# Module Transformation

The module Transformation supports the Helmert (similarity) and Affine-transformation methods. The similarity transformation is for 2D- and 3D-point clusters whereas the Affine-transformation is restricted to the 2D-calculation.

## Helmert (Similarity) Transformation (2D and 3D)

This module permits the transformation of coordinates between two global cartesian systems or between two local cartesian systems of coordinates.

The scale can be pre-defined.

An affiliated **covariance matrix** of the points is also transformed.

The transformation parameters can be derived from the coordinates of at least (obligatory)
**3 identical points**. **Pre-defined parameter** for the
transformation can also be used.

## Affine-transformation (2D only)

This module allows the 2D Affine-transformation between two systems.

The parameters are always defined by identical points. A 6-parameter or a 5-parameter transformation (with 2 translations, 2 scales and 1 orientation) is possible.

## Close Proximity Fitting

When calculating a 2D-transformation with identical points, the residual discrepancy (misclose) at the identical points can be eliminated with a close proximity adjustment. There are two calculation-methods available:

- The corrections are calculated using distance weighting. The misclose of each and very identical point is carried over to each individual net point. The adjusting function for the influence of the discrepancy upon the net point is s**(-1.5), ‘s’ being the distance between the net point and the identical point.
- The corrections are determined by a Membran model. In this model, the point cluster is separated by a Delaunay Triangulation into triangles and, subsequently, minimized by the square sum of all the triangle-area-weighted scale modifications.