Cloudcompare & PCL point cloud least square fitting plane

One 、 brief introduction

The essence of point cloud plane fitting is to replace the point cloud approximately located in the same plane with a fitting plane , Minimize the sum of squares of distances from all points in the point cloud to the fitting plane , The height of the point cloud is consistent with that of the fitting plane . There are many existing methods , Such as the least square method 、 Eigenvalue method, etc , This paper will use the least square method to realize simple plane fitting . among , There are two ways to program the least square method ：（1） By using the covariance matrix （ Symmetric matrix ） To solve it ;（2） Use partial derivative to solve , For details, you can read the literature [1].

But due to the CloudCompare Drawing a plane in often requires a transformation matrix , Therefore, this paper does not intend to obtain the pseudo inverse before sampling （ Point cloud least square fitting plane ） To fit the plane , instead PCA Get the eigenvalue of the point cloud to fit the plane , About PCA You can refer to ：PCA( Principal component analysis ) Algorithm , Its ultimate