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I use MapAnalyst, a FOSS tool for the accuracy analysis of old maps. The tool creates, between else, Distortion Grids and Displacement Vectors/Circles (see screenshot). These can be exported as Shapefiles.

However, when I export from MapAnalyst, the resulting Shapefile comes with no information about the CRS. Grids and vectors are displayed near NULL island. I can manually set a CRS, but whatever CRS I try (EPSG:3857 as the OSM basemap, EPSG:4326 etc.), it does not seem to be the correct one.

How can Grids and Vectors be exported from MapAnalyst to be able to visualize them correctly in QGIS?

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The trick is to apply the distortion grid to the new map (the OpenStreetMap basemap on the right side). This map is georeferenced, unlike the (ungeoreferenced) old map image, basically a scanned raster image with just pixel values.

Go to Menu Analyze and select New Map, then compute the distortion again. The distortion appears now on the right side, whereas the regular grid is on the left side, where the old map is (see first screenshot below).

To export the result, go to Menu file > Export New Map Graphics... (instead of ... old map graphics) > ESRI Shapefile.

When you open the resulting Shapefile in QGIS, it is correctly georeferenced in EPSG:3857 as can be seen on the second screenshot.

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