Opencast Coal Mine

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Kena Sugrue

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Aug 3, 2024, 12:45:59 PM8/3/24

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Copyright: 2023 Zhao et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: This study was supported in part by the Foundation of the Basic Scientific Research Projects of Liaoning Higher Education Institutions (grant No. LJ2017FAL015), the National Natural Science Foundation of China (grant No. 51974144), and Project Supported by Discipline Innovation Team of Liaoning Technical University (grant No. LNTU20TD-01 and LNTU20TD-07). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Constructing a digital elevation model (DEM) of geological objects is the basis of digital mining design in opencast coal mines [1]. The DEM is described by different types of structures, such as regular square grids (gridded DEM, GDEM), triangulated irregular networks (TIN) and contour-based structures. As the TIN has some advantages, such as perfect topology, high accuracy and variable resolution, it has been considered to be better than the GDEM [2]. Therefore, the TIN is usually a preferred DEM structure to describe the stratiform geological objects of coal deposits.

In the process the opencast coal mine digital mining design based on a 3D geological model, it is inevitable to clip the DEM described by the TIN of the geological object. Therefore, the TIN clipping algorithm has become the key algorithm in the digital mining design of opencast coal mines, and it can be applied in practice, such as for partially updating the deposit stratum DEM [3,4], rock and coal volume computing [5], the mining design scheme previewing or the playback of the mining and stripping process based on virtual reality (VR) technology [6], partial geological TIN generation for digital twin (DT) technology application [7,8], and other applications related to the digitalization and intellectualization of coal mines [9].

The rest of this paper is organized as follows: Section 2 introduces the algorithm idea and its detailed implementation process, including data structure design, grid index establishing, embedding CP into CTIN, obtaining boundary edges, clipping TIN with the boundary TIN generating and CTIN separating. In Section 3, the algorithm experiments are carried out with different amounts of data; based on that, the performance of the proposed algorithm is discussed by comparing it with the other algorithms. In Section 4, the application of the algorithm in the practice of digital mining design in an opencast coal mine is introduced. Finally, the study is concluded in Section 5.

To handle spatial queries effectively, a spatial index is needed. The spatial index of the CTIN and the CP can be used to rapidly locate and deal with the space object. The methods of creating a spatial index are classified as space-driven and data-driven spatial indexing methods [20]. Among the general spatial indices, the grid index is a kind of high efficiency, extreme conciseness and easily attainable index [21]. The grid index establishment procedure breaks up the minimum bounding rectangle (MBR) of the space object set into some grid cells with a given size and then maps the space object to the grid cells covered by the MBR of that object [21,22]. It is an effective means to improve the efficiency of the spatial operations.

If the maximum and the minimum values of the X- and Y-direction coordinates of all the triangles in CTIN are signified by Xmax, Ymax, Xmin, Ymin, then the two vertices of the CTIN minimum enclosing rectangle main diagonal are determined as (Xmin,Ymin), (Xmax,Ymax).

With the established grid index and the process for determining the point position with the triangles, determining which triangle the CP vertex falls in can be quickly solved by traversing the triangles that map to the same grid cell with the CP vertex.

There are three kinds of position relations between two line segments: coincidence, intersection and non-intersection. As illustrated in Fig 3, the intersection of two line segments p1p2 and q1q2 is resolved as:

The grid index and the line segment intersection algorithm (mentioned in Section 3.2 of this article) can be used to determine whether a triangle intersects with CP. The position relationship (inside, outside, on edge) between the point and the polygon can be concluded by the improved ray method [26], and the procedures are as follows:

Based on the reconstructed topology, the edge-triangle adjacent relationship can be obtained, and then the boundary half-edges that have only one adjacent triangle can be found. Those boundary half-edges compose the boundary polygon of the triangles that lie inside (outside) of the CP.

When the CP is embedded into the CTIN, the topology and the boundary polygon of the triangles that lie inside (outside) of the CP are rebuilt, and the next procedure of the TIN clipping is to generate the boundary TIN between the CP and the boundary polygon of the triangles that lie inside (outside) of the CP.

Fig 7 shows a simple test sample of the algorithm. Fig 7(A) presents the terrain TIN to be clipped, while the CP is shown with a red rectangle in Fig 7(B). If the local details of the terrain are neglected in the course of the CTIN being clipped, the clipping results are as displayed in Fig 7(C). Fig 7(D) shows the clipping result applying the algorithm proposed in this paper. The cyan triangles constitute the boundary TIN generated by the CP and the boundary polygon of the TIN to be clipped.

Fig 8 shows an experimental result of TIN clipping with a concave polygon. Fig 8(C) shows the clipping result of the remaining triangles inside the CP. The cyan triangles constitute the boundary TIN between the convex CP and the boundary of the CTIN inside the CP. Fig 8(D) displays the clipping result of the remaining triangles outside of the CP. Even if the CP is a typical concave polygon, the local details of the CTIN are well-reserved.

In the process of CTIN clipping, the algorithm proposed in this paper calculates the intersection of the CP and the CTIN and reconstructs the boundary TIN of the CP, which completely retains the morphological characteristics of the CP and the CTIN along the trace of the CP, and the CP is clipped precisely while considering the local details. Algorithm experiments have proved that whether the CP is convex or concave, the algorithm proposed in this paper can achieve precise clipping of the CTIN (Figs 7 and 8), which shows that the algorithm is robust.

This algorithm applies the grid index, the improved half edge data structure and the hash function to the construction of point, edge and face (triangle) spatial index of the cropped polygon, the cropped triangulation and the topology reconstruction of the cropped triangulation to improve the query and calculation efficiency of the midpoint, edge and face (triangle) objects in the cutting process to ensure that the algorithm can still have high time efficiency under the condition of a large data scale.

To test the efficiency of the algorithm proposed in this paper, 5 groups of TINs composed of different numbers of triangles are selected using the algorithm proposed in this paper and the algorithm proposed by Yang et al. [18] to clip the TIN and record the time efficiency of the two algorithms, as shown in Table 1.

Table 1 shows that the time efficiency of the algorithm proposed in this paper is better than that proposed by Yang et al. [18]. The main reason for the analysis is that when applying the algorithm proposed by Yang et al. [18] to clip the CTIN, the CTIN is locally modified, split and reconstructed according to the position relationship between the vertex and the triangle (Fig 9). Because subsequent TIN separation is required to complete the TIN clipping, the topology of the CTIN must be updated when locally modifying the CTIN, i.e., vertex aggregation and duplicate edge merging are performed again for the newly added points, edges and faces (triangles). When the number of CP vertices and triangles of the CTIN is large, the topology reconstruction of the TIN takes a great deal of time, which leads to a decline in time efficiency.

In the process of precise clipping of the CTIN using the algorithm proposed in this paper, when generating the boundary triangulation based on the CP and the boundary edge, a one-time edge-prior CDT (Constrained Delaunay Triangulation) growth algorithm [28] with high time efficiency is applied, and the topology of the CTIN is updated with the generation of the boundary TIN. On this basis, CTIN separation can be accomplished by simply modifying the edge attributes along the trace of the CP. Therefore, compared with the algorithm proposed by Yang et al. [18], the algorithm proposed in this paper has certain advantages in terms of time efficiency.

The limitations of this study are as follows: First, because the grid index of the CTIN is constructed based on the two-dimensional coordinates of the triangles and the edges, if there are two triangles, the X- and Y-direction coordinates of their edge vertices are equal, but the Z-direction coordinates are not equal, the TIN clipping algorithm in this paper treats such two triangles as the same triangle, that is, the overlapping triangles in the Z-direction of the CTIN cannot be distinguished by the algorithm. So, the TIN overlapping in the Z-direction cannot be clipped correctly in this study, particularly the closed TIN. However, because the digital mining design of the opencast coal mine described in this study is based on multilayer DEMs, the algorithm can work well in the digital mining design practice. If digital mining design is based on closed TIN models, the algorithm needs to be improved. Secondly, the algorithm in this paper achieves precise clipping of the CTIN by calculating the intersections of the CP and the CTIN and reconstructing the TIN between the CP and the boundary polygon of the triangles located inside or outside the CP, to ensure precise clipping of the CTIN, there may be long and narrow triangles in the reconstructed TIN, resulting in some triangles do not conform to the empty circumcircle criteria of Delaunay triangulation, that means the clipped TIN cannot be guaranteed to be the best in shape. To fully express the stepped topographic features of the stope and dumping site, the DEM of the opencast coal mine is usually a CDT TIN constructed with bench edges or contour lines as constraint edges, inevitably some shorter constraint edges cause long and narrow triangles in the TIN. These long and narrow triangles cannot be optimized with LOP (Local Optimization Procedure), otherwise, DEM distorts the representation of the modeling object. Therefore, the existence of long and narrow triangles in the clipped TIN that do not conform to the empty circumcircle criteria of Delaunay triangulation does not mean that TIN clipping is wrong. In summary, the limitations of this study do not affect the application of the TIN clipping algorithm proposed in this paper in the digital mining design practice of opencast coal mines based on multilayer DEMs.