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In this question I'm interested just in the theoretical part. So, let's say we have such GCP in local reference system:

 (-2,14) (186,180) Label "Point 1",
 (-2,13) (211,6072) Label "Point 2",
 (-1,13) (6108,6052) Label "Point 3",
 (-1,14) (6088,161) Label "Point 4"

This data is taken from a real world TAB file. At each row there are two pairs of coordinates - the first pair, as I know, corresponds to geographic coordinates and the second pair to image pixel points. It is important to notice, that geographic coordinates are not in some well known coordinate system, in other words there is no SRID or EPSG number, which describes these coordinates. However, I know perfect parameters, that can convert these coordinates to some well known coordinate system. Applying these parameters I can get this file as an output:

 (x1,y1) (186,180) Label "Point 1",
 (x1,y2) (211,6072) Label "Point 2",
 (x2,y2) (6108,6052) Label "Point 3",
 (x2,y1) (6088,161) Label "Point 4"

The parameters which converted (-2,14) to (x1,y1) are just sin, cos and x and y offsets. What I do not know is whether I should apply the same transformation to pixel coordinates like (186,180) at the first row. Should I rotate these coordinates to get correct positioning or not? It seems like I should, because when I publish my map I see some positioning errors (around 20-70 meters). But I'm not sure of that.

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