Mapping points on a surface like an Environment Map

Im trying to map curves on a surface in the same way an environment map uses textures.

The curves I want to map would be exactly like a reflection map except made out of curves.

Im basically trying to create cell shading that I can use in Illustrator.
All I need to do is map a coordinate to the surface normals. But its harder than it sounds.

Environment Map.3dm (225.4 KB)

If it is as simple as your attached image suggests you can split a sphere with some planes.

Here’s the result:

20230521_Environment_Map_Response_01a.gh (12.1 KB)