## 3 Experimental Results
### Test A  
The on-line point cloud data compression algorithm was tested in the industrial real-time measuring process and compared with existing methods (chordal method and bi-Akima method). The measuring system consists of a contact 3D scanning probe, a vertical lathe and a commercial computer numerical control (CNC) system of SINUMERIK 840D (Munich, Bayern, Germany) as shown in Figure 5. The proposed algorithm is integrated in the original equipment manufacturer (OEM) application that runs on the host computer of the CNC system. The product model of the contact 3D scanning probe is DIGIT-02 (Dalian, Liaoning Province, China). More detailed technical characteristics of the measuring instrument are shown in Table 1.  
The measured part is a half-ellipsoidal surface which is welded together by seven pieces of thin-walled aluminum alloy sheet, as shown in Figure 5d, with a semi-ma  
\begin{table}
\begin{tabular}{c c} \hline \hline  
Figure 5. The measuring system and measured 3D free-form surface: (**a**) vertical lathes; (**b**) computer numerical control (CNC) system; (**c**) scanning probe; (**d**) half-ellipsoidal measured part. semi-minor axis of 950 mm. A rotational progressive scanning mode is adopted, and the layer spacing is 7 mm. Figure 6 shows the spatial distribution of the initial point cloud data. The isochronous sampling method is adopted and the number of initial sampling points is 272,638. Using the same initial point cloud data set as shown in Figure 6, the comparison of data compression performance is made between the proposed method, chordal method and bi-Akima method under different required accuracies (i.e., from 0.001 mm to 1 mm). Table 2 summarizes the results of the data compression performance including the number of points and data compression ratio, where the compression ratio is defined as the ratio between the uncompressed size and compressed size:  
\[\text{Compression Ratio}=\frac{\text{Uncompressed Size}}{\text{Compressed Size}}=\frac{\text{Number of Initial Points}}{\text{Number of Compressed Points}}. \tag{17}\]  
Obviously, the proposed method has a higher data compression ratio than the chordal method and bi-Akima method, and the chordal method obtains the lowest data compression ratio under the same required accuracy. The number of data points obtained by the proposed method is about half of that obtained by the bi-Akima method under the same required accuracy. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Required**} & \multicolumn{3}{c}{**Number of Points**} & \multicolumn{3}{c}{**Compression Ratio**} \\ \cline{2-7}  & **Chordal** & **Bi-Akima** & **Proposed** & **Chordal** & **Bi-Akima** & **Proposed** \\  & **Method** & **Method** & **Method** & **Method** & **Method** & **Method** \\ \hline
0.001 & 237,363 & 122,929 & 67,448 & 1.15 & 2.22 & 4.04 \\
0.002 & 189,824 & 120,952 & 67,121 & 1.44 & 2.25 & 4.06 \\  
Figure 7 provides the comparison of the compression ratios between the three methods under the 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 other two methods. Obviously, the chordal method has the lowest data compression ratio. Therefore, we focus on comparing our proposed method with the bi-Akima method in the subsequent experiments. To make the comparison more vivid and intuitive, Figure 8 visually illustrates the difference between the proposed method and bi-Akima method by displaying spatial distributions of compressed point sets under different required accuracies. Subfigures a, d, g and j show the point cloud distribution compressed by bi-Akima method 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.