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Chaugnar

Basics of learning Math

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Hey, Lets take it for granted I know only the basics of math subtraction/multiplication and division and I didn't have the option of going to school to learn more math, where would I start? Do you guys know of any good books or resources to take me from being a complete newb to being somewhat proficient in 3D game development from a math standpoint. Also, could someone explain to me a practical example where sin/cos/tan are used. I get the picture they are important but I cannot for the life of me understand from what they are derived and what they are used in (did someone just decide to create a cos function and pulled the computations needed from his ass or)? i.e. what do they "mean"? Cross-product and dot-product are also a bit muddled in my brain. I've heard that linear algebra and trig was the single most important math elements you need to know in order to be able to do good as a game programmer, would you guys reckon that is true? Any help would be appreciated, Thanks in advance

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There's a lot of resources everywhere, starting with the Articles on this website but I think that even if the vector dot and cross products(example) are rather easy to understand they need a good time of practice to really master them. So read and use... a lot. (;

As a programmer your mathematics knowledge is mostly a tool. It sure never feels good to apply without being able to prove why but if you are simply working on the game editing tool interface you don't really care about that. On the other hand if you are writing a physic engine then yes, you'd better have a strong understanding of what's happening. The AI people do need understanding too but not on the same matters.

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I suggest you to buy a couple of books about these topics:
-Calculus (I think this is the english name of italian "Analisi matematica") where you find functions and, yes, sin, cos, tan...
-Linear Algebra (geometry) where you find vectors, matrices, spaces, coordinates,...
-Discrete mathematics. Perhaps the less usefull, but with many interesting topics.

You can take a look on the site of some university math courses: there you should find the precise fundamental topics and the books used.

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The most logical place would probably be to start with basic Algebra. Get a good grasp of that. (as far as moving parts of equations around to solve for different variables, factoring, being able to replace single variables of one equation with an equivalent group of variables (Like replacing the Force with Mass*Acceleration [a silly example but sometimes you need to do things like that]).

Get a good solid understanding of those 'tools' and then you can move on to trig, which can be summed up with the three functions you asked about. Sin, Cos, Tan. With your understanding of algrebra from above, you should be able to reason through where it comes from, and how it is used, and the incredible power it really gives you to solve geometric and physical problems.
Calculus is sort of a further extension of "solving for physical problems" and delves alot into numbers that approach infinity. Really you can do *most* things with just algebra/trig, but there are instances where calculus will be more elegant or faster.
So: get a book or two on basic algrebra and start going through it, do some of the problems, etc. Google for alternate sources if the particular book confuses you.

As for your other questions, sin/cos/tan are the three trig "functions". A function usually takes the form f(x). Think of it like a black mystery box. You plug in X, and it spits out some other number. (much like C/C++ functions:
float f(float x). Sin/cos/tan are just like that, except sin(x) instead of f(x).

The actual number it gives you is based on certain geometric thruths about the ratio of differnt side lengths, and angles of triangles. Suffice to say, they allow you to solve for missing sides/angles of a triangle as long as you have certain other required information about the triangle.

Possible uses are huge. An over simplified and stupid example:
I have a plane flying at some unknown altitude. It's 'radar' or whatever looks down at a 30 degree angle and hits the ground 500 feet away. By using the trig functions you can find how high the plane is (assuming level ground).
So sin(30) * 500 = 250 feet.
As for selecting which function to use when, well that you'll need to learn.

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I suggest you go apply at the local community college so you can take the math placement test. See what class they recommend you start in. If actually taking the course isn't an option then buy the book for the class and work through the exercises.

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That Calculus Made Easy book doesn't really cover a whole lot of ground, and the way it does a couple things is ancient.

I suggest buying some textbooks on math. Here is what you should buy:

Elementary and Intermediate Algebra
PreCalculus (Covers both College Algebra and Trigonometry)
Calculus

Read a chapter, and work some problems. Just work your way through each book. By the time you are finished, you will have the same math knowledge as most people who have gone up to Calculus III in college.

I hope you are willing to devote a year or two to this stuff.

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