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Essential Mathematics for Games and Interactive Applications: A Programmer's Guide, Second Edition Hardcover – 27 Jun 2008

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Product details

  • Hardcover: 704 pages
  • Publisher: CRC Press; 2 edition (27 Jun. 2008)
  • Language: English
  • ISBN-10: 0123742978
  • ISBN-13: 978-0123742971
  • Product Dimensions: 4.4 x 20.3 x 24.1 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Bestsellers Rank: 398,880 in Books (See Top 100 in Books)
  • See Complete Table of Contents

More About the Author

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Product Description


"It's the book with all the math you need for games." -Neil Kirby, Researcher, Alcatel-Lucent

About the Author

James M. Van Verth is a founding member of Red Storm Entertainment, a division of Ubisoft, where he has been a lead engineer for nine years. For the past eight years he has also been a regular speaker at the Game Developers Conferences, teaching the all-day tutorial "Math for Game Programmers,” on which this book is based. He has a B.A. in mathematics and computer science from Dartmouth College and M.S. degrees in computer science from the State University of New York at Buffalo and the University of North Carolina at Chapel Hill.
Lars M. Bishop is an engineer in the Handheld Developer Technologies group at NVIDIA. Prior to joining NVIDIA, Lars was the Chief Technology Officer at Numerical Design Limited, leading the development of the Gamebryo3D cross-platform game engine. He received a BS in Math/Computer Science from Brown University and an MS in Computer Science from the University of North Carolina at Chapel Hill. His outside interests include photography, drumming, and playing bass guitar.

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11 of 11 people found the following review helpful By C. Bamber on 16 Feb. 2009
Format: Hardcover
This is an utterly brilliant book, I don't work in games but in non-realtime CG, and the focus upon the mathematics and techniques rather than the code samples is refreshing. The book covers pretty much all the vital bases, but if it isn't enough, a HUGE reference and further reading list is provided at the end.

I'm reading this book front to back, but it shines as a reference manual.
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1 of 1 people found the following review helpful By Joe Alam on 25 Feb. 2012
Format: Hardcover
This book contains all of the Mathematical techniques needed for graphics and game programming.

I haven't yet come across any maths needed in game programming that can't be found in this book.
Everything is explained thoroughly will diagrams and formulae provided.

The book start from a fairly simple level, and it would be possible to read it with very little background in maths.

Very simple code samples are given, and the CD that accompanies this book has various examples and exercises to help learn how to put the techniques to practical application.

I recommend this book for anybody serious about learning game programming.
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By Martin Buscombe on 7 Jan. 2015
Format: Hardcover Verified Purchase
Very good and informative book, good delivery
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Most Helpful Customer Reviews on (beta) 0 reviews
43 of 46 people found the following review helpful
One of the best game math books 28 April 2005
By Dave Astle - Published on
Format: Hardcover
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.
14 of 15 people found the following review helpful
Bad math book 4 Jun. 2012
By Roy Klein - Published on
Format: Hardcover
This book is for people who already know the material the book is trying to teach. Because if you don't have any familiarity with it, you will not be able to extract any from this text. It is a mediocre math book, employing a dry tone and unimaginative approach to explain non-trivial material.

I've had a much better experience reading free online explanations on the concepts presented in the book that were both easier to digest and gave a much more lasting, intuitive understanding. I bought this book after glancing through an interesting presentation one of the authors gave at GDC, hoping that the book would follow suit and make the effort to arrange and present the material in the same accessible form, but it seems to me that there was no effort made here to make the frog easier to swallow.

To illustrate, here's the book's explanation for Basis Vectors: "So suppose that for a given vector space V, we can find a set beta of n linearly independent vectors in V that span V". Google search "basis vectors explained", click the first result, and you'll get a far superior explanation. I acknowledge the effort to transmit formal definitions in formal notation, but I honestly did not buy the book for that. I just want to understand, and that's something the book completely fails to deliver.

Graphics programming is a field littered with bad books, and this is no exception.
11 of 11 people found the following review helpful
A solid guide to beginner and expert alike 13 Jan. 2009
By Christopher Dannemiller - Published on
Format: Hardcover
I have read many math books for video games and there are two aspects of this book I really like. The first is the book is encyclopedic and terms of the amount of information that it covers. The second reason that I like this book is that it clearly explains where the equations come from not just what the equations are.
15 of 18 people found the following review helpful
Fabulous teaching! 25 July 2005
By R. Falck - Published on
Format: Hardcover
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.
3 of 3 people found the following review helpful
Essential Math a good basis 5 May 2010
By J. Meschke - Published on
Format: Hardcover Verified Purchase
As a novice game programming hobbyist, I've written applications using the DirectX SDK to render 3D visuals without really understanding what's happening behind the scenes. Applying a transformation matrix to a model and illuminating it with a spotlight just seemed to be magic beyond my understanding. This book has delivered enough information to get a good foundation in the understanding of the mathematics involved to bring points and images into a visual representation to the screen while going even further to discuss collision detection, interpolation, and rigid body dynamics.

If the reader wanted to develop a 3D application on a platform with no native support or SDK, there's enough material in this book to give the reader a core background to develop a software solution. Even though portions of the graphics pipeline are automatically handled by an SDK or hardware, the concepts are presented so the reader is taken every step of the way.

The reader should know algebra (of course), trigonometry, and calculus if they want to get something out of it. A history of linear algebra also helps, but it isn't necessary since the chapter on matrices that goes over the essential operations. The later chapters on collision detection and physics start getting more math-heavy. Having previously read a couple other books in the Morgan Kaufmann series: Real Time Collision Detection and Game Physics, I was expecting the discussions to be very similar; however, the reader would only get a basic understanding of the topics and would greatly benefit from continuing their reading into the aforementioned books.

Overall, I enjoyed this book very much and it gets my approval for anyone wanting to get into game programming and 3D simulation. The author also provides many resources and accompanies the book with a CD of precompiled visual examples that should better solidify the user's understanding. As previously mentioned, Real Time Collision Detection and Game Physics make fantastic supplements to this book.
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