[mbenjaminsmith]

> I prefer to teach 3D graphics without matrices because it's really not anything more complicated than a compact notation.

From a programming perspective it's much less verbose. Also the 1:1 mapping of "spaces" (camera space, world space) makes it very clean to manage transformations between them.

> and isn't easily separable because it steals the "w=1" constant for depth remap and also adjusts the "w" afterwards

I'm sure you already know this but x,y,z,w == x/w,y/w,z/w. It's easy enough to move between a 3D rep and a 4D rep of the same coordinates.

Using 4D coordinates may be somewhat awkward as they're not necessary for representations of points in 3D space but it is a very elegant solution for lighting where it is necessary to represent infinity.

[Edit]

Sorry, the point I was making is that I was also bummed to not see matrices in the article. They are a little bit to wrap you head around but they've a very elegant solution to a lot of stuff in 3D.