As 3D games grow more sophisticated, the math background required of game developers steadily increases. However, many of the developers who have come into the industry in recent years do not have the academic background in mathematics or sufficient experience to keep up. Based on the authors’ popular tutorials offered at the Game Developers Conference since 2000, Essential Mathematics for Games and Interactive Applications presents the core mathematics necessary for game development in the age of sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix manipulation and expands on this foundation to cover such topics as texture filtering, interpolation, and basic game physics. Unlike other books on the market, Van Verth & Bishop address the programming issues particular to 3D game development and includes optimization guidance throughout. Rigorously designed as a companion reference for titles in the Morgan Kaufmann Series in Interactive 3D Technology.

*The companion CD-ROM will contain code examples built around a shared code base, including a math library covering all the topics presented in the book, a core vector/matrix math engine, and a simple game engine written in OpenGL
*includes optimization techniques
*Presents just enough mathematical concepts so that a programmer will feel comfortable with the material without being overwhelmed with proofs and theory

"Even though I’ve worked with these systems for years, I found new ways of looking at several topics that make them easier to remember and use. For someone new to 3D programming, it is extremely usefulit gives them a solid background in pretty much every area they need to understand." Peter Lipson, Toys for Bob, Inc.

Based on the authors popular tutorials at the Game Developers Conference, Essential Mathematics for Games and Interactive Applications presents the core mathematics necessary for sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix manipulation and expands on this foundation to cover such topics as texture filtering, interpolation, animation, and basic game physics. Essential Mathematics focuses on the issues of 3D game development important to programmers and includes optimization guidance throughout.

*Covers concepts in sufficient detail for a programmer to understand the foundations of 3D without feeling overwhelmed by proofs and theory
*Companion CD-ROM with code examples built around a shared code base, including a math library covering all the topics presented in the book, a core vector/matrix math engine, and libraries to support basic 3D rendering and interaction
*Provides guidance for students trying to understand how games are actually developed, including optimization techniques

Outstanding

I am an avid tech book reader, especially about any technology related to game programming.

I found this book to be an outstanding reference for math related to game programming.

I think the authors are very good at explaining and focus on the core concepts instead of getting mired in the details.

I particularly liked the sections on rigid Body Dynamics - I needed a good overview to conceptually understand the implementation.

Great introduction and specifics

I’m a computer science and digital arts student. I’ve found this book to be an excellent primer on the math that I haven’t gone in-depths with for some time. The first few chapters provide excellent background materials to the actual mathematical basis for the following chapters.

a grab bag of germane maths topics

Do you know the history of quaternions? About a century ago, they were investigated, as an exercise in pure, abstract maths. Yet in recent years, people in computer graphics found this very useful in defining certain types of rotations. Interested? Well, this book has a good, clear section that explains how they are used. That requires only some basic knowledge of trigonometry and complex numbers.

Much of the book is like this. Though perhaps with concepts more readily apparent than quaternions. Ideas drawn from three dimensional analysis. But with topics that are not typically in maths courses, relating specifically to graphical displays. Like different types of tesselations, different shaders and texture maps.

Some physics also shows up in the book. Often related to ray tracing and approximating the effects of light on a surface.

Nothing too hard, despite some remarks by other reviewers. The really advanced and specialised material, like applying Monte Carlo methods, has been omitted. This is essentially a basic text. You should have mastery of this material to do useful contributions in graphics.

Very Difficult

The book presentation is very good but the presentation of the material ’jumps right in there’ with a good review and is very technical and a bit difficult to follow. It is an excellent book for someone that remembers their basic math, if your rusty, take a refresher course first.

Fabulous teaching!

See my other review. I bought this book and the other. I got stuck in that other book. I am learning linear algebra for the first time. This book is doing it! Although it gets quite abstract at times, and seems to be presenting the subject as if it is not related to 3D programming (like solving equations for an n-dimensional space), and it explains something and then says it is not used in 3D programming, it explains the concepts extremely well, and although it may take a while for a new concept to sink in for me, I do not find myself having to go elsewhere for help.

One note though, I tried to email one of the authors to find out about errata for the book and never got a response. I did eventually find it though. Don’t expect the authors to be available. They do not have a message board.

One of the best game math books

If only every topic in game and graphics programming were covered as well as math. Over the past several years, a number of exceptionally good books covering math for game and graphics programming have been released, and I’ve had the opportunity to review most of them. Although, not surprisingly, there is some overlap between them all, each covers unique material and presents information in an original way so that collectively, the books provide an impressive body of work.

Essential Mathematics stands out as one of the best books in the pack, especially in regards to its coverage of the math behind low-level rendering techniques.

The book is broken into 4 parts. The first part, Core Mathematics, covers vectors and matrices, transformations, and number representation. This part will be useful to anyone doing 3D graphics.

Part II, Rendering, covers topics such as lighting and shading, texturing, projection, and rasterization. This part was of particular interest to me because I’ve been working on a commercial renderer, but it should also be useful to those who want a better understanding of what graphics engines do under the hood.

Part III, Animation, covers curves (very in depth) and representation of orientations (Euler vs. axis-angle vs. quaternions). Finally, Part IV, Simulation, covers intersection testing and rigid body dynamics. There are also a couple of appendices to help you brush up on trig and calculus, if needed.

The book includes many C++ code samples and demos, including a handy math library and a simple rendering/game engine using OpenGL and GLUT. The authors are to be commended for their writing style as well. It’s very easy for a book of this nature to get bogged down in an extremely heavy academic tone, but this book manages to avoid that, making for a remarkably easy read.

I’m glad I don’t have to choose just one game math book, but if I did, this would probably be the one I’d pick.

Clear, Comprehensive, and Educational.

The strength of this book lies in its author’s ability to make complex subjects accessible to programmers of various levels. The book covers all necessary subjects of 3D development and algorithmic motion, while providing primers in the relevant Math and Trigonometry. The writing is clear, and the examples combine notation in Math, Pseudo Code, and Open-GL implementation. I could see various uses for this book; from reference guide to required course reading. It explains the most fundamental subjects of Vectors and Matrices, and later capitalizes on this knowledge towards subjects that every professional in the field should know. To make sure the book is right for you, I suggest reading the Introduction, which portrays the book accurately and proceeds to recommend alternative and additional resources.