Rendering pixel by pixel every frame is very impractical for any kind of computer, so I made every horizontal row of pixels of the ground display a sprite, each of which are cropped from the sprite sheet and scaled using a 3D perspective equation.
Ah yes, I've always wanted to do this! But I'm just terrible at the perspective math, so I never got to it. I'd love to know how the math really works.
UPDATE: Sorry that I haven't been responding for a while. I have been working on making an engine for 3D platform games using this pseudo-3D engine, and have even turned it in for a school assignment! It can be downloaded using the key seen in this post's screenshot.