Project a game on a dome

Hello to all,
I’m new to Unity and I’m currently working on a project that is:
I have a projector, a condenser, a fisheye lens and a dome. I’d like to use these setups to create an immersive game: people can play inside the dome and have a 270-degree view of the scene projected in front of them on the dome.

What I plan to do first is to create a simple game, which only has an endless corridor and a player can walk in it. However, because of my limited knowledge of Unity, I’m stuck in finding a way to map the normal 3D view of this game to a spherical view so I can project it on my dome through the fisheye.
I’m wondering if there is any existing toolkit or function that can easily achieve this goal. If not, what should I look for? (I even have no clear idea what this question is called)
Thank you for your help!! Any piece of your advice is appreciated!!

There are a lot of examples of fisheye or dome rendering with Unity. Try a google search, you should come across a couple of tutorials and github projects. The hard part is every dome setup needs a different projection, and figuring that out is kind of on you.

However the short version is render your view to a cubemap, output a pre-distorted image as your final image to display on the projector. Again, what that distortion is depends on your setup, so there’s no one size fits all asset that can solve this. This might get you close enough though: