# A Coal Mine Excavation Tunnels Modeling Method Based on Point Clouds
## 5 Discussion
### Limitation of the Algorithm  
While the proposed algorithm has been specifically designed for rectangular cross-section tunnels, such as those commonly encountered in coal mine excavations, its application to tunnels with different shapes, particularly circular or irregularly shaped tunnels, presents significant challenges.  
Figure 22: Instantiated model based on Unreal Engine. (**a**) Tunnel model with anchor nets. (**b**) Tunnel model with equipment.  
Firstly, during the point cloud coordinate transformation process, the algorithm relies on identifying the long and short edges of the rectangular tunnel to determine the rotation angle, which ensures that the tunnel's floor is aligned parallel to the XOY plane. In the case of circular tunnels, however, the absence of distinct long and short edges makes it impossible to define this rotation angle. Although for arched tunnels, the floor plane can be utilized to determine the rotation angle, this method is not applicable to fully circular cross-sections.  
Secondly, the tunnel contour extraction method employed in this study is based on the characteristic density distribution observed along the X or Z axes for rectangular tunnels. In these cases, one side of the tunnel typically exhibits a peak in the histogram of the density distribution (for instance, the left wall producing a peak on the X-axis). This feature aids in accurate contour extraction. However, circular tunnels do not present clear peaks or valleys in the density distribution, which renders this extraction method ineffective.  
Moreover, tunnels with complex geometries, including those that are not flat or horizontal, such as those featuring both horizontal and vertical arcs, may further complicate the contour extraction process. The arched edges could obscure the expected density characteristics, potentially leading to challenges in accurately identifying the tunnel profile. Additionally, the presence of arched profiles may affect the performance of the hole-filling algorithm, which is based on tunnel symmetry.  
Despite these limitations, other steps of the algorithm, including centerline extraction, normal optimization, and Poisson surface reconstruction, are not strictly contingent upon the tunnel having a rectangular cross-section. These components can still be applied to circular tunnels. Therefore, future adaptations of the algorithm for circular and irregularly shaped tunnels will primarily necessitate modifications to the point cloud extraction and contour determination methods.  
Additionally, in this study, the algorithm was specifically developed for point clouds obtained via Mobile Laser Scanning (MLS), largely due to the stringent safety regulations that govern underground mining operations. The MLS equipment used had been rigorously tested and certified for explosion safety, ensuring it met the required safety standards for coal mine environments. Given the confined dimensions of these tunnels--approximately 5 m wide and 3 m high--MLS provides the necessary accuracy and density for effective modeling. However, it is important to note that we have not yet conducted experiments using point clouds derived from Terrestrial Laser Scanning (TLS), as TLS and MLS (SLAM) clouds give completely different densities and uniformity distribution [49]. This represents a significant limitation of our study. While we anticipate that the algorithm could potentially be adapted for TLS-acquired point clouds through appropriate voxel downsampling to mitigate density distribution differences, further experimental validation is required to confirm its efficacy in this context.