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I have a map with a "strange" projection (it's basically hand-painted, not an exact one). I can easily georeference it in QGIS using the Georeferencer plugin and the Thin Plate Spline transformation with a set of some 2000-3000 control points into simple WGS 84 (EPSG:4326) "latlong" projection and process/enhance it further with other data, like from Natural Earth or OpenStreetMap.

Now I'd like to perform the inverse operation: Transform one of those raster layers (or rasterised vector layers) back into the hand-painted quasi-projection, ideally using the same set of control points, so that the images match when overlaid in a graphic editor. How do I do it?

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interesting situation. Maybe you don't georeference the hand-painted map at all. Use the hand-painted map as 'ground-truth' and get your control points based on the local coordinate system ( say, top-left corner of hand-painted map is 0,0 and each pixel is a unit ). Then 'georeference' your rasters to this local coordinate system. – spatialthoughts Jun 1 '12 at 12:20
@spatialthoughts: This would work for rasters rather well, however I would also lose the precision of vector layers and the possibility to do calculations with them (area of a feature, length of a segment and so on). That's not an insurmountable problem, of course. Being able to reverse the georeferencing just wouldn't have those limitations. – Martin Sojka Jun 1 '12 at 13:20
@Martin Do you want the vector calculations in WGS84 or in the hand-painted image coordinates? If the former, sounds like your need to transform vectors to the hand-painted coordinates is totally separate from your need to do calculations on the vector -- and I would second spatialthoughts' suggestion. Just means you need to do these tasks in separate QGIS projects. – Jeff G Jun 11 at 13:29
In general it's not guaranteed that an inverse exists for all transforms. With polynomial transforms, if you could get the plugin to log the coefficients it used, you could calculate the inverse mathematically. With thin plate spline, maybe an inverse is possible as well: the GDALCreateTPSTransformer function takes a "bReversed" argument: – Jeff G Jun 11 at 13:32

You could try using the spatial adjustment toolbar. Since you already have the control points, you should be able to transform your data back to the original "projection". Open the toolbar, in the Spatial Adjustment drop-down menu, set the adjustment method then select the links menu and load control points. I haven't tried this yet so you may have to play with the control points or create a link file from the control points. Once you have the links set up, you can transform back and forth using the links and your preferred transformation method.

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