I have modeled an aircraft Attitude Indicator, but I have a serious problem unwrapping and texturing the ball it consists of. As we can clearly see in the references, all line thicknesses are perfectly preserved, there are no distortions - just like a marker painted the lines with no distractions on the surface of the ball.
For texturing I use Substance Painter.
1. What unwrapping method would be optimal?
2. How to paint it in Painter?
3. What ball’s topology would be most suitable?
I’d model it first, then generate my maps from it.
Do you really need it to be unwrapped?
Because a Sphere allows other projections, due to it’s unique topology. So even an equirectangular texture should be enough for this.
I would do this one in a weird way.
I would create geometry for the lines, because it would be easy to place/duplicate edges where the lines need to be and then extrude them outwards by simply scaling extruded edges and give them uniform width with solidify. And then I would bake selected to active with emission shaders.
That’s easy and quick and the UV map can be anything you want.
And you can add stuff later, by unchecking Clear Image and baking again. I am surprised this is not a very popular technique. At least as far as I know… I haven’t seen many people doing this, but maybe that’s just me… Anyway, I think it’s really easy and precise way to texture stuff.
This is what I said!
If this is done with geometry then one might not even need a texture map..
As usual: it depends on the use case… 
You can always bake the AO as a stencil for start as a texture base. I’d begin with an Icosphere and a duplicate set to Wireframe modifier for getting the thickness and divisions.
Yeah, whatever works. And Shrinkwrap can be used for text.
What the most optimal topology and unwrapping would be for a sphere is also an interesting question. I have no idea to be honest. I would use any, but what’s the most optimal?..
Looking at the texture in question, it is wrapping similar to an UV Sphere - and I typed Icosphere anyway, my brain went goofy there.
Properly the best way is what humans did with “ancient” globes… using a “gore segmenting” like so:
I used the same image for “North” also for “East”, “South” and “West” because this is “cumbersom” 
The lines i drew are not “perfectly” rectangular but if done then the lines in the middle of one segment is the same width form top to bottom..
i also just drew some horizontal lines.. the correct postion has to be found.
Edit… ohh… and the reson for this is the grid painted on it: 4 directions subdivided into 3 sectors and again into 3 sectors are 36 sectors and from top to equator 3 times 3.. so 18 over all..
I might sound weird because i’m a bit tired to think about this now .
