## 3 Results
Once the length of cube's edge \(L\) is determined, the projection points are determined, and the projection points are usually far less than 1/3 of the number of the points. Our algorithm consists of the following steps: create hash table, search hash table, Create 3D points, compute normal vector, and interpolation. The computation complexity are O(N), O(1), O(N), O(N), and O(N), respectively. The time complexity of our algorithm is O(N). We can get the same conclusion from Figure 7. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Object Model** & \begin{tabular}{c} **Points** \\ **(million)** \\ \end{tabular} & \begin{tabular}{c} **Projection** \\ **(million)** \\ \end{tabular} & **Cubes** & \begin{tabular}{c} **Time** \\ **(ms)** \\ \end{tabular} & \
\begin{tabular}{c} **Time (3.0L) (ms)** \\ \end{tabular} &
\begin{tabular}{c} **Time of** \\ **EGG (ms)** \\ \end{tabular} \\ \hline Famer Statue & 0.121 & 0.038 & \(156\times 102\times 121\) & 234 & 101 & 924 \\ Blade & 0.178 & 0.078 & \(101\times 143\times 383\) & 266 & 139 & 1253 \\ Mother Statue & 0.516 & 0.114 & \(297\times 200\times 134\) & 828 & 353 & 2742 \\ Engine Cover & 1.272 & 0.248 & \(444\times 267\times 162\) & 2259 & 846 & 6759 \\ Engine & 2.875 & 0.450 & \(621\times 314\times 191\) & 5023 & 1802 & 16,130 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The details of the experiment. Figure 6: The shading model of simulation spheres according to our method with different numbers of points \(N\). (**a**) \(N\) = 0.1875, (**b**) \(N\) = 0.375, (**c**) \(N\) = 0.75, (**d**) \(N\) = 1.5, and (**e**) \(N\) = 3.0 million. Figure 7: (**a**) Comparison of the quantity-time curve on actual point cloud and (**b**) comparison of the quantity-time curve on simulation spherical. The number of projection points is the key factor in determining the efficiency of the algorithm, which is closely related to the length of the cube. We have tested the length of the cube, which varying from \(1.0L\) to \(3.0L\) on the model in Figure 5, and gotten time-length curve. The curves about time and \(L\) are nonlinear, and the ordinate decreases sharply with the increase of \(L\). Figure 8a shows the result of the normal vector estimation of different lengths of the cube. When the cube's length is over \(2.0L\), the time remains almost the same. The reasonable length of cube is about \(1.5L\), which ensures the efficiency and accuracy of the algorithm. Figure 8b is the result of the normal vector estimation of simulation spheres, and the error greatly increased, while the length of the cube is over \(3.0L\). We have explored the proposed algorithm on simulation sphere data in terms of accuracy, and the statistical results show that the average deviation of the normal vector is less than 0.0065 mm. In our algorithm, over 75% interpolation calculation uses four normal vectors with an average error of 0.005 mm,!14% interpolation calculation uses three normal vectors with the average error of 0.008 mm; and 11% interpolation calculation uses two normal vectors with the average error of 0.0102 mm. The experimental results show that the proposed algorithm is more effective and efficient compared with the existing methods of the normal vector estimation.