Mathematics for 3D Game Programming and Computer Graphics, Second Edition (Game Development Series) (Hardcover)

~ (Author)

Editorial Reviews

Product Description

This completely updated second edition illustrates the mathematical concepts that a game programmer would need to develop a professional-quality 3D engine. Although the book is geared toward applications in game development, many of the topics appeal to general interests in 3D graphics. It starts at a fairly basic level in areas such as vector geometry and linear algebra, and then progresses to more advanced topics in 3D game programming such as illumination and visibility determination. Particular attention is given to derivations of key results, ensuring that the reader is not forced to endure gaps in the theory. The book assumes a working knowledge of trigonometry and calculus, but also includes sections that review the important tools used from these disciplines, such as trigonometric identities, differential equations, and Taylor series.

Key Features
* Includes four new chapters: the graphics pipeline, the stencil shadow rendering technique, curves & surfaces, and numerical methods
* Concentrates on key mathematical topics for programming 3D game engines
* Discusses applications in the context of the OpenGL architecture due to its cross-platform nature and long-standing industry acceptance. Sample rendering code is presented using ARB vertex programs and fragment programs
* Selected topics include quaternions, homogeneous coordinates, ray tracing, bump mapping, portal systems, polygonal techniques, shadows, and physics
* Includes exercise sets for use as a textbook

New to This Edition
The following are selected revisions in the second edition:
* A new preliminary chapter that provides a review of the 3D rendering pipeline
* A new chapter containing an advanced discussion of the stencil shadow rendering technique
* A new chapter covering various numerical methods pertinent to 3D graphics programming, including numerical solutions to linear systems, numerical eigenvalue determination, and numerical integration
* A new chapter covering curves and surfaces, including Bézier curves and B-splines
* New discussions of texture filtering, mipmapping, and infinite projection matrices
* Updated lighting method implementations and collision detection techniques
* Additional exercises in all chapters

About the Author

Eric Lengyel (Sunnyvale, CA) is the Chief Technology Officer for the game engine development studio, Terathon Software. He holds an M.S. in mathematics from Virginia Tech and has written several articles for gamasutra.com and the Game Programming Gems series. He is also the author of The OpenGL Extensions Guide.

Product Details

• Hardcover: 551 pages
• Publisher: Charles River Media; 2 edition (November 18, 2003)
• Language: English
• ISBN-10: 1584502770
• ISBN-13: 978-1584502777
• Product Dimensions: 9.3 x 7.6 x 1.4 inches
• Shipping Weight: 2.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (12 customer reviews)
• Amazon.com Sales Rank: #109,649 in Books (See Bestsellers in Books)

  Popular in this category: (What's this?)

  #92 in

  Books > Computers & Internet > Programming > Game Programming

• This item is part of The Charles River Media Game Development Series.

Customer Reviews

Most Helpful Customer Reviews

19 of 20 people found the following review helpful:

5.0 out of 5 stars Essential reference for any 3D graphics work., June 30, 2004

By	Francis J. Kane (Seattle, WA USA) - See all my reviews (REAL NAME)

Finally, no more searching through all my college math textbooks for the reference I need for real-time 3D software development. The basics of vectors and matrices are of course included, but in much more depth than you got in school, more than likely - and with emphasis on how they are useful in 3D game programming. So many game developers lack an intuitive feel for such basics as transformation matrices, dot products, and cross products and are hobbled by this; just read up to chapter three and the lights will go on, so to speak. The chapter on lighting is particularly, well, enlightening - not only are the various lighting models explained in detail (including some I was unfamiliar with before), but the author provides means for accomplishing them in real-time using texture and vertex shaders.

The notation used in the book is modern and consistent, and the code samples clearly written. I believe this is the first volume to combine complete mathematical explanations of essential 3D computer graphics operations with practical advice on how to implement the sometimes complex math efficiently in real-time systems.

The chapters on picking and collision detection are also complete and include practical advice on implementation in addition to the theory behind it.

This is not a book for most high school math students - the author assumes you've at least been through some higher level math and can talk the basic language of mathematics. However, it does not presuppose that you are familiar with anything but basic calculus, and more importantly, it doesn't assume that you're familiar with some quirky notational system specific to the author. I haven't been in a math class for ten years, but I had no trouble understanding any concepts introduced in this book upon the first read.

I don't forsee this volume leaving my desk anytime soon!

17 of 18 people found the following review helpful:

5.0 out of 5 stars Great book!, March 6, 2004

By	Guillaume Schmid "gschmid105" (Paris, France) - See all my reviews

This book explain the mathematics behind a game engine, and it does it pretty well. If you are looking for code to cut and paste into your programs, then this book is not for you. But if you want to really anderstand the theory, it has, in my opinion, a very good balance between explanations, demonstrations and examples.
I got this book because my math was a little 'rusty' and it does a perfect job in bringing all this stuff back in memory, and mutch more as I discover a lot of new stuff and how it can be used in a game engine. I really enjoy this book!

15 of 16 people found the following review helpful:

5.0 out of 5 stars This book is fantastic, August 3, 2004

By	Waylon "Waylon" (Austin, TX) - See all my reviews

This book is great. Its material is well explained, the topics covered are complete (for the most part), and the examples make sense. It is a fantastic reference that should be on the shelf of any professional game programmer or aspiring game programmer. However, this book isn't a hand holding guide to making "cool" games, as some reviewers expected it to be. There is no single book for that. There are so many topics to cover, it would be impossible to put them all into one text. Please don't be fooled by reviews from non-professionals, as this book is a must have. For a list of beginner books to give yourself an introduction to game programming, feel free to send me an email.