# Feature-Preserved Point Cloud Simplification Based on Natural Quadric Shape Models
## 3 Experiments and Discussions
### The Discussion of Self-Adapting Experiment Parameters
Figure 9: Comparison of the simplified surface and original surface: (**a**) the parameters of FPPS are \(k=10\) and \(\sigma=1000\); (**b**) the parameters of FPPS are \(k=25\) and \(\sigma=400\); (**c**) the parameters of FPPS are \(k=50\) and \(\sigma=200\); (**d**) the parameters of FPPS are \(k=80\) and \(\sigma=130\); (**e**) the parameters of FPPS are \(k=100\) and \(\sigma=100\). estimated. Furthermore, the different local areas selected will result in different simplification sizes and simplification surfaces, which are shown in Table 3 and Figure 8. In Table 3, we list the reduced triangle number and reduced point cloud size. The simplification ratios calculated from the reduced point cloud size and original point cloud size are also listed. The number of triangular faces is between 6346 and 7336, and the simplification ratio is distributed between 9% and 12.3% by the FPPS. So, the changes in the simplification ratio and the number of triangular faces is small. However, we can see from the reconstruction surfaces in Figure 8 that the surfaces are different, especially on the richer surface features areas. Then, we compare the effect of the reconstruction surface. The result of the comparison of two surfaces is shown in Figure 9; these are the surface reconstructed by \(S\) and the surface reconstructed by \(R\). From Figure 9, we can see that if \(c\) is the same and \(k\) and \(\sigma\) are different, different effects on the reconstruction surface are obvious. In Figure 9, the left column is the deviation value of the two surfaces, which is noted by the color code. The experimental results show that \(k\) and \(\sigma\) influence the protected features in FPPS. Compared to the deviation value of Figure 9a-e, the maximum deviation value of Figure 9a is in the range [\(-\)0.005, \(+\)0.005], which shows that experiment (a) produced a better effect. With a decrease in \(\sigma\), the deviation range extends, and the simplification effect is worse. However, the range of Figure 9d is [\(-\)0.006, \(+\)0.006], which shows that if more key points are chosen, the simplification effect is revised. So, in order to find the suitable parameter \(k\), \(\sigma=1\) 000 was fixed in experiment (a), and parameter \(k\) was changed. The upper and lower limits of the deviation value in the simplification result comparison are extracted in Figure 10. In Figure 10, the boundary value is the absolute value of the upper and lower limits of deviation, and this is used to estimate the simplification effect. The boundary value changes with parameter \(k\), as shown in Figure 10.  
From Figure 10, we can see that when parameter \(k\) is set smaller than 50, that is 0.13% of the bunny's size, the experiment produces a worse simplification effect. However, as \(k\) increases, a greater burden on the experiment running time will be produced. Fortunately, the inflection point is shown in Figure 10. The experimental results show that the number of key points \(k\) is greater than 0.2% of the number of points, the local area \(Neighbors(p_{i})\) matches \(PCMM\) well, and the simplification rules fit the shape features. Eventually, a better simplification effect will be reached. In this experiment, we assumed that the three types of key points were balanced in terms of their influences on simplification. Thus, parameter c should be set similar to the size of \(R\), and the number of key points \(k\) should be set greater than 0.2% of the size of \(R\) for the simplification to be satisfied. For example, because the volume of the bunny data set is 35,947, parameter \(c\) was set as 35,000, which is similar to 35,947. The lower limit for the number of key points \(k\) was 70. Figure 10: The boundary values with the number of key points \(k\).