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Side-effect of flattening a globe
(startrek.website)
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You can easily do it without distortion. The issue is continuity. You'd have to make cuts and effectively unwraped the globe like you would a 3D sphere. Some countries might literally be cut in half, but it would at least be accurate
There will still be distortion, just less. The more cuts, the less distortion. But you can't make an unwrapped sphere lay perfectly flat.
Erm, yes you can, just run it through the infinite-cuts device!