Ignoring matrix transformations is easy, as long as the eye point is at the origin. Then yes, the algebra is almost trivial: projection is just divide-by-z. But the moment you move the camera, or stretch and turn objects, or worry about clipping, you need the full machinery that matrices provide. They're not that mysterious. I wish they were taught in high school, because they would motivate kids to learn graphics and programming.
Nope, you totally don't need matrices to rotate, scale, and translate stuff. It's all very simple addition, multiplication and a wee tiny bit of trigonometry. As trivial as the perspective divide. In a 3D renderer, this is among the simplest and most straightforward of things. You can take it step by step and each step should be pretty straightforward to explain and illustrate. That is what is needed to build intuition and dispel the magic. After that, matrices are just a convenient abstraction, and perhaps more importantly, a reasonable way to express your intent to the underlying graphics library or hardware. Which you don't necessarily want to use.
Agreed: moving, turning and stretching don't need matrices, to be understood. But moving the camera away from (0 0 0) is going to require a change of coordinates. I'm not sure how to explain that process in a simple way that avoids matrices.
> I wish they were taught in high school, because they would motivate kids to learn graphics and programming.
Learned Linear Algebra (matrix calculations and some analytical geometry) + Calculus in eleventh grade, around 1995. I think it was the standard curriculum in all Eastern Europe and the countries from the ex Soviet Union.
I learned some degree of linear algebra sometime during high school (in optional math classes that a lot of my schoolmates never reached), but mostly as a set of rote-learned operations without a connection to anything useful. As a consequence, I ended up re-learning a lot of it in university, and then catching up on it again on my own while learning about 3D graphics. (American, in high school during early 00's)
The math courses from my first university year where 90% a redo of the math from my last two years of high school. The difference was that in university they emphasized the theory over exercises, basically forced us to learn 1 - 2 hours demonstrations of some theorem.
