Transformation of Internal CAD's 3D Coordinate System and IFC Files Coordination

Combining files in shared coordinates from software's internal coordinates is a widespread problem in BIM working processes because only some programs support both coordinate types. The mathematical algorithm was proposed to prevent manual operations and increase accuracy. The algorithm's practical implementation finds transformation parameters between CAD's internal 3D-coordinate system and shares coordinates using at least 3 points in both systems use a method of square leasts. The proposed algorithm is a particular case of general geodetic Helmert transformation used in a local area without some parameters (only dX, dY, dZ and ω_z are using). To check the accuracy of calculated parameters was entered a linear error that equals a returning value of square leasts’s method for most optimum decision and comparing that linear error with acceptable value in CAD systems.  By way of file converting example, a popular exchange data format in BIM projects as IFC files were considered. The program's implementation was executed in C# program language as a desktop application and class library, that will let change any IFC-files to adding the needing shared coordinates. All source code was published at GitHub https://github.com/GeorgGrebenyuk/IFC_GeoSupport.