Getting rid of unwanted distortion in JOSM?

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I am new to GIS but I am working on a project mapping a building using floor plans and JOSM. Using the PicLayer plugin I added the .png floor plan as a layer. I wrote a .cal file to set the scale, rotation, and center position of the image. In the JOSM default Mercator projection, the image moved only slightly when the center was changed (using lat and lon decimal degrees). The image was still centered somewhere around zero, but it was however still rectangular.

When I switched to WGS84/EPSG:4326 in JOSM settings, the image moved to the correct coordinates but it was sheared and stretched due to the projection and the square building was now more of a rectangle. I tried EPSG:3857 (used by Google Maps) and got a nice-looking display but couldn't find the image at the expected coordinates or at 0. How can I get the floor plan undistorted and in the correct location, similar to how the building appears on Google Maps?



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