Pole distortions while mapping an equirectangular texture map to an icosphere?

Hi BAers!

I’m having texture distortions at the poles while mapping an equirectangular texture map to an icosphere. Vertices of my icosphere are pretty well spread out, so I think the geometry is fine, and it’s the texture mapping that went wrong.

Details and some screenshots are here: https://gis.stackexchange.com/questions/245315/pole-distortions-while-mapping-an-equirectangular-texture-map-to-a-3d-sphere.

I’ve read some very similar posts on this forum and elsewhere. People’ve suggested switching from uvsphere to icosphere to avoid triangular faces at poles, which I already did – my sphere consists of only quads. People also suggested some manual editing for the eyes, but unfortunately I can’t freely modify the mesh for visual purposes, as my goal is to create a scientifically accurate model. :frowning:

Is there theory or principled way of eliminating such pole distortions brought by equirectangular maps? I’ve read stereographic maps don’t have this problem, but what if I have only equirectangular maps?

Many thanks and looking forward to some responses from the experts here! :wink: