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I often need a world file including rotation, would it be possible
that the Georeferencer plugin had the option of writing a world file
for order 1 polynomial? (perhaps it is possible for Helmert also, as the scaling could be done by modifying the resolution?).

Also, what do you understand by Linear? As far as understand, Helmert and order 1 polynomial are linear also.

I've tried with option Linear, but the transformation does not include rotation. I do not know if this is intentional (i.e., a narrower definition of linear) or perhaps a bug (rotation parameter is not
correctly saved to the world file). In other words, the image is not rotated if I select Linear (both with and without world file) but
it's rotated if I select order 1 polynomial (but what I need is the
world file).

Note world files are ready for rotation parameters:
http://www.omg.unb.ca/~jonnyb/processing/geotiff_tifw_format.html
http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//009t00000028000000

Also, could the plugin output the parameters of the transformations (linear or not)?

Thanks!