## 3 Experimental Results
### Test B  
The overall structure of the model in Test A is relatively simple. In order to further verify the universality and adaptability of the proposed method, we chose a more complex surface model with a large number of details, edges and sharp features for experimentation. As shown in Figure 10, the tested model is a piece of jewelry, which is inlaid with 30 diamonds of different sizes. Figure 11 shows the initial point cloud data acquisition result. The progressive scanning mode and equidistant sampling mode were adopted. Scanning lines are along the \(X\)-direction (horizontal direction). The distance between two adjacent scanning layers is 0.1 mm, and the distance between adjacent points is 0.05 mm in each scanning layer. The initial point number is 63,376. The comparison is made between the proposed method and bi-Akima method under different required accuracies (i.e., from 0.001 mm to 1 mm). Table 3 gives the results of data compression performance, including the number of points and data compression ratio. Obviously, the proposed method has a higher data compression ratio than the bi-Akima method. The number of points obtained by the proposed method is about half of that obtained by bi-Akima method under the same required accuracy. Figure 12 provides the comparison of the compression ratios between these two methods under different required accuracies. With the decrease in accuracy requirements, the compression ratio increases for all methods; however, for all levels of required accuracy, our proposed compression method manifests a superior compression ratio than the bi-Akima method. Figure 13 visually illustrates the difference between the proposed method and bi-Akima method by displaying spatial distributions of the compressed point sets under different required accuracies. Subfigures a, d, g and j show the point cloud distribution compressed by the bi-Akima method,  
Figure 10: The tested complex surface model: jewelry. while subfigures b, e, h and k give the point cloud distribution after data redundancy identification by the proposed method, with the identified redundant points marked in red. In subfigures c, f, i and l, the identified redundant points are eliminated. These subfigures show the distributions of the final compressed point cloud data. By contrast, we can clearly observe the difference in point cloud density between these two methods under the same required accuracy. Take subfigures j, k and l, for example: when using the bi-Akima method, we can observe that there are many curves roughly along the vertical direction (Figure 13j). This is because the bi-Akima method can only deal with the point set in the current single scanning line, which is along the horizontal direction, and the data redundancy outside the current scanning line  
In order to verify the accuracy of the proposed algorithm, Figure 14 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, which proves that the proposed 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 less than the required accuracy in most of the measured area.