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Essential Mathematics for Games and Interactive Applications: A Programmer's Guide [Hardcover]

James M. Van Verth , Lars M. Bishop
5.0 out of 5 stars  See all reviews (2 customer reviews)

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Hardcover, March 25 2004 --  
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Essential Mathematics for Games and Interactive Applications: A Programmer's Guide Essential Mathematics for Games and Interactive Applications: A Programmer's Guide 5.0 out of 5 stars (2)
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Book Description

March 25 2004 Morgan Kaufmann Series in Interactive 3D Technology
"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 useful-it 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

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"Fledgling graphics and games developers will find it a valuable introduction; experienced developers will find it an invaluable reference. Everything is here..." -David Luebke, University of Virginia, co-author of Level of Detail for 3D Graphics

"...If you program graphics, let alone games, you need this book...Highly recommended."

--Rick Wayne in a review for Software Development Magazine

Book Description

From the authors' popular courses at Game Developers Conferences

Inside This Book (Learn More)
First Sentence
Over the past decade or so (driven by increasingly powerful computer hardware), 3D games have expanded from custom-hardware arcade machines to the realm of "hardcore" PC games, on to consumer "set top" videogame consoles, and even onto handheld devices such as personal digital assistants (PDAs) and cellular telephones. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index
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5.0 out of 5 stars Clear, Comprehensive, and Educational. May 8 2004
By A Customer
Format:Hardcover
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.
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5.0 out of 5 stars Essential book for 3D developers of all kinds May 8 2004
By A Customer
Format:Hardcover
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.
Was this review helpful to you?
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 3.9 out of 5 stars  16 reviews
43 of 46 people found the following review helpful
5.0 out of 5 stars One of the best game math books April 28 2005
By Dave Astle - Published on Amazon.com
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.
11 of 11 people found the following review helpful
5.0 out of 5 stars A solid guide to beginner and expert alike Jan. 13 2009
By Christopher Dannemiller - Published on Amazon.com
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.
11 of 12 people found the following review helpful
1.0 out of 5 stars Bad math book June 4 2012
By Roy Klein - Published on Amazon.com
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.
15 of 18 people found the following review helpful
5.0 out of 5 stars Fabulous teaching! July 24 2005
By R. Falck - Published on Amazon.com
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
5.0 out of 5 stars Essential Math a good basis May 4 2010
By J. Meschke - Published on Amazon.com
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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