FYI, like many others, I did it in "high school" for 3D but most never apply it again. (When studying Math at uni this was covered in just a week at best)

So while most think they still master it they are quite rusted. Or reluctant like I am.°

I'm quite confident about 3D because it's very visual. The abstraction to higher dimensions is a door I never really actively passed.

(It's "too trivial" for mathematicians ;)

I hope my explanation was of help, do you need the algorithm as explicit code?

°) instead of remembering the rules like engineers do, we tend to deduce it from basic axioms