Quote Originally Posted by selden View Post
Can you provide an example of what you don't like?

Depending on how your land masses are distributed, orthographic projections of opposite sides of the globe might be appropriate.

What type of map projection are you starting from? Or are you using a 3D paint program to draw directly on the surface of a sphere?

Sometimes multiple gnomic projections of relatively small areas are an appropriate starting place. There are programs which can then stitch them together on the surface of a sphere or reproject them into whatever format that you prefer.

All 2D flat maps of a 3D spherical surface have to stretch or shrink things somewhere. You have to choose a projection that best shows the type of information that you're interested in. https://en.wikipedia.org/wiki/List_of_map_projections shows examples of many projections.
I'm trying to come up with a projection like the one below. IMG_3379.JPG

I drew an equirectangular map and was able to distort it to polar coordinates and got IMG_3380.JPG