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I'm a first-grade highschool student who has been making games in 2D most of the time, but I started working on a 3D project for a change. I'm using a high-level engine that abstracts most of the math away from me, but I'd like to know what I'm dealing with!

What books should I read on 3D mathematics? Terms like "rotation matrices" should be explained in there, for example. I could, of course, go searching these things on the interweb, but I really like books and I would probably miss something out by self-educating, which is what I do most of the time anyway.

I mostly know basic mathematics, derivatives of polynomial functions is the limit to my current knowledge, but I probably do have some holes on the fields of trigonometry and such (we didn't start learning that in school, yet, so basically I'm only familiar with sin, cos and atan2).

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When you say you're a "first grade high school student", you probably mean "first year high school student", since "first grade" sounds like you're 7 years old (the first year of elementary school is called first grade, at least in the US). –  KCd May 27 '12 at 23:03
    
Maybe in the American/UK/whathaveyou school system, here I'm a "first grader" all over again. ;) But yeah, that's what I meant. –  jco May 28 '12 at 7:47

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The Pharr and Humphreys book Physically Based Rendering is excellent. It comes with a lot of sample code. The diagrams are superb. It is exhaustive, and will keep you busy for a long time. Drawback: It costs a hundred bucks.

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Damn, I just spent a lot on some other books so I'm kinda short. I'll see if I can download it somewhere, and if I'll like it, I'll buy it later. Thanks! –  jco May 28 '12 at 7:48

In addition to computer graphics books like Computer Graphics Using OpenGL by Hill and Kelley, you might want to check out a linear algebra textbook such as Linear Algebra and its Applications by Gilbert Strang.

I haven't read the open source linear algebra book called A First Course in Linear Algebra, but it seems interesting.

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"Computer Graphics: Principles and Practice, Third Edition, remains the most authoritative introduction to the field. The first edition, the original “Foley and van Dam,” helped to define computer graphics and how it could be taught. The second edition became an even more comprehensive resource for practitioners and students alike. This third edition has been completely rewritten to provide detailed and up-to-date coverage of key concepts, algorithms, technologies, and applications."

This quote from Amazon.com represents the high regard this text on computer graphics has commanded for decades, as Foley & van Dam presents algorithms for generating CG as well as answers to more obscure issues such as clipping and examples of different methods for rendering in enough detail to actually implement solutions

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