## 2 Materials and Methods
### Variants of Documentation Remodelling  
The principle of converting CAD data into BIM and GIS is shown in Figure 5. The GIS environment in our case consists of geographic objects (GO) of 3 types:  
* VGO--a virtual geographical object that does not yet physically exist in the real world, but exists in the form of an idea for a future building. * RGO-CAD--a real geographic object with CAD documentation, i.e., a 3D geometric model of the object. * RGO-BIM--a real geographical object with documentation in BIM technology, i.e., an information model of the object. \begin{table}
\begin{tabular}{c c} \hline \hline
**CDE** & **Number** \\ \hline Bentley ProjectWise & 5 \\ Proconom & 1 \\ AspeHub & 1 \\ BIM360 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Occurrence of CDE platforms in RA pilot BIM projects. \begin{table}
\begin{tabular}{c c} \hline \hline
**Tool** & **Short Overview** \\ \hline Share & It is a basic tool used to upload (share) data from individual desktop software (offline) to the CDE environment (online). \\ ProjectWise Web Connection & ProjectWise also exists as a desktop application, this tool in the online CDE is used to connect to the offline version of the application. \\ Deliverables Management & This tool is used to accept documentation. Both the client and the contractor are represented in the CDE and the handover (making available to the other party) takes place via this tool. \\ Project Insights & Here you can find an overview of basic information about the project. \\ Portfolio Insights & Here you can find an overview of basic information about the portfolio (i.e., all projects of the user). \\ Issue Resolution & The BIM model can be commented on. Each participant in the process can be assigned a task to do. These comments may (but need not) be linked to a specific location in the 3D model. \\ Forms & Tool used to create forms that can be used to facilitate the coordination of people. The advantage is the possibility of predefining the content of the form and the impossibility of unauthorized persons to interfere with the template. \\ Components Center & With this tool, it is possible to insert small BIM models of individual building \\ PlantSight & This tool is used for analyses and summaries of model elements. \\ iModel Manager & This tool is used to manage, view and coordinate 3D models. It is a basic tool that allows \\ OpenTower IQ & This relatively new tool is used to streamline communication in relation to 5G networks. \\ OpenUtilites Digital Twin Services & This tool is used to visualize utility networks. \\ ProjectWise ContextShare & Tool to manage data storage so that you don’t have to copy documents and \\  & overwhelm memory. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Bentley ProjectWise Common Data Environment Tools. Mathematical model of CAD to BIM remodelling  
\[(C_{P}\times C_{L}\times C_{A})\cup C_{T}\rightarrow\bigcup_{i=1}^{n}B_{i}\cup B _{T} \tag{1}\]  
where  
\(C_{P}\) is set of point elements in CAD  
\(C_{L}\) is set of line elements in CAD  
\(C_{A}\) is set of area elements in CAD  
\(C_{T}\) is set of attributes in CAD  
\(B_{i}\) is set of 3D elements in BIM (Level of Development)  
\(B_{T}\) is set of attributes of BIM elements. Equation (1) can be divided into graphical and non-graphical parts. Graphical part:  
\[(C_{p}\times C_{L}\times C_{A})\rightarrow\bigcup_{i=1}^{n}B_{i} \tag{2}\]  
Non-graphical part:  
\[C_{T}\to B_{T} \tag{3}\]  
The projection in Equation (2) is a single-valued function, the projection in Equation (3) is not a single-valued function--see Figure 6.  
Figure 5: GIS—BIM in the context of the construction life cycle. CAD—3D geometric model of the building. BIM—Building Information Model. VGO—Virtual Geographic Object—non-existing feature (idea). RGO-CAD—Real Geographic Object—existing feature in CAD. RGO-BIM—Real Geographic Object—existing feature in BIM. Red line—geodetic surveying of existing structure. Blue line—transformation G-ABD to BIM. Green Line—transformation G-ABD to GIS.