Computing and applying an affine transformation to a vector layer using gvSIG and Quantum GIS

Geomatics Supervisor and Egyptian Archaeology PhD student Anna Hodgkinson told me that she is trying to apply an affine transformation to a set of coordinates. These are originally in an unknown local coordinate system. She has provided 4 reference points for which both the local coordinates and the EPSG:32636 coordinates are known:

ID ; EPSG_32636_X  ; EPSG_32636_Y   ; Local_X     ; Local_Y
1  ; 300646.885431 ; 3231905.223285 ; -144.333424 ; -50.678221
4  ; 300939.099675 ; 3232334.126771 ;  100.477740 ; 407.439814
7  ; 300519.458438 ; 3232235.904115 ; -304.216081 ; 262.236955
8  ; 300717.256565 ; 3232552.638076 ; -141.107317 ; 602.476276

First we need to compute which affine transformation takes the coordinates from the local grid to EPSG:32636. To achieve this, we can use the raster georeferencing tool in gvSIG since it lets you input by hand the source and target coordinates and then creates a WLD file whose 6 parameters are actually the affine transformation matrix. We'll use those 6 parameters to transform our vector layer (the local grid points):

In gvSIG, we create a view and add some layer so that gvSIG lets us start the raster georeference dialog. The "file to georeference" is irrelevant, just pick a random image from your computer:

Then enter the pairs of coordinates. The more coordinates the better, but at least three:

Then click on Apply and Exit, and gvSIG must have created a 6-line text file (probably *.wld or *.jpgw) next to the random image we used. In this case, the content of that file (called "the world file") is:

1.0001718355858875
0.10286004764601794
-0.11221180701761306
0.9922215770511519
300796.5805726947
3231940.256725514

Those are the 6 parameters of an affine transformation matrix. Now we switch to Quantum GIS [Juan, you are fired!] where we have installed this plugin. We can now add a shapefile with our vector features in the local coordinate system, start the editing mode and use the affine transformation plugin:

We'll see a little dialog where we must enter the 6 parameters we got using gvSIG. In reality, the dialog is a bit wrong in the sense that the first four parameters should not be called like that, because when you have a rotation angle which is not zero, the meaning of each parameter cannot be described by saying simply "Scale factor in the X axis" or "Rotation in the X axis". Anyway, this is the correspondence between the 6 parameters from the world file and the parameter names QGIS is using:

- Scale X is the 1st parameter in the world file.
- Scale Y is the 4th parameter
- Rotation X is the 3rd parameter
- Rotation Y is the 2nd parameter
- Translation X is the 5th parameter
- Translation Y is the 6th parameter

And that's it, the vector layer must have been transformed correctly and now should match the coordinates in EPSG:32636, with a little error of course which depends on how well the reference points were chosen and the accuracy of the coordinates provided.