The lore I share with students has to do with the difference between real time and render time graphics, or performance in general.
That's a topic best broached in terms of time or frequency (frame rate).
As brainiac mathematicians, we humans are able to develop an algebra and mechanics that allows us to model a lot of what goes on, but not in real time.
Even a flash arithmetic specialist doesn't matrix multiply in real time as a cognitive process, getting answers in microseconds. Rather, we take our "slow" algebra and translate it into running algorithms, simulation engines, a segue to the topic at hand (physics engines etc.).
A computer game like 'Call of Duty' (which I've not played yet, lots of 'Uru' and 'Halflife 2' in my day) is meant to be responsive in real time, and a lot of math is "on the fly" and done in ways that maintain a frame rate of 30/sec or so (enough to look "smooth" to the human player).
A computer movie like 'Shrek' or 'Over the Hedge' is going to take its sweet time with each and every frame, slower moving than molasses but with the same screaming computer power. The new 3D films... Heavy use of render farms.
One could say lots more "information per frame" for a deeper experience at the movies, but at the cost of no interactivity (you're the passive audience, not players (and you *like* it that way, movies are not physically challenging to watch usually, for most, ya just sit there)).
The render farm (sounds like some kind of slaughterhouse): vast piles of computers each meditating on its own little piece of the action, a frame of 'Shrek'. The workflows tend to be proprietary, sometimes less because they're big secrets and more because no one has the time or job description to spell it all out (more organizational anthropologists needed) -- too busy making movies.
These movies go into exquisite detail in ways the early games could never hope to do. That's where the GPU comes in. Motherboards that are so-called "parallel" or "concurrent" don't necessarily add CPUs and GPUs (graphics processing units) in the same proportions. Again, lots of secrets. Intel inside.
On the ground, as seat work, I've had people working with POV-Ray + Python quite a bit (I'm not leading anything like that currently, but have lots of blogged write-ups from when I did).
That's a synergy of choice, with Python doing the up close "slow algebra" in ways that are backward compatible with analog math, and writing out files that are in turn grist for the mill for other programs. The Litvins' book is a good resource here (math text with computer language).
POV-Ray eats something written in .pov format by Python (just a text file, human readable, all about coordinates and textures, reflectivity, color). Or a VRML browser eats something written in .wrl format, for a more real-time interactive view (more game like).
Polyhedrons are my favorite test subjects (easily morphed into avatars in the imagination). They're bare, stripped to the metal, pure geometry. No frills. Good subjects for learning the basics (and I'm not saying you need to forsake R&R gaming, just remember your studies are a kind of athletics too, so staying in shape is more than just working out (meditation has real benefits too)).
I've got all this down and documented at a public / open source web site (4D Solutions / Oregon Curriculum Network).
Other teachers get ideas, are inspired to roll their own.
Here's a good entry point based on what I've just covered, a kind of review but also another step into it:
On Tue, Nov 27, 2012 at 12:52 AM, roberto03 <email@example.com> wrote: > Thank you, Kirby. Your comment is really rich. > > Now, for the grades I'm teaching in (high schoolers), I think another very good opportunity is well described in this site I came across: > http://callofduty.wikia.com/wiki/Call_of_Duty_game_engine_mechanics > > As far coordinates and basic algebra are concerned, I think this would definitely be an option. I'll test this in Math class and possibly post feedback from students, if anyone is interested. > > > Best, > Roberto.