Doom: At Doom's Gate
Nestalgica Lyrics

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Most interesting comment from YouTube:

Kris

@Captain Ravioli Yo neither are 3d It's devilishly, simply, high school math. Without getting into details about how the engine figures out what to render.... it basically does line intersections.

Walls are drawn as vertical slices of graphics. The length of that slice is calculated based on the distance from the player to a given wall. And since walls are only ever drawn vertically, that's why you can't truly look up or down in Doom.

Wolfenstein used a technique called "raycasting" to do this. Doom, being a more advanced engine, uses some principles of raycasting, but not completely (Doom doesn't do grid testing, so it can have walls of any angle). But if you look up some of that stuff you'll get the basic idea.

There's a lot of neat stuff going on in the Doom engine. I'm by no means an expert though, and I'm sure someone better can explain it... better.

Edit: Here's an explanation of what Wolfenstein does. Doom, being more clever, doesn't check for wall "tiles" like Wolf. Doom levels are compiled in such a way that the engine can already know which part of the level the player is in, and thus, what walls are in view and can automatically do distance checks on them... whereas Wolfenstein has to scan until it hits something.

But again, the principle is very similar in terms of how you take 2D information and make it look 3D.

-jdmoser https://www.reddit.com/user/jdmoser/