Math is for Game Development!

Posted by Rampant Coyote on September 7, 2012

Okay, this one’s for the kids.

Wanna make videogames? Learn to love math! I’m not sure if videogames or sending space ships to other planets represent the culmination of all that great work by the mathematicians  and scientists of the past like Euclid, Archimedes, Newton, Decartes, Acharya, and Fibonacci. But it ranks pretty highly up there in my biased opinion. Game development is all about math, but the math is actually pretty fun.  Math in videogames is what makes explosions work, what makes the AI move around cover to find you, what makes that lobbed grenade hit its target, what makes the physics puzzles work.  Okay, yeah, sometimes the thrills it gives are pretty geeky,  but I come from an era where these games were pretty geeky to begin with, so it appeals to me. 🙂

I think my game-development habit in my younger years was what helped me get through my math classes. While the rest of the class got glassy-eyed learning trigonometry, not really sure what possible value sines and cosines would have in real life, I was eating that stuff up, because I saw how they solved problems in game development. In some cases, I’d already learned some of it on my own. So I guess, in a sense, my passion for making videogames actually made math kinda fun – which is quite an accomplishment on its own, and I think in turn that made some things a lot easier to learn.

Algebra and trigonometry are things I use almost every day. I was reminded of this the other night when I found myself writing code for slope-intersects… another one of those things taught in math class that few of my fellow students really could see a practical application for.  I survived a semester of Statistics my final year in college mainly because the first quarter of the class was all about probabilities – something I’d internalized pretty well spending years playing Dungeons & Dragons.While the deeper secrets of samples and distribution were a lot more challenging for me, anybody who is working in the MMO field and has to deal with large populations of players could benefit from this kind of knowledge.

I use Calculus a lot less in my work in games (and simulation, my day job) – but the foundation it provided was helpful. The physics classes I took in college – which required Calculus – were probably even more useful.

Want to program?  Programming *is* math, guys. On its most basic level, programming is all about transforming meaning into numbers and vice versa – everything in a computer is a number, and every instruction is, at a fundamental level, a mathematical operation. Even at the higher level at which we programmers generally operate nowadays, programming is the embodiment of those “word problems” the kids complain about in school.

There have been times – especially when I was younger and really learning all this stuff – when I DREAM in code. I remember one windy night when I couldn’t sleep, and my brain got stuck in this loop describing the swaying of trees in the wind in terms of mathematical equations. Years later, working with Curtis (Califer on the board here) on the archer rats on the Tale of Desperaux video game, when we researched the algorithm for artillery trajectories to implement in the AI code to make the archery AI more accurate and give their arrows a more realistic “lob” effect. Programmers are always solving for X, performing summations, and otherwise performing basic arithmetic and algebra.  If you are working in 2D or 3D space – as you are when writing many videogames – knowing where to perform an arctan (and its limitations) or calculating the distance between two points ( sqrt(  (x2-x1)*(x2-x1) + (y2-y1)*(y2-y1)), for 2D space – it’s second nature ) are frequent problems. Particularly in 3D code (AI, graphics, or physics), you’ll find frequent uses for things like dot products, cross products, matrix math (hoo, yeah!), calculating intersections between planes / lines, and the like.

Designers? Oh, heck yeah. As a designer your math background may not need to be quite as extensive as a programmer’s, but designing videogame mechanics is really an exercise in math. Remember how I said I thought probability calculation was pretty intuitive in my Stats class because of Dungeons & Dragons? That’s what I’m talking about. Mechanics design is all about understanding and manipulating the mathematical relationships between game elements. Good designers know a bit about an awful lot of topics – drawing from all art, science, literature, history, current events, or whatever – but they also need a solid math foundation.

And yes, math plays a role even for the artists. In some companies where I’ve worked, we’ve had a Technical Art Lead whose job it was to help keep the artists meeting the technical specifications, but an artist who understood the technical (math-based) environment for which he or she was creating assets was oftem more productive by the simple fact that they didn’t need to re-do so much work.

So – if you are a student, or know a student who is interested in video games… let this serve as a reminder about the importance of math.

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