## 2 Materials and Methods
### Variants of Documentation Remodelling
Orange Line—object (construction) without geographic context (core of the construction). Violet Line—object (construction) with geographic context (object + environment)—built environment. Mathematical model of CAD to GIS remodelling  
\[(C_{p}\times C_{L}\times C_{A})\cup C_{T}\rightarrow(G_{p}\cup G_{L}\cup G_{A}) \cup G_{T} \tag{4}\]  
where  
symbols \(C_{P}\), \(C_{L}\), \(C_{A}\), \(C_{T}\) have the same meaning as in the Equation (1),  
\(G_{P}\) is set of graphical point elements in GIS (point layers)  
\(G_{L}\) is set of graphical line elements in GIS (polyline layers)  
\(G_{A}\) is set of graphical area elements in GIS (area layers)  
\(G_{T}\) is set of element attributes in GIS. We can also divide Equation (4) into graphical and non-graphical parts. Graphical part:  
\[(C_{p}\times C_{L}\times C_{A})\to G_{G} \tag{5}\]  
where  
\(G_{G}\) is set of graphical elements in GIS. Non-graphical part:  
\[C_{T}\to G_{T} \tag{6}\]  
The projection in Equation (5) is not a single-valued function, the projection in Equation (6) is a single-valued function. Currently, railway infrastructure constructions in the Czech Republic are not designed using BIM, this approach is only gradually being introduced. On the other hand, there is an existing 3D CAD documentation of the railway infrastructure on the length of the railway tracks of approximately 9600 km, which is subject to remodelling into the necessary newly emerging BIM and GIS platforms. Figure 5 shows two possible interaction processes of CAD--BIM--GIS technologies in the construction life cycle:  
1. The intention to implement a new building (selection of a suitable location of the VGO based on spatial analyses in GIS), design of the building in CAD (3D geometric model) and its supplementation with information in BIM (building information model) including storage in CDE. After the construction is completed, the as-built state of the construction is geodetically surveyed and the information obtained is added to the BIM + stored in the CDE. The next step is the conversion to GIS, which gives the BIM building information model a geographical context. 2. In the case of an existing building with CAD documentation based on a geodetic survey of the as-built state of the construction. The next step is to convert to BIM including saving to CDE. Then the whole model is converted to GIS, giving it a geographical context. Simplistically we can say that the BIM model itself contains detailed information about the building without a wider geographical context, the object in the GIS environment contains less internal information about the object, but with a real geographical link to the  
Figure 6: Conversion from CAD to BIM. surroundings, i.e., the geographical context. Thus, the combination of both technologies provides the maximum information content about the internal object and its relation to its surroundings. The first step of the G-ABD conversion to the BIM and GIS environment was to compare the classification of elements of the data model defined by the RA M20/MP005 standard [59], according to which the G-ABD was prepared, and the data model of the data standard [4], to which the data were to be alternatively transformed, both to the BIM environment and subsequently to the GIS. This section is elaborated in more detail in Chapter 3. Only those elements of the data model that were present in the subject building were compared in the analysis, not all elements of the data model. The set of elements contained an element from each object category of the RA standard.