codes Ive seen in SadiQ demo, the bouncing ball. Since the ball is deformed in all angle, it could be possible to use this approach to map a square texture that is fullscreen and then maybe and rotate / scale it, "mode 7" style. So far my attempt at faking it use another rendering method based on a lot of simple elements being draw in a way that it give a 3d feel.
I've asked SadiQ about this and it uses (real code) matrices. You can do skews, rotations, and translations with matrices, although this isn't true 3D (actually, further up in 3D game programs, they use special matrices that work for 3D, and it operates in the same way). However, I haven't used these, since I've worked with drawing polygons to make 3D stuff, which allows "real 3D".
However, if you look at something like Sonic R, there's like 8 images for each car/driver. There's no fancy stuff happening, except maybe with the track. And I've drawn polygons that might suit your needs.