Technical Background
For Transformations the external libraries https://github.com/dd-bim/egbt22trans and https://github.com/dd-bim/dbva are used and included in TRA.Tool. As only 2/3D-Coordinates can be transformed the remaining geometry parameters length, heading and radii have to be modified separately. Preserving a best-possible, valid overall geometry after transform, is one of the main functionalities of the TRA.Tool. Scale and meridian convergence as additional output of the coordinate transforms are used for adapting the geometry parameters as follows:
is applied:
- to the Length parameter as mean of Scale at elements start- & endpoint
- to r1 & r2 of a circle geometry as mean of Scale at elements start- & endpoint
- for Bloss & Klothoid r1 is multiplied by scale at element start and r2 is multiplied by scale at element end
before and after Transformation is subtracted as delta from original heading
Using the previous described approach, still include deviations between geometry elements and systematic errors. 
For better results the previous modified geometry parameters are optimized by a kind of Helmert2D transform. This is enabled by default in the transform-container, but can be disabled separately for heading and length. First heading is fitted to align the current geometries end-point best with the successor elements start point by ∆T. Second length parameter is scaled by the remaining deviation ∆L. As this is done in two separate steps and the length parameter applied to the geometry changes the result again, this is done iterative (for most cases the default threshold 1E-04 is reached within the first iteration).
As result the deviations can be reduced significantly as shown in following image: 
Apart from the actual transformation, it is important to be able to make a statement about the quality of the transformed geometry. By interpolating Points of the original geometry by using the [[How-To-Use#Interpolate]|Interpolation], these points are transformed along with the geometry. In the target coordinate system these points are projected to the new geometry and the remaining deviations can be used as quality indicator. Deviatons for each projected coordinate can be shown as arrow by enabling Show Projections in the Plot-View. The mean deviation of each geometry element is shown in a new column to the data-table of the TRA-element.