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!
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.
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.