This is rather fascinating. I am shocked that such a relatively simple rendering tweak hasn't been widely used in games and movies to date.

I'm guessing that the math is not describable using a transformation matrix. It might have been too heavy for very old graphics hardware, but any GPU from the last 15 years should be able to do this kind of thing no problem.

Here's a minecraft video where you can see the effect in real-time as well as pushing the field of view too far: https://www.youtube.com/watch?v=ZNSW6Ga7Wmo