl[ncols*r + c] - centroid->data.fl[c];
	// Evaluate SVD of covariance matrix.  
	CvMat* A = cvCreateMat(ncols, ncols, type);
	CvMat* W = cvCreateMat(ncols, ncols, type);
	CvMat* V = cvCreateMat(ncols, ncols, type);

	cvGEMM(points2, points, 1, NULL, 0, A, CV_GEMM_A_T);
	cvSVD(A, W, NULL, V, CV_SVD_V_T);

	// Assign plane coefficients by singular vector corresponding to smallest singular value.  
	plane[ncols] = 0;
	for (int c = 0; c < ncols; c++) {
		plane[c] = V->data.fl[ncols*(ncols - 1) + c];
		plane[ncols] += plane[c] * centroid->data.fl[c];
	}
	// Release allocated resources.  
	cvReleaseMat(&points);
	cvReleaseMat(&centroid);
	cvReleaseMat(&points2);
	cvReleaseMat(&A);
	cvReleaseMat(&W);
	cvReleaseMat(&V);
}

计算点到平面的距离

//计算点到平面的距离
//Ax+By+Cz=D
//|点（a,b,c） 到平面bai Ax+By+Cz=D的距离du

//= | A * a + B * b + C * c - D| /√(A ^ 2 + B ^ 2 + C ^ 2)
void calculateDist(vector<float>dx, vector<float>dy, vector<float>dz, float* plane, vector<float> &dist)
{
	for (int i = 0; i < dx.size(); i++)
	{
		float ds = fabs(plane[0] * dx[i] + plane[1] * dy[i] + plane[2] * dz[i] - plane[3]);
		float dfen = sqrt(plane[0] * plane[0] + plane[1] * plane[1] + plane[2] * plane[2]);
		if (!(dfen > -0.00001 && dfen < -0.00001))
		{
			float ddist = ds / dfen;
			dist.push_back(ddist);
		}		
	}
}

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

-53.883533,55.133049,895.801941
-40.928612,32.402653,897.237793
-21.391739,50.161041,899.748901
2.107507,62.850151,902.479065
3.594930,37.490810,902.427490

具体代码为：

fstream fs;
	fs.open("E:\\wokspace\\PROJECT\\ThirdTrailInspection\\matlab\\dResult.txt");
	if (!fs.is_open())
	{
		return;
	}
	vector<float> dx;
	vector<float> dy;
	vector<float> dz;
	int i = 0;
	string buff;
	while (getline(fs, buff))//是否到文件结bai尾
	{
		int nfist = buff.find_first_of(',');
		int nLast = buff.find_last_of(',');
		string st1 = buff.substr(0, nfist);
		string st2 = buff.substr(nfist + 1, nLast - nfist - 1);
		string st3 =(buff.substr(nLast + 1));
		dx.push_back(stof(buff.substr(0, nfist)));
		dy.push_back(stof(buff.substr(nfist + 1, nLast - nfist - 1)));
		dz.push_back(stof(buff.substr(nLast + 1)));		
	}
	fs.close();


	//代入最小二乘算法中
	float plane[4] = { 0 };
	vector<float> dx1;
	vector<float> dy1;
	vector<float> dz1;
	dx1.assign(dx.begin(), dx.begin() + 96);
	dy1.assign(dy.begin(), dy.begin() + 96);
	dz1.assign(dz.begin(), dz.begin() + 96);
	cvFitPlane(dx1, dy1, dz1,  plane);
	vector<float> dist;
	calculateDist(dx, dy, dz, plane, dist);
	fstream fws("e://de.csv", fstream::in | fstream::out | fstream::trunc);
	for (int i = 0; i < dist.size(); i++)
	{
		fws << dist[i] <<"\r";
	}
	fws.close();

对应的matlab代码

clc;
close all;
clear all;
%https://www.ilovematlab.cn/thread-220252-1-1.html

data = importdata('E:\wokspace\PROJECT\ThirdTrailInspection\matlab\dResult.txt');
x = data(1:96, 1);
y = data(1:96, 2);
z = data(1:96, 3);
% x = data(113:192, 1);
% y = data(113:192, 2);
% z = data(113:192, 3);
scatter3(x, y,z, 'r');%画点  散点图
hold on;
X = [ones(length(x),1) x y];
[b,bint,r,rint,stats] = regress(z,X,95);

% 图形绘制
xfit = min(x):0.1:max(x);
yfit = min(y):0.1:max(y);
[XFIT,YFIT]= meshgrid (xfit,yfit);%用于生成网格采样点
ZFIT = b(1) + b(2) * XFIT + b(3) * YFIT;
mesh(XFIT,YFIT,ZFIT);

%%测试结果
%data = importdata('C:\Users\apr_z\Desktop\dResult.txt');
xx = data(:, 1);
yy = data(:, 2);
zz = data(:, 3);
[row, col] = size(xx);%求矩阵的行数和列数
dist = ones(row, 1);
for i = 1: row
    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 );
end
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。