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Eric Lengyel
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Mathematics for 3d Game Programming and Computer Graphics (Game Development Series) First Edition

by Eric Lengyel (Author)
4.5 4.5 out of 5 stars 21 ratings
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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

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  1. ISBN-10
    1584500379
  2. ISBN-13
    978-1584500377
  3. Edition
    First Edition
  4. Publisher
    Charles River Media
  5. Publication date
    December 18, 2001
  6. Language
    English
  7. Dimensions
    7.75 x 1.25 x 9.75 inches
  8. Print length
    382 pages
  9. See all details
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Customer reviews

4.5 out of 5 stars
21 global ratings

Top reviews from the United States

Frank Kane
5.0 out of 5 stars Essential reference for any real-time 3D programming
Reviewed in the United States on January 11, 2002
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!
85 people found this helpful
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John
4.0 out of 5 stars Reference use only, lacks sample source code
Reviewed in the United States on November 17, 2002
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For reference only. This book is basically just filled with formulas (hence, all the other reviewers calling it a math book). This is not the kind of book that I would sit down and read from front to back, however I will keep it in my library.
Anytime you need a formula for your 3d application, you'll more than likely find it in this book. However, much of the book is lacking explanation. Some may like the fact that it is very much to the point, no messing around, here's the formula. I bought this book because I wanted to know more about matrices, rotation, views, and lighting. I was expecting to see more source code samples, especially source code that converts complex formulas into usable code. There are a few OpenGL snippets that do this, but not enough to satisfy my thirst. Hopefully, a newer edition will show each formula along with the corresponding code, or pseudo-code so that you can quickly make use of the formulas. Now, if you are interested in nifty things like decals, edge collapse, and billboarding, you'll find this info in the book. There are other useful tidbits like projectile motion, basic physics and fluid sim. There are many other topics so check the TOC.
4 stars:
For lacking source code samples and for lacking explanation. Front cover exploits OpenGL, but very little code exists (Less than 10 pages of code).
Introduction lacks definition of common 3D terms, so unless you have previous knowledge, this book will be a stumper.
22 people found this helpful
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Bidit Mazumder
5.0 out of 5 stars Easy to read, understand and serves as a good reference.
Reviewed in the United States on July 11, 2011
Verified Purchase
Coming from a strong math background, I already knew much of the material covered in the first three chapters.

Lengyel filled the gaps, explained and emphasized the more subtle points, like how to transform the normal by the inverse transpose of the tangent's transformation matrix and achieve run-time efficiency.

Chapter three introduced a few concepts, like Quaternions, that were new to me at the time but I was able to understand them easily--Lengyel shows the need for a solution before he derives and applies the solution.

Everything from chapter four onwards was new but thanks to my brilliant teacher, I was able to understand the math and create my first 3D engine.

Chapter 5.2, on surface intersections, was particularly useful when I was writing a ray-tracer.

Overall, I found this book easy to read; and it does not trivialize the subject. A few advanced topics like projections and shadows, omitted in this edition, are remedied in later editions.

This is the First Edition (2001) that has been out-of-print for some time. If you are planning on buying this book, I recommend you go for the Third Edition (2011) and use it along with a good textbook, like Interactive Computer Graphics (Angel).
2 people found this helpful
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Amazon Customer
5.0 out of 5 stars Great book for anyone feeling lost in 3D programming
Reviewed in the United States on April 4, 2012
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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. I knew a few things about how computer graphics worked, but once I started wanting to do more than just draw a line or a circle, I found myself painstakingly searching on Google for tutorials and college lecture notes to help me accomplish my goals. Not anymore. This book has truly given me the tools needed to really dive into 3D programming and produce really awesome things.

Like others have said though, I hope the author publishes a Volume 2 of this book, which takes the Math to the next level for those of us that already grasp the majority of the concepts laid out in this book (some sections on more complex Physics would be awesome!).

Highly recommended.
2 people found this helpful
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Jing Garcia
4.0 out of 5 stars bought for my son
Reviewed in the United States on May 31, 2014
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another second-hand book that looks brand new and never used. my son needed it, so i got hime one. very useful indeed.
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A. Palomba
5.0 out of 5 stars Excellent concise book
Reviewed in the United States on March 1, 2002
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This book is great! It explains all the pertinent theorems and formulas that you would encounter in developing a real-time 3d graphics title. I highly recommend it. After a hiatus from the game industry it was good to have a concise source of information to help me brush up on my math.
12 people found this helpful
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Top reviews from other countries

Bruce Rubinstein
4.0 out of 5 stars Good book worth money
Reviewed in Canada on February 22, 2024
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book covers basic of 3d math. Short and concise does not cover great details Covers matrices
plane intersections and camera well. Little light on texture and lighting. Also
covers basic physics for games. It does collision and boundary box very well/
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StephenDS
3.0 out of 5 stars Bought for Grandson so limited feedback
Reviewed in the United Kingdom on February 24, 2019
Verified Purchase
One of my grandsons will soon be at university working in some field related to 3D programming. I bought this for him, hoping it would be helpful. He has been polite about its usefulness, so I imagine I did not quite hit the spot with this particular book, but that is not due to any fault with the book.
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