Thanks for the info. I have seen something like this in SkyView2 (an Aeronautical Information Management app, provided by Eurocontrol and developed by www.luciad.com). Whenever you draw a line on the map, it's not a straight line, but follows a great circle, and when you change the map projection, the lines are reprojected accordingly and shown again as great circle lines. Maybe there are some vertices added during calculations, but they are invisible to the user, who sees only the starting and the ending vertex and a curved line between them.
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