Tuesday, October 15, 2013

Calculus in Mathbreakers

When talking about Mathbreakers one subject that always comes up is our level editor. We are determined to make it possible for someone to create any type of math within our game world. Calculus is a popular subject, because it is relatively complicated when compared with elementary subjects currently in the game. How could we interact with something like Calculus in a 3-D game world?

I just had a great conversation with my dad, who is a software engineer, about how Calculus could work in the game. I was pretty surprised to see him getting excited about it -- he is definitely not a gamer, but when we started getting into the details of Calculus, he was suddenly very interested.

What we talked about was a giant wavy field of blocks. These blocks would represent a 3-D graph. Now, one of the key parts in understanding Calculus is taking the area under a curve, and breaking up a graph into smaller and smaller bits is a way to get a more accurate area. Well, in a 3-D world this has some very interesting results. Together we invented an idea of how a multiplayer Calculus match would stack up:

• You cannot see your opponent because the graph is too "coarse". You're standing on a 3-D graph with big blocks, and some of them are blocking your view.
• You can take some action to break the blocks up into smaller chunks. One block becomes 8 blocks (instead of 1x1x1, it becomes 2x2x2). Now, because some of the bigger blocks have disappeared and been replaced with many smaller blocks, the graph is more smooth and you can see more clearly.
• But maybe your opponent moved to a *different* part of the graph where it's still coarse.
• If you want to aim something like a projectile, you can use a part of the graph that has a curve that would cause a projectile to hit some object in the air, perhaps a power up. By making the graph more smooth, you increase the accuracy with which you can hit these targets.
• By taking the integral or derivative of a graph, and then graphing the result, you can create a more wavy or less wavy landscape, which can achieve game goals such as making your opponent slide into a pit, or create a staircase where you can reach a higher level.
• You can enter a 2-D or 3-D equation into a graph generator, which will change the 3-D landscape you're playing on.

The list goes on. There are lots of neat ways to represent Calculus in a 3-D game world, it turns out, and we can't wait to try some of them out!

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