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Helmert Transformation (2D)

Helmert transformation is one of several transformation types you can use in Gemini.

In Helmert transformation, the parameters are calculated from common points, i.e., points that are coordinate-fixed in both the coordinate system you want to transform to and the coordinate system you want to transform from.

Limitations and Requirements for Calculating Transformation Parameters

  • The common points must be located on two different application layers and have the same point ID in both projects
  • All points that are common in the two projects are used in the calculation. You cannot select a subset within each of the projects
  • At least three points must be common in the two projects. In practice, the number of common points should be larger than this and distributed across the transformation area
  • The common points must not have the status of known points, but this is recommended to achieve a good result

Procedure

Calculation of transformation parameters

  1. Open the Gemini Terrain Settings dialog
  2. Select General and Plan Transformations...
  3. Click New... and select transformation type Helmert
  4. Specify file with common points in the coordinate system you want to transform from
  5. Specify file with common points in the coordinate system you want to transform to
  6. The result for calculation of transformation parameters is displayed in a text document that appears on the screen (you do not need to save this file)
  7. In the dialog with the calculated transformation parameters, you must enter an ID
  8. The transformation parameter set is saved to the file trans.ini in the User folder

How to Transform?

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

Procedure

  1. Select application layers to be transformed
  2. Go to Tools - Transform in plan... on the context menu in the vertical list field
  3. Select the transformation set you want to use and click OK
  4. The transformation is performed

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

Formula

Helmert transformation is based on the following formula:

\(X = CX + A \cdot x + B \cdot y\)

\(Y = CY - B \cdot x + A \cdot y\)

Where:

\(CX\): Translation (displacement of X-coordinate)

\(CY\): Translation (displacement of Y-coordinate)

\(A = (m \cdot \cos v)\): Rotation and scale

\(B = (m \cdot \sin v)\): Rotation and scale

Note

If \(B\) in the parameter set is negative, the sign must be removed in Gemini.

Calculation Principle

  1. Calculate centroid coordinates
  2. Create error equations (preliminary values for the unknowns are 0)
  3. Create normal equations and calculate the unknown transformation parameters