## Appendix B  
We referred to the method in [7; 10] to evaluate the accuracy of the shape of the 3D point cloud obtained by our prototype. The flatness of 4 surfaces (as shown in Figure 11) in the 3D point cloud were analyzed to evaluate the accuracy of the 3D point cloud in shape more comprehensively. We extracted 4 ideal planes from the 4 surfaces respectively and calculated the deviations from the points to the ideal planes. When selecting the surfaces, we carefully avoided the door and the projection screen hanging on the wall, because they might reduce the accuracy of the extraction of the planes. These 4 surfaces are named surface 1 to surface 4, respectively.  
We evaluated the shape accuracy of the 3D point clouds obtained by our prototype in 7 modes, as shown in Figure 12. In Figure 12, the 3D view, side views (X-Z view and Y-Z view) of each surface are included, as well as the distribution of the deviations from each point to the ideal plane. The horizontal axis of the distribution graph describes the signed value of the deviations, while the vertical axis describes the number of points corresponding to each deviation, and the total number of the points is equal to the number of points contained in this surface.  
From Figure 12, the following conclusions can be drawn.  
1. We can observe that the points in each surface are roughly evenly distributed on both sides of the ideal plane, which indicates that the surface and the ideal plane fit well. This shows that the shapes of these surfaces are very close to planes. Since they were obtained by scanning to the walls using our prototype, this can further indicate that the shape of the 3D point cloud collected by our prototype is correct.
2. For each surface, its X-Z view and Y-Z view show that the distribution range of the points which are distributed at both sides of the ideal plane is roughly coincident with the accuracy of the 2D lidar (which is \(\pm\)40 mm) used in our prototype. There is no case where a large number of points exceed this range, which indicates that the surface is obviously distorted.
3. From the X-Z view and Y-Z view of each surface in Figure 12, we can find that very few sampling points exceed the range of \(\pm\)0.04 m, which is the accuracy of the 2D lidar. So we can know that the shape error of the 3D point cloud caused by the self-reasons of our prototype (such as mechanical error, etc.) is relatively small compared to the error 2D lidar. Under the influence of the latter, the former is almost hardly noticeable.
4. From the distribution graphs of the deviations, we can find a law of normal distribution (for surfaces with more points, their normal distributions are more obvious), which indicates that the deviation values from the points to the ideal plane are approximately normally distributed. This verifies the previous conclusion, that is, the shape of the 3D point cloud collected by our prototype is correct. If the 3D point cloud is distorted, the distribution of the deviations from the points to the ideal plane willbe severely affected by the shape of the distorted surface, and it will be not easy to find out a normal distribution in the distribution graphs of the deviations.  
Since the shape accuracy of the 3D point cloud has been verified, we can focus on the calibration of the attitude error of the 3D point cloud.  
Figure A2: Cont.