最小二乘法拟合平面。

本文采用了opencv的一些函数来对平面进行拟合。

//Ax+by+cz=D
void cvFitPlane(const CvMat* points, float* plane){
	// 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(¢roid);
	cvReleaseMat(&points2);
	cvReleaseMat(&A);
	cvReleaseMat(&W);
	cvReleaseMat(&V);
}

CvMat*points_mat = cvCreateMat(X_vector.size(), 3, CV_32FC1);//定义用来存储需要拟合点的矩阵 
		for (int i=0;i < X_vector.size(); ++i)
		{
			points_mat->data.fl[i*3+0] = X_vector[i];//矩阵的值进行初始化   X的坐标值
			points_mat->data.fl[i * 3 + 1] = Y_vector[i];//  Y的坐标值
			points_mat->data.fl[i * 3 + 2] = Z_vector[i];<span style="font-family: Arial, Helvetica, sans-serif;">//  Z的坐标值</span>

		}
		float plane12[4] = { 0 };//定义用来储存平面参数的数组 
		cvFitPlane(points_mat, plane12);//调用方程 

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