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

by Eric Lengyel
4.4 out of 5 stars  See all reviews (22 customer reviews)


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There is a newer edition of this item:
Mathematics for 3D Game Programming and Computer Graphics, Third Edition Mathematics for 3D Game Programming and Computer Graphics, Third Edition 4.1 out of 5 stars (16)
$43.26
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Book Description

December 18, 2001 1584500379 978-1584500377 1st
This resource illustrates the mathematics that a game programmer would need to develop a professional-quality 3D engine. The book starts at a fairly basic level in each of several areas such as vector geometry, modern algebra, and physics, and then progresses to somewhat more advanced topics. Particular attention is given to derivations of key results, ensuring that the reader is not forced to endure "gaps" in the theory. The book discusses applications in the context of the OpenGL architecture. It assumes basic understanding of matrix algebra, trigonometry, and calculus, and concentrates on key math topics for programming game engines and computer graphics. Included are exercise sets which should allow the book to be used as a textbook. The book discusses applications in the context of the OpenGL architecture due to its cross-platform nature with references to certain 3D hardware such as the GeForce from Nvidia and the Radeon from ATI Presents mathematical theory and subsequently provides examples using practical applications.


Editorial Reviews

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

  • Series: Charles River Media Game Development
  • Hardcover: 382 pages
  • Publisher: Charles River Media; 1st edition (December 18, 2001)
  • Language: English
  • ISBN-10: 1584500379
  • ISBN-13: 978-1584500377
  • Product Dimensions: 9.5 x 7.6 x 1 inches
  • Shipping Weight: 2.2 pounds
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (22 customer reviews)
  • Amazon Best Sellers Rank: #1,615,628 in Books (See Top 100 in Books)

More About the Author

Eric Lengyel is a veteran of the computer games industry with over 16 years of experience writing game engines. He has a PhD in Computer Science from the University of California at Davis and an MS in Mathematics from Virginia Tech. Eric is the founder of Terathon Software, where he currently leads ongoing development of the C4 Engine.

Customer Reviews

Most Helpful Customer Reviews
85 of 88 people found the following review helpful
5.0 out of 5 stars Essential reference for any real-time 3D programming January 10, 2002
Format:Hardcover|Verified Purchase
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!
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61 of 65 people found the following review helpful
5.0 out of 5 stars Oh yes March 20, 2002
By A Customer
Format:Hardcover
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.
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20 of 20 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
Format:Hardcover
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.
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9 of 9 people found the following review helpful
5.0 out of 5 stars For a rock-solid understanding of 3D math October 16, 2003
Format:Hardcover
This book provides a solid foundation for anyone who wants to develop a good understanding of the math behind computer graphics. The author provides clear and concise explanations of the concepts covered, backs them up with mathematical proofs, and usually discusses how the concepts can be applied in games, often with sample code. Each chapter has accompanying exercises that I recommended working through.
The topics covered include things you would expect like matrices, vectors, transformations, 3D geometry, and lighting, but also includes are topics like collision detection, ray tracing, visibility determination, and techniques such as billboarding and shadows. It concludes with several chapters on physics including fluid simulation, and a few useful appendices covering trig, complex numbers, and Taylor series.
If you're brand new to graphics and game programming and haven't had a math class in a while, then the somewhat textbook-like language may be a little daunting, but otherwise, this book is an excellent resource for those interested in solidifying their knowledge of 3D math.
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Most Recent Customer Reviews
5.0 out of 5 stars Will pin point your maths you need
I use this book as a reference, every time I need to add a new feature to my 3D engine I always this book as an excellent starting point. Read more
Published 12 months ago by Isaac de la Vega
5.0 out of 5 stars Great book for anyone feeling lost in 3D programming
I have to be honest, until I found this book I was quite lost on how it all "worked" with regards to 3D graphics programming. Read more
Published on April 3, 2012 by Amazon Customer
5.0 out of 5 stars Easy to read, understand and serves as a good reference.
Coming from a strong math background, I already knew much of the material covered in the first three chapters. Read more
Published on July 11, 2011 by Bidit Mazumder
4.0 out of 5 stars Excellent source of applications for a Calc III class
If you're trying to find examples of 3D vector operations (dot and cross products, especially) that keep the interest of a mixed class of 18-25 year olds, this book is a fantastic... Read more
Published on September 10, 2007 by David Matthews
4.0 out of 5 stars good reference for computer graphics math
like others books in charles media , written by someone in the industry , which means value infos will be in the book . Read more
Published on March 24, 2004 by Ahmed Saleh
5.0 out of 5 stars Excellent
Excellent Book, I am very pleased with it and encourage it to anyone who already has ground knowledge in Trig + Calc. No fluffer in this book, all content and well written.
Published on December 21, 2003 by Nathan Handley
5.0 out of 5 stars A Book for The Whole Life
Surely this is the book I was looking for.
Mostly of the 3D games books just presents codes and some few mentions to the maths techniques, without regarding the concepts... Read more
Published on September 16, 2003 by Rodrigo Domingues
4.0 out of 5 stars Reference use only, lacks sample source code
For reference only. This book is basically just filled with formulas (hence, all the other reviewers calling it a math book). Read more
Published on November 17, 2002 by John
2.0 out of 5 stars Disappointment : much to basic
When I read the reviews of this book, I thought this book would finally help me find heights on triangles (eg.terrains), and other stuff I thought would be in a book like this... Read more
Published on October 14, 2002
5.0 out of 5 stars Excellant Mathematics Book
The book covers the mathematics behind today's 3D rendering engines quite impressively. Theorems and methods are backed by proofs and visual aid. Read more
Published on July 23, 2002
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