## 2 Methods and Steps
### Data Acquisition and Processing Methods
#### 2.2.2 Data Sample Processing Method  
In order to restore the real heaped-up bulk characteristics after cast blasting as much as possible, the sample size of the 3D point cloud data should be increased on the basis of the collected 3D point cloud data, so as to improve the restoration accuracy of the heaped-up bulk characteristics. Through a literature review and analysis, this paper intends to adopt the method of the discrete point moving fitting distance weighted average interpolation to increase the sample size of the 3D point cloud data [27]. Secondly, for the added sample data, it is also necessary to conduct a data feature test, so as to improve the accuracy of the data. Firstly, the idea of a data dimension reduction was proposed. In order to simplify the research process and reduce the dimension of the data index, 2D space was used to replace 3D space; that is, the surface characteristics of the heaped-up bulk were used to replace the 3D characteristics of the heaped-up bulk. Secondly, considering that the bending degree of each position of the heaped-up bulk surface is determined by the curvature of each point, according to the bending characteristics of the surface, this study divided the shape of the heaped-up bulk surface into a convex surface, a concave surface, and a straight surface. Finally, the characteristic model of the heaped-up bulk surface was constructed. Suppose \(n(x_{n}j_{n})\) as the fitting surface after \(\overline{Z}=\overline{f}(x,y)\); the location of the points on the tangent plane with the center point and the relative position of the surface are used to determine the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Project** & **Parameter** & **Description** \\ \hline The data collection & — & 360\({}^{\circ}\) scan and panoramic photo collection \\ The laser wavelength & 1550 nm & No visible light \\ The scanning angle & 0\({}^{\circ}\) to 360\({}^{\circ}\) & Horizontal angle \\ The scanning distance & \(-\)45 to 80\({}^{\circ}\) & The vertical angle \\ The scanning distance & 0.5 m to 700 m & — \\ The scanning speed & 7000 p/h & — \\ The transmitter resolution & 1 cm & Precision can be up to 10 cm \\ Scanning angular resolution & 0.01\({}^{\circ}\) & Accurate to 0.02\({}^{\circ}\) \\ Image acquisition & 432 million pixels & Panoramic scope\({}^{\circ}\) \\ The sensor & — & IMU obliquity sensor, altimeter, GNSS \\ Wireless communications & 802.11 b/g/n & Integrated wireless communication \\ Data storage & 256 GB,USB3.0 & Actual storage \\ Length of equipment & 209 mm \(\times\) 243 mm \(\times\) 419 mm & Length, width, and height \\ Appropriate temperature & \(-\)10 \({}^{\circ}\)C to 45 \({}^{\circ}\)C & Working temperature \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Equipment parameters of the high-precision scanner. Figure 2: Schematic diagram of the field equipment collection. relationship between the changes in the concave and convex surfaces. As such, the \(n(x_{n}j_{n})\) location points fitting the surface \(\overline{Z}=\overline{f}(x,y)\) center (\(x_{0},y_{0}\)) are expressed as follows:  
\[\overline{Z}=\overline{f}(x_{0},y_{0})+\frac{\partial\overline{f}}{\partial x} (x_{0},y_{0})\cdot(x-x_{0})+\frac{\partial\overline{f}}{\partial y}(x_{0},y_{ 0})\cdot(y-y_{0}) \tag{1}\]  
If the tangent plane is located above the fitting surface, the surface of the heaped-up bulk element is convex. If the tangent plane is located below the fitting surface, the surface of the heaped-up bulk element is concave. If the tangent plane coincides with the fitting surface, then the surface of the heaped-up bulk element is a straight face. Therefore, with the elevation at its center position \(\overline{Z}(p_{k})\) and its actual elevation value \(Z(p_{k})\) of the mean value being defined as the difference between the surface point location in form features, we have the following:  
\[G=\frac{1}{n}\sum_{k=1}^{n}\left[\overline{Z}(p_{k})-Z(p_{k})\right] \tag{2}\]  
When \(G>0\), the heaped-up bulk slope is convex, and the larger \(G\) is, the greater the convexity.