To map a sphere and not having the obvius deformation.
I dont know where i start to figure out how can i transform any image into that projection. Any clue?
I am not sure but almost, that you dont even need a shader.
Take a look at the example in examples/3d/3DPrimitivesExample and simply use a sphere primitive
then use its mapTexCoordsFromTexture function to map the texture to the sphere, which is also used in the example.