Skip to content

Affine Transformation

Affine transformation is one of several transformation methods you can use in the program.

In affine 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.

If you know the parameters of the affine transformation, you can enter these manually.

Limitations and Requirements for Calculation of Transformation Parameters

  • The common points must be located in two different projects 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 make a selection within each of the projects
  • At least four 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 status as known points, but this is recommended to get a good result

Procedure

Calculation of Transformation Parameters

Procedure

  1. Open the Settings Gemini Terrain dialog
  2. Select General and Plan transformations...
  3. Click New... and select transformation type Affine
  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

Manual Entry of Parameters

Procedure

  1. Open the Settings Gemini Terrain dialog
  2. Select General and Plan transformations...
  3. Click New... and select transformation type Affine
  4. Click Cancel when prompted to specify a file
  5. Enter parameters manually

How to Transform?

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

Procedure

  1. Select application layer 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

Affine transformation is based on the following formula:

\(X = A0 + A1 \cdot x + A2 \cdot y\)

\(Y = B0 - B1 \cdot x + B2 \cdot y\)

Where:

\(A0\) : Translation (displacement of X-coordinate)

\(B0\) : Translation (displacement of Y-coordinate)

\(A1 = ( m1 \cdot \cos u )\) and \(A2 = ( m2 \cdot \sin u )\) Rotation and scaling parameters for x-axis

\(B1 = ( m1 \cdot \sin v )\) and \(B2= ( m2 \cdot \cos v )\) : Rotation and scaling parameters for y-axis

\(u\) : rotation of x-axis

\(v\) : rotation of y-axis

\(m1\) : scaling along x-axis

\(m2\) : scaling along y-axis

Calculation Principle

  1. Calculates preliminary values by performing a Helmert transformation
  2. Creates error equations with the corrections as unknowns
  3. Forms normal equations and calculates the final transformation parameters