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futlib

Can't decide which math/physics basics book to get

13 posts in this topic

I've been pondering which math/physics basics book to get for hours now.

  • My math basics are quite good from my BSc in CS. It's been a while though, and I would like a reference of things relevant to game development.
  • My physics basics are not very strong. I know some basic mechanics but that's about where it ends.
  • I'm mostly working on 2D games. I've worked on 3D games and would like to learn more about the graphics pipeline and rasterisation and such, but I can still get a specialised book on that.
  • I'm looking for information on collision detection and response algorithms.

There are several promising books, I've narrowed it down to just two:

 

Mathematics and Physics for Programmers

  • Very basic, starts at grade school level
  • More of a textbook than a reference, it seems
  • Covers all the relevant basic math topics: trigonometry, calculus, linear algebra
  • Seems to cover the relevant physics basics, but I can't tell for sure
  • Covers a broad range of topics, even some game theory and AI
  • Has a chapter on tile-based games, which is probably quite relevant to me
  • Uses lots of IMO rather difficult to read pseudo code
  • Uses slightly weird terminology, e.g. they're talking about "squares" instead of boxes when discussing collision detection, and of "collision resolution" instead of "collision response" (which gets much more relevant hits on Google at least)
  • Not well-known authors, doesn't get much praise

Essential Mathematics for Games and Interactive Applications

  • Seems appropriate for my level
  • Seems to use proper terminology
  • Does not cover trigonometry or calculus, doesn't even include a reference of the trigonometric identities
  • Covers linear algebra in much more depth
  • Covers rigid body physics
  • Has a highly interesting chapter on interpolation
  • Covers the graphics pipeline and shaders
  • Semi-popular authors, gets considerable praise
  • It's not on gamedev.net Books for some reason

I really am torn. Getting both seems wrong, as they cover much of the same ground.

 

MAPFP seems to be less known and less sophisticated, yet I could use a refresher on calculus and would like my reference to include trigonometry. It also has some interesting hands-on topics.

 

EMFGAIA seems more appropriate for my level, yet covers various things I don't really need right now, working on 2D games. But it seems to be more industry-connected, and at the same time more scientific/accurate.

 

So, what do you think, which one should I get? Or can you recommend another one appropriate for me?

 

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Mathematics for 3D Game Programming and Computer Graphics is not on your list, but I own it and think it's excellent. It has chapters on everything from simple topics to advanced, and will function as permanent reference material when you are done reading it.
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Mathematics for 3D Game Programming and Computer Graphics is not on your list, but I own it and think it's excellent. It has chapters on everything from simple topics to advanced, and will function as permanent reference material when you are done reading it.

 

It was in fact on my list, but I thought it didn't cover physics. Just saw that it does. Would you say that it manages to bring across the basics well? It's only 20 pages on linear physics, doesn't seem much. I don't want to write the next Box2D, I just want a solid foundation. It has a trigonometry reference, that's a plus. Would you generally say it's useful for 2D games? Do you have a more basic math book accompanying that one?

Edited by futlib
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It was on your list? You mention 2 books in your post. That wasn't one of them.

You don't need to worry about 2D vs 3D. There isn't a new type of math for every dimension. A 2D collision check is the same as a 3D one minus one dimension.

I only have the second addition, but it starts at points, then vectors, matrices, volumes, collision detection (of every type), collision response, physics, graphical techniques (like polygon reduction), ocean simulation, and then it ends with a bunch of small chapters on general purpose techniques that are good to know. Third addition has more.

If a chapter looks short, it's because the book isn't full of source code. It explains concepts and shows formulas.

It's all general purpose knowledge.
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I got good use from Mathematics and Physics for Programmers, Mathematics for 3D Game Programming and Computer Graphics, Game Physics Engine Development, and Real-Time Collision Detection.

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It was on your list? You mention 2 books in your post. That wasn't one of them.

 

On my list before I narrowed it down, is what I meant smile.png But sounds good, didn't notice it covers collision response. And the other books don't allocate many more pages to that anyway. It's definitely on my list now. And since it's apparently quite famous, it's a good candidate, too.

 

I got good use from Mathematics and Physics for Programmers, Mathematics for 3D Game Programming and Computer Graphics, Game Physics Engine Development, and Real-Time Collision Detection.

 

You have both Mathematics and Physics for Programmers and Mathematics for 3D Game Programming and Computer Graphics? I havent read the former (obviously), would you say its too basic for someone with a CS degree? Or is it still something you refer back to occasionally?

Edited by futlib
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I recommend you "Real-Time Collision Detection", it's very practical with lot of algorithms and useful information.

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"Real-Time Collision" by Christer Ericson and "Game Physics" by Dave Eberly.

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If you think Mathematics for 3D Game Programming and Computer Graphics is too advanced for you, (or at least too fast on the basic) you should take Practical Linear Algebra: A Geometry Toolbox.

The first half is about linear algebra in 2D and the other half about 3D and some pages about the curves. It's a pretty good book and it will give you an intuitive look about linear algebra with practical explanation of the maths and drawings, rather than an approach with proofs and theorems.

 

I found this book on http://www.realtimerendering.com/books.html (at the end).

 

And of course do the exercises :) but don't be scared, you don't need a calculator.
 

Edited by Rakilonn
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Don't get the same book for "math" and "physics"... that's not very effective.  There's just too much to cover to expect a single book to do a good job.  For the physics part, I suggest "Game Physics Engine Development" as being easier to consume, highly practical, but less theoretical than the Eberly alternative.  Make sure you get the most recent edition (by Ian Millington, published 2010 July 23).

 

Which is the best math book for 3D graphics is more difficult to choose, but you've got some good suggestions already.

 

For "collision detection" I'd suggest you buy "Real Time Rendering", even though collision-detection is only one of many topics in this fabulous book.

 

Also, here is the single best resource to get you started on "narrow phase collision detection": https://mollyrocket.com/849 .  After you watch the video, wander through the forum.  This is a great resource.  If you decide to implement GJK for narrow-phase and/or sweep-and-prune for broad-phase and/or need to perform collision-detection on arbitrarily irregular "concave objects", you can contact me for more detailed conversations.

Edited by maxgpgpu
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If you think Mathematics for 3D Game Programming and Computer Graphics is too advanced for you, (or at least too fast on the basic) you should take Practical Linear Algebra: A Geometry Toolbox.

You could also attend the Khan Academy, in th elikely case that he doesn't have a 10,000$ book budget.

https://www.khanacademy.org/math/algebra
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Thanks for all the advice, I've pondered quite a bit on this.

 

I've decided to get Mathematics and Physics for Programmers now. It covers a lot of ground I'm already familiar with, but it really seems like a comprehensive reference of all the basics, explaining them much better than Wikipedia (which I usually turn to for refreshers). And it really covers a lot of ground, from what I've seen pointing to more advanced books for further reading. But it does seem to cover all the things I really need right now.

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Essential Mathematics for Games and Interactive Applications

Seems appropriate for my level
Seems to use proper terminology
Does not cover trigonometry or calculus, doesn't even include a reference of the trigonometric identities

 

Nope, I've this book, in the disc provided with it, you've 4 appendices. Perhaps you didn't look at the TOC properly.

Appendix A - Trigonometry

Appendix B - Calculus

Appendix C - Coordinate Systems
Appendix D - Taylor series

 

My review of the book is that it covers the basics extremely well, the authors seem to be very sincere in what they did, giving so much of attention to detail. I've come up till Chapter 6, and so far so good!

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