## 3 Experimental Results
### Test A
These subfigures show the distributions of the final compressed point cloud data. By contrast, we can clearly observe the difference of point cloud density between these two methods under the same required accuracy. Take subfigures g-i, for example: when using the bi-Akima method, we can observe that there are many curves roughly along the welded region (Figure 8g), because the bi-Akima method can only deal with the point set in the current scanning line and the data redundancy outside the current scanning line cannot be eliminated. With the involvement of our proposed method, redundant data points are identified and marked in red (Figure 8h) and the data redundancy in the adjacent scanning layers is eliminated and the final compressed point cloud data is obtained (Figure 8i). To verify the accuracy of the proposed algorithm, Figure 9 analyzes the spatial distribution of deviation between each initial sampled point and the interpolated surface obtained from the final compressed point cloud data under different required accuracies. As can be seen, all the deviations are within the allowable range of required accuracy. Our method can tightly control the deviation within the error tolerance range (i.e., the deviation between each initial sampled point and interpolation curve is less than or equal to the required accuracy). In addition, deviations are far lower than the required accuracy in most of the measured area. In Figure 9d, there is an interesting and noteworthy phenomenon: the upper right sector has a higher deviation. As mentioned earlier, the measured part is a large thin-walled surface which is welded together by seven pieces of aluminum alloy sheet (Figure 5d). The aluminum alloy sheet has a thickness of only 0.8 mm, but its size is very large (the semi-major axis of the ellipse is 1450 mm). The part has undergone great deformation after welding. There is a large and random deviation between each welded part and the original design size. According to past experience, the maximum deviation in a local section can even reach 3 mm. Consequently, we infer that the upper right sector has a higher deviation because of deformation in this area. In the case where the required accuracy is on the order of millimet  
Figure 7: Data compression ratios under different required accuracies. \(\epsilon\)\(=1\) mm in Figure 9d), the compressed point cloud data is very sparse. Therefore, this phenomenon is formed in a region where the point cloud density is low and the local deformation is large. However, in any case, the proposed method can tightly control the deviation within the preset range. Figure 8: Spatial distributions of compressed point cloud data under different required accuracies \(\varepsilon\): (**a**) bi-Akima compression, \(\varepsilon=0.001\) mm; (**b**) redundancy identification, \(\varepsilon=0.001\) mm; (**c**) redundancy elimination, \(\varepsilon=0.001\) mm; (**d**) bi-Akima compression, \(\varepsilon=0.01\) mm; (**e**) redundancy identification, \(\varepsilon=0.01\) mm; (**f**) redundancy elimination, \(\varepsilon=0.01\) mm; (**g**) bi-Akima compression, \(\varepsilon=0.1\) mm; (**h**) redundancy identification, \(\varepsilon=0.1\) mm; (**i**) redundancy elimination, \(\varepsilon=0.1\) mm; (**j**) bi-Akima compression, \(\varepsilon=1\) mm; (**k**) redundancy identification, \(\varepsilon=1\) mm; (**l**) redundancy elimination, \(\varepsilon=1\) mm. Figure 9: _Cont._