Mathematics for 3D Game Programming and Computer Graphics, Second Edition

Rating:
Summary: Essential reference for any 3D graphics work.
Review: 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!

Rating:
Summary: Even better than the first edition
Review: I gave the first edition of this book a 5 star rating, so considering that the second edition provides updates to the original as well as four new chapters, it's no surprise that the second edition earns a 5 star rating as well.

The new material includes a brief but informative chapter covering graphics pipeline essentials. This should make the book somewhat more accessible for beginners - though it'll still be daunting for someone without at least high school level math. The shadow volume coverage from the first book has been broken out into its own chapter and greatly expanded. The remaining two chapters are dedicated to numerical methods and curves and surfaces.

If you already own the first edition of the book, then the updates and new chapters probably aren't worth the cost. Otherwise, considering that they retail at the same price, there's no reason not to get this edition instead of the first. It's an excellent resource for anyone who wants a deep and broad knowledge of 3D math.

Rating:
Summary: An Essential Source for Robust 3D Graphics Engine Design
Review: I have not yet been able to purchase the second edition of this book. However, since it is a refinement of the first edition, I feel that I am somewhat competent to review this later version of Lengyel's text on this knowledge of the fundamental chapters which are included in both editions.

Definitely, the subject of 3D Computer Graphics draws programmers and gamers inward like a bug lamp draws insects inward. The ability to express one's own inspiring representation of the world seems to attract the deepest longings of the subcreative nature of the human person. However, the coder quickly realizes that the realization of this dream is extremely difficult due to the complexities of visualization in nature. Lengyel's text helps to break through many of these complexities.

In order to make sure that the reader is "up to speed" on the essentials in mathematics which are necessary for a 3D engine, Lengyel gives a quick, but thorough, review of Vector and Matrix operations. I was indeed impressed by the amount that he condensed into the beginning of the text. While this is far from a complete treatise on Linear Algebra, this material gives the reader the basics which will be necessary for all the other chapters. This is further augmented by his treatment of 3D geometry, its representations, and calculations relevant to it.
Using this, he treats on various subjects that are extremely important for making a lean, mean, and beautiful rendering machine.

His treatment of transformations gives the reader a base in this knowledge that is independent of the rendering context. This is an excellent approach because knowledge of how something works allows for one to use it more fully. He also goes further in introducing Quaternions and deriving rotations around any arbitrary axis.

The chapter on Ray Tracing gives the necessary background for the work done in the following chapter on illumination. While the latter is often implemented by the graphics environment that the coder is using, the full knowledge of this allows for further application in subjects such as bump mapping (which he treats) as well as reflective surface simulation.

Perhaps the most interesting and important subject covered in the text, however, is the chapter on visibility determination. Since this is critical to the speed of rendering, this topic is central to game engine design. Lengyel works through the various methods for bounding box construction as well as bounding spheres, ellipsoids, and cylinders and then explains how these can be tested against the view frustrum in order to determine if an object should even be rendered. Another chapter on various techniques which can be applied to polygons outlines procedures for reducing the complexity of meshes, without compromising quality.

The remaining chapters touch on collision detection, linear and rotational physics, and fluid simulation. These topics allow for the addion of various levels of realism to be added to 3D engines and are of importance once the rendering environment has been established. Furthermore, his appendices are a nice addition for those times when our memories fail to recall various facts.

And so, I give this book my definite approval. It is hard to come by a text so compact, yet thorough, on the foundations truly needed for 3D Graphics. These mathematical foundations allow for greater things to be explored and should interest any 3D programmer as well as individuals with a general interest in mathematics, especially in the applications of linear algebra and calculus.

Rating:
Summary: Great book!
Review: This book explain the mathematics behind a game engine, and it does it pretty well. If you are looking for code to cut and paste into your programs, then this book is not for you. But if you want to really anderstand the theory, it has, in my opinion, a very good balance between explanations, demonstrations and examples.
I got this book because my math was a little 'rusty' and it does a perfect job in bringing all this stuff back in memory, and mutch more as I discover a lot of new stuff and how it can be used in a game engine. I really enjoy this book!

Rating:
Summary: Almost completely useless for Games!!!
Review: This book is all but usefull. It basically gives you the math to implement OpenGL/Direct3D in software, but gives near to no details on using theses libaries to make cool games. The only part that was applicable to a game today imo was the shadow and lighting section. The shadow was so short on details that it was useless in the first place and the lighting part is the reason why this book gets 2 stars instead of 1. If you want to learn the internals of a 3D engine, I would even go as far as to suggest Andre Lamoth's book . If you want to know how to use math for a game in today's world and not back in 1990, then forget about this book. Plus, it's cluttered with proofs. A lot of pages are wasted proving that something is true.

Rating:
Summary: This book is fantastic
Review: This book is great. Its material is well explained, the topics covered are complete (for the most part), and the examples make sense. It is a fantastic reference that should be on the shelf of any professional game programmer or aspiring game programmer. However, this book isn't a hand holding guide to making "cool" games, as some reviewers expected it to be. There is no single book for that. There are so many topics to cover, it would be impossible to put them all into one text. Please don't be fooled by reviews from non-professionals, as this book is a must have. For a list of beginner books to give yourself an introduction to game programming, feel free to send me an email.