Helmert (3D)

This is a three-dimensional transformation, 7-parameter, which contains translation along and rotation about the three axes in the source system, as well as a scale change.

This transformation does not convert from map plane coordinates to geocentric coordinates in one system and over to map plane coordinates in another system (e.g., from EUREF89 to NGO48).

Parameters

• 3 parameters for translation (T1, T2, T3)
• 3 parameters for rotation (Rx, Ry, Rz)
• 1 parameter for scale change (D)

Formula

$$ \begin{bmatrix} X \ Y \ Z \end{bmatrix}_{Target \space system} = \begin{bmatrix} T_1 \ T_2 \ T_3 \end{bmatrix} + (1 + D) \cdot R_Z \cdot R_Y \cdot R_Z

\cdot \begin{bmatrix} X \ Y \ Z \end{bmatrix}_{Source \space system} $$

Where:

$$ R_X = \begin{bmatrix} 1 & 0 & 0 \ 0 & \cos (\phi) & \sin (\phi) \ 0 & -\sin (\phi) & \cos (\phi) \end{bmatrix}

R_Y = \begin{bmatrix} \cos (\phi) & 0 & -\sin (\phi) \ 0 & 1 & 0 \ \sin (\phi) & 0 & \cos (\phi) \end{bmatrix}

R_Z = \begin{bmatrix} \cos (\phi) & \sin (\phi) & 0 \ -\sin (\phi) & \cos (\phi) & 0 \ 0 & 0 & 1 \end{bmatrix} $$

The rotation angles are given in radians.

Creating Transformation

Procedure

1. Open the dialog for Gemini Terrain Settings
2. Select General and Horizontal Transformations...
3. Click New... and select transformation type 7-parameter
4. Enter the 7 parameters, give the transformation an ID and select source coordinate system and target coordinate system

How to Transform?

Standard application layers and surveying application layers contain information about reference systems and can be transformed directly.

Procedure

1. Select the application layer to be transformed
2. Go to Tools - Transform in Plan... on the context menu in the vertical list field
3. Now you get the transformation parameter sets that are available. Select the transformation set you want to use and click OK
4. The transformation is performed

Additional Information

For standard application layers, you can also transform data during import and export.