I took some backup from my university to solve this problem (a physicist and a professor in mathematics). It turns out, that imperfect polar caps are the effect of the mathematical definition of the perfect sphere and the limited resolution of our LDraw spheres. Ray tracers do not have this problem. The image on the wikipedia article, which was mentioned by Roland, was generated by a raytracer. An alternative solution would be to cut off the polar caps and use a planar projection only on the (nearly planar) polar caps.

The problem is not solvable mathematically under this circumstances and I do not intend to find a workaround which might expand the current TEXMAP spec.

This night, I will upload a video and more screenshots with different angle configurations to better visualise the capabilities of the TEXMAP meta command.

The problem is not solvable mathematically under this circumstances and I do not intend to find a workaround which might expand the current TEXMAP spec.

This night, I will upload a video and more screenshots with different angle configurations to better visualise the capabilities of the TEXMAP meta command.