## 1 Introduction
Some practical solutions to the problem of transformation between local geodetic coordinate systems, as well as between the local geodetic system and global reference systems, are described in reference [13]. In reference [14], the problem involving the transformation of cadastral map coordinates to the national coordinate system in Turkey is presented. The importance of a correct procedure for the transformation task is discussed in reference [15]. A solution for improving the precision of coordinate transformation using the classification and weighting of coordinate components is provided in reference [16]. A new method for calculating transformation parameters and assessing the precision of transformation is presented in reference [17]. The importance of correct coordinate transformation for monitoring surface deformations is presented in reference [18]. Moreover, when using Interferometric Synthetic Aperture Radar (InSAR) [19] and Light Detection and Ranging (LiDAR) [20] technology, it is essential to execute the transformation task correctly. The problem of coordinate transformation has been the subject of a number of studies carried out for the area of the Czech Republic. Reference [21], concerning the Karvina-Ostrava Coal District, indicated the optimum transformation relations that disallow interfering with the accuracy of calculations and measurements obtained in the Otto coordinate system. In reference [22], the authors present the results of a study on inter-system transformations for the georeferencing of old mine workings. Furthermore, the basic features of the transformation between the analyzed systems to obtain coordinates in the European Terrestrial Reference System were defined. The research conducted by the authors of this article has shown that a significant problem of transformation carried out independently (separately) for each mining area involves finding the different coordinates of identical points in the national coordinate system, which is particularly important in the case of boundary points of neighboring mines. Therefore, there is a lack of topological consistency in these areas. The above-mentioned problem prevents the appropriate integration of spatial data at the municipal, provincial, and national level, which is important for making decisions on spatial planning and management, including the appropriate management of mining and post-mining areas. This problem was the subject of the research continued by the authors (including [23]). An authorial transformation procedure based on the method of independent models (MIM) has been developed. The method is used in photogrammetry, and more precisely in aerotriangulation. The first mentions of the method appeared in the 1920s with the beginning of the development of an independent model of air triangulation. The principles of this method were discussed in the article by [PERSON] [24]. [PERSON] in their work [25] emphasized the contribution of [PERSON] to the development of the air triangulation method. In the 1940s, solutions related to independent models reappeared (e.g., [26]). The research described in references [27; 28] allowed for the robust development of MIM. The 1970s were a period when independent models were considered superior to non-iterative methods [29]. In later years, the method of independent models was used in various areas. The studies mentioned in references [30; 31] are noteworthy, where the authors indicate the possibilities of using MIM to build 3D models and the advantages of this method in this field. In Poland, studies related to this topic were described in references [32; 33; 34; 35]. A new application of MIM in relation to the transformation of the coordinates of boundary points of neighboring areas is presented in this article. The procedure and results of the transformation task of the coordinates of boundary points of 14 mining areas located in the southern part of Poland, i.e., in the Upper Silesian Coal Basin, are presented.