# A Coal Mine Excavation Tunnels Modeling Method Based on Point Clouds
## 3 Methods
### Tunnel Point Cloud Completion  
After acquiring the tunnel's point cloud, occlusion caused by internal equipment often results in numerous gaps along the boundary of the point cloud, which can negatively affect the final modeling outcome. Therefore, filling these gaps becomes necessary. Given the tunnel's symmetrical structure, the filling process is performed sequentially, first based on the left-right symmetry axis, followed by the top-bottom symmetry axis. The left-right symmetry completion addresses cases where one side of the tunnel is obstructed by objects such as conveyor belts or ventilation ducts, while the other side remains unobstructed. The top-bottom symmetry completion, on the other hand, focuses on situations where materials or equipment are present on both sides of the tunnel.  
Completion based on the left-right symmetry is shown in Figure 7. For the holes in the ceiling and floor of the tunnel, the position \([X_{0},X_{1}]\) that needs to be filled is determined, where \(X_{1}-X_{0}>d_{hole}\), based on the hole threshold \(d_{hole}\). According to the positions of the left and right walls of the tunnel determined in previous section \(X_{\lambda_{max}}^{left}\) and \(X_{\lambda_{max}}^{right}\), the corresponding range on the opposite side of the symmetry axis is calculated as \(\left[X_{\lambda_{max}}^{left}+X_{\lambda_{max}}^{right}-X_{1},X_{\lambda_{ max}}^{left}+X_{\lambda_{max}}^{right}-X_{0}\right]\). For a point \(P\big{(}X_{p},Y_{p},Z_{p}\big{)}\) in the non-hole side, the coordinates of the completion point \(P^{\prime}\Big{(}X_{\lambda_{max}}^{left}+X_{\lambda_{max}}^{right}-X_{p},Y_ {p},Z_{p}\big{)}\) are calculated. For holes in the left and right walls of the tunnel, the gap positions \([Z_{0},Z_{1}]\) are determined, where \(Z_{1}-Z_{0}>d_{hole}\). For a point \(P\big{(}X_{p},Y_{p},Z_{p}\big{)}\) in this range in the non-hole side, the coordinates of the completion point \(P\Big{(}X_{\lambda_{max}}^{left}+X_{\lambda_{max}}^{right}-X_{p},Y_{p},Z_{p} \big{)}\) are similarly calculated.  
After the left-right completion, areas where point cloud data is missing at symmetric positions still need to be further completed based on the top-bottom symmetry axis. Completion based on the top-bottom symmetry is shown in Figure 8. For gaps in the ceiling and floor of the tunnel, the positions \([X_{0},X_{1}]\) requiring completion are identified, where \(X_{1}-X_{0}>d_{hole}\), based on the hole threshold \(d_{hole}\). For a point \(P\big{(}X_{p},Y_{p},Z_{p}\big{)}\) in this range in the non-hole side, the coordinates of the completion point \(P^{\prime}\Big{(}X_{p},Y_{p},Z_{\lambda_{max}}^{top}+Z_{\lambda_{max}}^{bottom }-Z_{p}\Big{)}\) are determined. For holes in the left and right walls of the tunnel, the hole position \([Z_{0},Z_{1}]\) is similarly identified, and the reference point cloud range \(\left[Z_{\lambda_{max}}^{top}+Z_{\lambda_{max}}^{bottom}-Z_{1},Z_{\lambda_{max} }^{top}+Z_{\lambda_{max}}^{bottom}-Z_{0}\right]\) is calculated. For a point \(P\big{(}X_{p},Y_{p},Z_{p}\big{)}\)  
Figure 6: Point cloud density distribution curve along the X-axis.  
in this range, the coordinates of the completion point \(P\prime\Big{(}X_{p},Y_{p},Z_{\lambda_{max}}^{top}+Z_{\lambda_{max}}^{bottom}-Z_{p} \Big{)}\) are computed.