this similar thread http://www.cartographersguild.com/sh...ge-to-Mercator has a rec for 'flexprojector' which i haven't used. i don't know if it will let you change the orientation.
the winkel projection has sinc functions, but most of the other projections i've noted have much simpler relationships between the spherical and 2d form, which would only take a bit of time with a steady head and an environment where you can read and write the data (eg. any programming language, matlab, octave).
i'll check back in case no available softwares can be found.
the other solution, since i'm guessing that's height field information you wish to use for a 3d app, would be to forget about everything below the water and use photoshop to drag the continents around and liquify/squish them to the new map using layers. only issue then would be you'd have to be 'creative' with the arctics.



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