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what kind of math is involved with making a game?

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I was wondering becasue, I never was good with math really, just never was my subject...but I am willing to learn and brush up on it, and I was wondering if any of you guys could tell me what I need to brush up on, or what kind of math is involved here... thanks chris

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I think this days, linear algebra is a must.

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When you''re starting you need things like Vectors and Matrices and the basic trigonometry(sin, cos).When you''re a little further quaternions are really useful.

Also things about coordinate systems(2d, 3d, polar, cylindrical, spherical).

Geometric entities such as lines and planes are a must. And if you want to go a little further you should have a good grasp of calculus.

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1.) Graphics

* vectors, matrices. linear algebra, that is

2.) Physics (and I mean practical game physics!)

* basics of ordinary differential equations (the concepts and numerical approximation)
* basic intuition on dynamic systems, eg. how to construct "stretchy" object (eg. cloth) by using connected particles.
* rigid body dynamics won''t do harm (although you can fake rigid bodies using verlets)
* and some more advanced topics: contact forces, friction and joints. all can be approximated, and all can be made into hard sciences, depending on your point of view.

3.) Collision handling

* in practice "only" points, lines, triangles, and spheres (extended as cylinders) and convex objects (more rarely complex ones). but even these will lead to algorithms complex enough
* btw, even in "academical" studies higher-order surfaces are rarely used for collisions. this is because lots of low-order objects is enough to approximate higher-order objects (this is a fact some higher-order advocates rarely understand...), with easier implementation and more numerous usages.

3.) AI

I''m not really qualified to answer Chess-like (discrete) AI requires more algorithms than math. Dunno about continuous "FPS-like" games.

4.) Others

Of course games aren''t just engines, so some basic knowledge of math (you don''t need to be able to proof all things, just understand them, eg. by geometric intuition) can be required in implementing the "game code" (in opposite of "engine code").

- Mikko

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3d math = math involving 3 dimensions.

But usually, it tends to be 4 dimension:

X, Y, Z, and Time.

so, many of the algos you''ll work with will have these 4 variables all the time.

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As people have said, linear algebra is an absolute must. They are used so often across so many different areas, that you''d be hard pressed not to have to use them. Calculus is also a must, not only for physics modelling in solving various forms of DE ( they won''t always be ordinary, but usually are ), but also for graphics programming. Thats about it really, this is excluding totally basic stuff like trig, because everyone knows that anyway. You might want to read up on set theory aswell. It really does depend on what you want to do though.

3D math does indeed equal maths which is performed in 3 dimensions. However, for graphics programming you''ll generally work in homogenous coordinates, which puts things into 4 dimensional vectors. Mechanics generally works on 3 dimensional quantities, with an added time variable around somewhere.

You have to remember that you''re unique, just like everybody else.

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Dot products and cross products are the Legos of computer graphics. With knowledge of only a few of their properties you can build amazing things.

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If you take uni level multivariable calculus and linear algebra, youll have most of the math you need. The linear algebra course i took at USC essentially dealt with n-dimensional systems, which is obviously enough for 3d systems....

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BTW.... Eric, we use your book as a required read in our game programming class

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Guest Anonymous Poster
http://www.geocities.com/pcgpe/graphics.html

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I always though of it as you don''t need to be good at math, but need a good understanding of how it works. There''s a connection between the twho and I doubt you can have one without the other though.

I say this because you have a big calculator sitting in front of you. You don''t do the work, but you have to know what work to tell the computer to do.

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It depends on the game. A 3d game with accurate physics and complex interactions will involve some pretty hard math. A simple side-scroller will involve much simpler math.

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Guest Anonymous Poster
CORRECTION! Pardon the unregistered nature of this post!

If you''ve not done any maths for a while, I wouldn''t read the 2nd edition of Eric''s book. It''s a bit confusing sometimes, and really (meaning completly) lacks examples.

I think the content is good, but you have to go elsewhere (Google) to actually understand the subjects if you''re not a natural mathematician. Most of the EXERCISES are very good (writing ray tracers, etc) though.

I''d go with one of the 3D math primer books off Amazon. Seems to be better for us people who aren''t natural genius''!

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Another question on a related note: how applicable to game programming would the math courses offered at my college be? Here's some links:

http://www.digipen.edu/programs/catalog/mat.html
http://www.digipen.edu/programs/catalog/phy.html

[edited by - camomilk on March 15, 2004 2:30:02 PM]

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It all depends how far you are willing to take it. *Potentially*, you could incorporate the most complex mathematics into your games.

Realistically, you only need trigonometry and basic algebra, and a knowledge of how to perform things like vector rotations with matrices.

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