A Polar Bear...

...is just a Rectangular Bear after coordinate transformation.

The nice thing about traveling cross country is having lots of time to read. My current text is: Game Engine Architecture. 6+ hours flight time each way means quite a bit read even with the occasional cap nap to digest the information.

By the time I got back to San Diego, I had finished just over half of the text. One thing that is making this a fairly easy read even as a upper division college text is that all the complicated math is something that I have already seen, just not in the context of gaming. I studied Mechanical Engineering for a while in college before ending up with what amounted to a applied mathematics degree. Vector math was done all over the place in both Statics and Dynamics. Not to mention that I also took various levels of advanced linear algebra though out my time in college as well.

What I recall from all of this was that it is very easy to succinctly express various concepts of rotation and translation in terms of vectors and matrices. However computing said expressions was a lot of tedious work. Even a dot product of two 3D vectors is 5 operations. Start adding in matrix multiplication and you start getting a lot of math going on.

In engineering, most of you learn is how to avoid doing lots of math by finding short cuts. And computer engineering is no different. In gaming it all comes down to getting an output close enough fast enough that people don't notice. We get to play with the fact that the human eye cant really see much faster then 20 Frames per second.

In the end, many of the concepts I have read about so far in game programming haven't been completely new. Math is math. Just the application of the math changes.