## 4 Discussion  
The problem presented in this article, concerning the implementation of the transformation of identical boundary points of neighboring mining areas, is of key importance, especially in post-mining areas, particularly in the period of mine liquidation. It should be noted that, both in closed areas and active mines, numerous threats are observed, including the threat of surface deformation and water or seismic hazards, and the correct assessment of the possibility of such threats is crucial for making decisions regarding their management, which would ensure public safety. This is related, among other things, to the access to information on the coordinates of the boundary points of mining areas, especially the neighboring ones, where these coordinates were documented using local rectangular flat coordinate systems, and the implementation of tasks at the municipal, provincial, or national level requires access to spatial information in one binding national coordinate system. Therefore, the above fact necessitates the transformation of coordinates from the local system to the national one, including the coordinates of the boundary points of the mining areas that are adjacent to each other. Another problem is the fact that, in the currently used solutions involving the implementation of the transformation task separately for each mining area, there is a lack of topological consistency, despite the fact that the transformation errors meet the current accuracy criteria, i.e., they do not exceed the transformation error of 0.05 m (Table 2). The minimum value of the transformation error is 0 m and the maximum value is approximately 0.04 m. The calculated coordinate differences in selected identical boundary points after transformations performed separately for each mining area are included in Table 3. The summary of basic statistical measures covering the full range of transformed points is presented in Table 4. The values of the differences in the position of identical boundary points in the analyzed areas after the transformation ranged from 0.002 m to 1.945 m, the standard deviation of the differences in the position was about 0.349 m, and the difference in the coordinates \(\Delta x\) and \(\Delta y\) reached a maximum value of about 1.937 m and 0.542 m, respectively (Table 4). The analysis of the distribution of differences in individual classes indicated that, in as many as 40% of cases, the differences in location exceeded the value of 0.05 m, and in 32 cases, they ranged from 0.50 m to about 2.00 m (Figure 6). The above situation absolutely eliminates the possibility of a correct assessment of the location of the occurrence of post-mining hazards and, consequently, their safe development. This article presents an authorial procedure for the implementation of the transformation task based on the method of independent models that eliminates the above-mentioned  
Figure 6: Distribution of differences in the location of identical boundary points after transformation [m]—the separate method. problem. The transformation errors also meet the assumed accuracy requirements, and the differences in the coordinates of identical boundary points, when using the method of independent models, reach a maximum value of 0.001 m in the entire analyzed set. The standard deviation of the differences in position was also about 0.001 m, while both the difference in coordinates \(\Delta x\) and \(\Delta y\) reached a maximum value of only 0.001 m.  
The analysis showed that this resulted from the rounding up of significant figures. At the same time, it can be assumed that the transformation procedure developed in this study ensures the acquisition of equal values of identical boundary points. For the developed procedure, it does not matter what local coordinate system is used in a given area (it does not matter whether the input coordinates are in the Sucha Gora, Borowa Gora, 1965 systems, etc.).