Useful Game Math?

[camelCase]

So, I've got a "Game Math and Physics" module coming up next semester. However, I'll be the only student taking it. This is because while everyone else was taking the module, I was away on an internship. Now, when everyone is on their internship.. I'll be taking "Game Math and Physics".

The lecturer came up and to me and told me that, because I'm the only student, the curriculum can be much more flexible. He asked me to come up with a list of math and physics topics I might be interested in.

I know enough trig. to get stuff working so far; I've forgotten most trig. identities, though. Like, 99% of them. I used to know basic matrices but never really used them much because all the libraries I've been using have had them internally and abstracted it away to "Transform" classes. I know basic vector math; projections (I don't know why the formula works, though), dot-products (and omg, how useful they are), cross-products, angle, magnitude, etc.

Eh, not sure what else I know. So, yeah, one thing I'm thinking of learning is maybe.. Graph-theory? I think that's used for nav-meshes, right? Like, manipulating points and forming convex polygons from the soup of vertices.

I wanna' learn calculus, too, I guess. I know nothing of that shit. Maybe I know a little about derivatives (tangent to a curve, can be used to get.. velocity from a displacement graph and acceleration from a velocity graph?) and what a limit is (the limit as x approaches blah-blah but not why it's exactly useful..).

Eh.. So, what kinda' Math and Physics that's important that I've missed out?

 

[s3rius]

Basic physics, like gravity or calculating the new forces after objects collide.

Space transformation of graphics cards is interesting and useful. Doing 3D graphics you usually have a bunch of different spaces, such as Model Space, Clipping Space, Normalized Device Space, etc. That's how you can actually get the 2D prepresentation of your 3D models.

Quaternions are probably useful. I've never been able to really use them because I lack the knowledge. They're better than transformation matrices for things like interpolation.

...

I could use such a course aswell ... alas - my university doesn't provide something like that.

 

[KaerfNomekop]

What about game theory or probability? Not physics, but still math.

 

[camelCase]

Game theory sounds too tiresome =x Probability might be useful but all random numbers generated by the computer is pseudo.. So I don't know how applicable it might be.

@S3rius, yeah, during a 2 week break, I was trying to make a basic 3D game engine using just the Android SDK (didn't plan anything). I got to the point where I was doing rotations in 3D space, stopped, thought for a bit.. And told myself, "I have no idea how this works," and gave up xD

 

[s3rius]

Regarding probability: It's probly a small chapter, but adjusted randomness is a nice idea. Normal randomness is often perceived as not-so-random (e.g. people complain when they get Tails Tails Tails because "3 times in a row is totally not random"). So people often use adjusted randomness which makes sure the results are a bit better distributed while maintaining a certain success-rate (% chance to get Tails).

One area of use is stuff like critical hit chance in games.

 

[KaerfNomekop]

I was actually thinking of game theory in terms of AI development, in which case probability (random or pseudo-random) ought to add to the equation. But maybe that's thinking too far ahead?

 

[TheDamien]

Linear algebra is the most important topic.

 

[seph ir oth]

Linear algebra is the most important topic.

This. I did a bunch of 3D calc stuff and quaternion manipulation with this project.

2D is pretty straightforward (assuming you've done some stuff already, being on these forums).

Probability can be useful if you're doing certain types of games to analyze outcomes. Wouldn't sweat it though.

While A.I. is more theory, it's always good to touch up on that stuff as well. Their work is heavily logical in nature & usually if you're an A.I. guy that is ~all~ that you do. Tackling large-scale problems can result in laying out linear systems. *shudders*

 

[tom_mai78101]

Quaternions! And how to apply matrices, quaternions, geometry, applied physics into applications via writing up in C or C++.

THIS IS IMPORTANT AS HELL!! Because I'm dying to know also! Is the professor going to record his lessons?

Reason: These are useful when it comes to doing graphical representation of the physics model.

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Or you can ask for some advanced topics, such as voxel manipulations, optimizations (this uses some math and logic), water simulation, or procedural AI.

 

[Narks]

wow, only student, that's pretty lucky for you