Mathematics for 3D Game Programming & Computer Graphics (Game Development Series (Charles River Media).) [ILLUSTRATED] (Hardcover)

by Eric Lengyel (Author) "Vectors are of fundamental importance in any 3D game engine..." (more)
Key Phrases: box collides, frustum planes, view frustum, Solving Equation (more...)

Editorial Reviews

Product Description
This book illustrates the mathematical concepts that a game developer 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 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 the Taylor series.

Key Features:

* 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. Makes references to modern 3D hardware such as GeForce 3 from Nvidia

* 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

About the Author
Eric Lengyel is a Senior Software Engineer at the 3DO Company in Redwood City, CA. He holds an MS in Mathematics from Virginia Tech and has written several articles for industry periodicals including gamasutra.com. He is also the area editor in geometry management for Game Programming Gems 2.

Product Details

• Hardcover: 400 pages
• Publisher: Charles River Media; 1st edition (December 18, 2001)
• Language: English
• ISBN-10: 1584500379
• ISBN-13: 978-1584500377
• Product Dimensions: 9.3 x 7.5 x 1 inches
• Shipping Weight: 2.2 pounds
• Average Customer Review: 4.2 out of 5 stars See all reviews (20 customer reviews)
• Amazon.com Sales Rank: #794,886 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

69 of 71 people found the following review helpful:

5.0 out of 5 stars Essential reference for any real-time 3D programming, January 10, 2002

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!

47 of 49 people found the following review helpful:

5.0 out of 5 stars Oh yes, March 20, 2002

By A Customer

What a wonderful book.

Any beginner to computer graphics and game development is often overwhelmed by the mathematics that runs the show.

Until now, anyone new to the field has been forced to run self-taught refresher courses on Linear Algebra and Calculus while trying to learn an already-difficult subject. Small wonder that many developers quit out of frustration.

Most computer graphics books provide small backgrounders on the mathematics needed to get by, but almost none of them provides a thorough education and solid explanation on what's really going on. The worst in the group (such as "3D Game Engine Design") provide no assistance whatsoever, and leave the reader floundering by the end of the preface.

Mr. Lengyel's book provides solid mathematical theory on most of the major subjects in computer graphics/game development, and can be looked at as a companion volume to almost any computer graphics text.

3D transformations, lighting calculations, collision/intersection detection-- those are a few of the subjects discussed in the book, in such a way that the intermediate reader can follow along and learn the theory without having to cry for mother.

Please note that you need at least *some* mathematics background to make use of this book; if you're unfamiliar with basic calculus terms for instance, you'll probably want to take a pass, as this book isn't a complete hand-holder. You can only accomplish so much in 400 pages, after all.

For everyone else who took their college math classes (and subsequently forgot most of the material), this book is a great refresher and will get you ready for fully exploring computer graphics.

My only regret is that there's no second volume to discuss curved surfaces and slightly more advanced topics-- no one can have it all I suppose.

12 of 12 people found the following review helpful:

4.0 out of 5 stars One of the better books so far..., April 4, 2002

By A Customer

If this book had all exercises answered in the Answers section I'd give it a 5. It is a wonderfully clear book (so far, I am not done with it yet). It does more than crank out rote formulas, it proves them in an accessible fashion!

I have been able to use what I have taught myself to do my work with a better understanding (I recently joined a CAD company after years in non-graphics work) and this book has been helpful. I will finish this book as it is way better than its comptetion for covering the maths needed for modern computer graphics.

I have but one regret regarding this book, that I didn't have it 5 years ago when I started playing with OpenGL using the Red Book. I have wasted much time and money trying to find the information in this book to grasp the real tools beyond mere APIs.