## 6 Discussion  
Coordinate transformation is a very important and frequently used mathematical procedure in geodesy and geoinformatics when dealing with different coordinate systems. The aim of this article was to unify all coordinate transformations, explain the computation procedure of the transformation parameters, define the main transformation metadata, and explain the reversible transformation on the example of the Croatian territory. In [PERSON] et al. [14], a similar issue was processed, but in this article, the computation procedure of transformation parameters was shown in a more detailed way. In a coordinate transformation procedure, a set of transformation parameters is not sufficient to carry out the transformation unambiguously. Additional metadata about the rotation matrix, which is used to calculate transformation parameters, are also required. The first metadata is the convention that defines the rotation matrix. Although it is usual that CFR convention is used for transformation between global and local, and the PVT convention between two global coordinate systems, it is good to know which convention determines the parameters in case the user is unsure about the systems in question. The second important metadata is rotation matrix form, based on which the transformation parameters were calculated, so that the same rotation matrix can be used in transformation procedure. Using different forms of rotation matrices (simple rotation matrix, rotation matrix \(R^{XYZ}\), rotation matrix \(R^{ZYX}\)) can result in different output coordinates with errors at the centimeter level, as demonstrated in the numerical example of the 7-parameter transformation. This highlights the importance of this metadata. Reversible transformation, in cases where it is necessary to switch from one system to another and then return to the original one, should be performed with a single set of parameters, wherein the general expression for the transformation must be inverted. In that way, upon returning to the original system, identical coordinates to the ones we started with will be obtained, whereas this will not be the case if two sets of parameters and the same expression for the transformation is used, as demonstrated by the numerical example in the case of a 7-parameter transformation. Selecting a specific transformation model in practice largely depends on the expected results: more precisely, the level of accuracy that is aimed to achieve with the transformation. Models that use a smaller number of parameters typically yield results with lower accuracy, but their application is more straightforward. On the other hand, models using a larger number of parameters deliver higher accuracy results but are mathematically more complex. The application of 3-parameter and 5-parameter models is suitable when lower accuracy is acceptable and there is a need to transform a large amount of data. In practice, 7-parameter models are most commonly used because they effectively align reference frames at a global level and belong to conformal models while maintaining satisfactory accuracy. Theoretical and realized ellipsoid parameters differ, resulting in errors in the conversion of ellipsoidal coordinates to Cartesian, upon which transformation parameters are calculated. Due to the inability to define whether the minor and major semi-axes are proportionally different, the 8-parameter model is suitable because it assigns one scale factor to the minor semi-axis and another scale factor to the major semi-axis. By calculating the transformation parameters of 3-parameter, 7-parameter, 8-parameter, 9-parameter, and 12-parameter transformations, similar results were obtained as in [PERSON] et al. [14]. The results are not exactly the same because of the different common points used for the computation of the transformation parameters. The main difference compared to [PERSON] et al. [14] can be noticed in the 5-parameter Molodensky transformation, more precisely in the approach to calculate transformation parameters. In [PERSON] et al.