How to turn a country's irregular border inside out (Win 10, 64-bit)?

[Runninghead]

Try generating a stereographic projection at your desired circle's center, inverting with respect to your desired circle, and then an inverse stereographic to get back to your spherical projection. It's the precise steps that you described, but you should be able to get all of the components that you need (with the possible exception of the invert step, which is easy to code up) using standard GIS tools. I'm certainly no mathematician, but something in the dark reaches of my brain was muttering something about "inverting a Riemann sphere". This term may mean something to the more mathematically inclined, but it's far too early in the morning for my conscious brain to make much of it.

What data do you want to do this to? Is it a raster image or a set of vector data?

Not sure how useful this might be but Cinema 4D has some excellent tools for managing projections on globes- might go something like...
Make spline from country coastline > Project Spline on to Sphere Primitive, etc.


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