How to display a plane on a sphere?

Question

Geometry

Actually, that's the whole question. There is a plane with a map of the world on it, I want to somehow convert it into a sphere, I'm looking for the right way to do it.

Answer 1

This is a very controversial topic. Without some distortion, you will never get a projection. The sphere and plane have incompatible topological characteristics.
One variant that preserves angles but does not preserve proportions is the Mercator projection. In fact, this is a cylindrical projection: https://en.wikipedia.org/wiki/Map_projection#Cylin...
First, project and parametrize your map by selecting a rectangular world map in it. Then project this rectangle onto a cylinder around the sphere. And then project each point of the cylinder onto a sphere.

Answer 2

Maybe so?:
https://www.google.com/search?q=sweep+globe