I found a "solution" here, but this would extend the current TEXMAP specification and assumes that every geometry placed around the polar caps is a triangle.

On the one hand, there is loss of texture information near the caps, since you can't project every point from the 2D image on the sphere.

On the other hand, it is impossible to find a solution for surfaces which are streched across the caps.

How do we proceed now?

On the one hand, there is loss of texture information near the caps, since you can't project every point from the 2D image on the sphere.

On the other hand, it is impossible to find a solution for surfaces which are streched across the caps.

How do we proceed now?