Our review:Item 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
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Buyer Testimonials
Average Buyer's Review:
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Little more than an outline
I was disappointed in how little explanations were included in this math book. It seemed more like a dictionary. It was as if someone listed all the math concepts that could be included and then put the list into a hard cover binder.
I did read some of the other reviews thinking I had missed something. One suggested spending a year on the book. But there is so little there. My college book on linear algebra did a much better job of explaining the material. Theorems were explained, samples worked out and 10 to 20 problems were given at the end of each section. This book as 50 problems for the entire book. This book spends eight pages on quaternions. Studying these pages over an extended period of time would not give the understanding you could get from a book like Kuipers' Quaternions and Rotation Sequences. It took 75 pages but one is able to understand the system and how it relates to game programming.
With all the colleges now offering game programming degrees, their must be a book written by someone who is use to explaining the material. That person would know the best way to present the material and could anticipate questions and include the answers in his or her explanations.
Buyer's review: 
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a disappointment
the second edition brings a new chapter on the graphics pipeline. Well done, except that it is extremely obscure, for those who already understood the arcanes of the graphics pipeline.
Chapter 5 on "ray tracing": 6 pages on root finding of quadratic, cubic and quartic polynomials;
to compare with Chapter 7: "Visibility determination": The spatial partitioning deserves solely 4 pages.
What's the point on dwelling so much on something that is trivial and botching something that is hard to grasp and of paramount importance ?
Buyer's review: 
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One of a kind
As a professional 3D graphics programmer, I can not stress enough the quality of this book. This book covers 3D math fundamentals, algorithms, and it is complete with easy to understand (!) proofs. The math is difficult because there is so many problems to be solved in 3D (and they draw from many different branches of mathematics), but it is written in such a clear way that every topic is made approachable. Unlike esoteric Ph. D papers, you aren't assumed to have any specific knowledge of math idioms or jargon. You simply need a decent grasp of college calculus and trigonometry to make the most of it. There are a few samples too to test your knowledge.
Expect to spend at least a solid year to really make the use of this book. Treat it as you would a two - three semester course in college. During this process, you'll find yourself occasionally wanting to get more practice and referring to a respective book on it.
If you could only own two books for 3D programming, buy this first and buy Ericson's book on collision detection next.
In summary, Eric Lengyel's attention to detail and mastery of 3D math / algorithms really shines and this book is an example of it.
Buyer's review: -
Great book
This book is great for anyone interested in computer graphics. Even for people who do not have a lot of math/graphics experience, this book starts you off with the basics of vectors and matrices and has exercises/solutions for each chapter. It saves you the time of looking through your old linear algebra and differential equation math books and contains the must know information you will use as a graphics programmer.
Buyer's review: 
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Math majors rejoice
To be honest, while I find this book to be a decent reference, I find it to be pretty inaccessible in terms of sitting down and reading through it in an attempt to learn the concepts. As a non-math major (I'm actually an engineer and software developer) these math concepts are by no means beyond me. But rather than simply being presented with equation after equation, proof after proof, what I find a lot more valuable is more discussion on the usage of these equations. Specifically I'd like to see examples, diagrams, and code, and there is precious little of any of that in this book.
In other words, this book is very much like what you expect to find in a very dry upper devision college math text for the consumption of math majors who are used to such things. But for a non math major just trying to make use of these concepts in order to get the job done and make games? eh, not so much.
Still, I do think this book is useful as a reference when I want to look up an equation as there are a ton of them crammed into this book, but for me, I just don't find this book to be very good as a learning tool.