Anyone with knowledge on the translation of dome designs from 3d to 2d?

Hello all, I'm a first time user and poster so please forgive me if this isn't the right space to post this question. I'm taking on a project where I take the designs of the inside of a dome and translate them into a 2d piece, so I'm looking for anyone with knowledge on how a design changes when its viewed on a flat surface vs when viewed curved and from a distance, and what a designer can do in order to maintain visual harmony without compromising any design elements or losing anything in the translation. Sorry if I'm explaining it a bit awkwardly, please feel free to ask any clarifying questions if you think you can help! Thanks :)))