3D Math Primer for Graphics and Game Development (Wordware Game Math Library)

I found that Mathematics for 3D Game Programming & Computer Graphics was a "copy and paste" of parts of a linear algebra textbook. It had the interesting parts for graphics developers, but it did nothing in terms of reaching / teaching the reader, explaining things and helping to smooth the learning curve. It was pure math.

Well, 3D Math Primer for Graphics and Game Development it's just the opposite. It's clear, concise and mathematical rigorous, but at the same time it tries to reach the reader, explains the math of 3D graphics AND the reasons behind that math. Whenever possible it always gives you a graphic interpretation of what you are reading and if that's not possible, it gives you extra explanations. The authors know where the hard parts are and excel at helping you to understand them. Where most books give you a theorem and left you in your own (face it: most books) this one tries to help you to get a step beyond and understand the math and the workings of it.

There is a clear feeling in all the book: usefulness.

This book -in terms of smoothing the learning curve- is to current basic 3D math what Realtime Rendering is to current 3D algorithms and techniques.

The bad:

1.It's very basic. Don't expect to go from 0 to 100 with this book. It will give you the basics, but you will need to continue.
2.It's not mean to give you full working code. The code examples are to illustrate how the concepts can be implemented in software, not to provide a full working library.

To sum it up: a book to understand, not just "know" the math behind 3D math written in a clear and non-pretentious way.


Very good book to get started with   October 17, 2003
 74 out of 74 found this review helpful

The authors state early on that this book is intended as the first book an aspiring game programmer should read, and I would agree that for the most part it lives up to that goal. Many 3D game programming books include math primers covering a chapter or two, but really, 3D math is a huge topic deserving an entire volume. This book provides a great service, then, in that it thoroughly covers most of the basic topics that graphics programmers need to know, in a tutorial style that should be accessible to all beginners. Hopefully, we'll start to see more game programming books that focus on their core material and defer coverage of 3D math to books like this one rather than trying to pack unavoidably incomplete coverage into a few dozen pages.

So, what exactly does it cover? It starts off with a couple of chapters on coordinate systems, and then spends three chapters on vectors, followed by another three chapters on matrices and transformations. It then covers orientation, comparing matrix, Euler angle, and quaternion representations (including one of most clear explanations of quaternions that I've encountered), before diving into several chapters covering geometric primitives, including detailed coverage of working with triangle meshes.

The book closes with a chapter applying 3D math to graphics in areas such as lighting, fog, coordinates spaces, LOD, culling and clipping, and so on, and another chapter on visibility determination, touching on things like quad- and octrees, BSP trees, PVS, and portal techniques. The explanations in these chapters are much less complete, taking more of an overview approach. Others have criticized the book for this, but I feel that an overview is appropriate, since it then sets the stage for these topics to be covered in detail in other game programming books.

I'd definitely recommend this book to anyone just getting started with game and graphics programming.


Best bet for getting a solid understanding of 3D math   July 17, 2002
 23 out of 28 found this review helpful

Our goal in writing this book was not to cover as many topics as possible, like some other books, but rather to hit the most important concepts thoroughly. If you are a beginner, or have some "holes" in your understanding of matrices, Euler angles, left-handed vs. right-handed coordinate spaces, or key graphics concepts like zoom or the lighting equation, this book is for you.

A feature of this book over other books is the extent to which we have tried to develop the reader's geometric intuition, rather than just presenting numbers and equations. We show what the geometric interpretation of each mathematical operation is, why you would ever use that operation, and, in many cases, how the equation was derived in the first place. We do not gloss over "minor details" such as row vectors versus column vectors, or left- versus right-handed coordinate spaces. These "minor details" make all the difference in the world when you are trying to use an equation out of a book.

For the more advanced reader, we offer some of the clearest and complete discussions of some more advanced topics such as quaternions and barycentric coordinates. The book can be used as a reference for many important vector and matrix operations and identities. It also has a toolkit of many important equations for geometric primitives and intersection tests.

Our focus is on theory, so the book is not a big code dump like many books. The code we have provided consists primarily of "utility" classes for vectors, quaternions, and matrices. I think you will find that our code is simpler to read and understand than most code you will find elsewhere. We also offer some unique and thoughtful advice on good class design, specifically targetted to classes for doing 3D math and getting it right the first time, without twiddling minus signs or swapping numbers experimentally until it looks right


excellent book for game developers   September 21, 2006
 4 out of 4 found this review helpful

I'm about 2/3 through this book now, and I've found it very helpful. The explanations are good, and what I particularly like is how he illustrates most of the topics with pictures and graphs, explaining the relevance to rendering graphics in games. Unlike most math books and courses I've taken, I'm not left wondering "what the heck relevance does THIS have?" every time I turn a page. He also does provide C++ code game graphics rendering at the end of most topics. The code is very useful, and well explained. I can definitely see myself using some of it in future projects.

I don't want to kid anyone though, this material is complicated, and if you struggle with math, or don't have a math background (some advanced high school classes or college math) then you may find this book a bit much.


Excellent for Linear Algebra Students In Computer Science   December 22, 2004
 6 out of 7 found this review helpful

If you are taking Linear Algebra in college, you know that most of the available textbooks are a little short on practical details and examples of how vectors and matrices will matter to you later on in your programming career. This book provides excellent pictures, diagrams and explanations on the basics of how you can put your Linear Algebra knowlege to work. You don't need to be interested in game development to benefit from the clear and very readable presentation that this book provides. Thank you Fletcher Dunn and Ian Parberry - for the outstanding work.