Mathematics for 3d Game Programming and Computer Graphics

by Eric Lengyel

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 * 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

Genres: Programming, Mathematics, Reference, Computer Science, Nonfiction, Technology, Science

Hardcover

First published December 1, 2001

Reviews

[Andy · Rating 2 out of 5]

This book is basically 'cut-and-paste' from Wikipedia. For example, for presenting Gram-Schmidt Orthogonalization (basis vectors), it simply states the algorithm process without adding any example or why the algorithm works.

This may be a good "formula reference book" in the 1980s when the Internet was not for everyone, but in this era, you can just Google and find all the related formulas on Wikipedia.

This book lacks examples and any explanatory words when presenting anything, it is just like a dictionary rather than a tutorial book. It a waste of money for me.

[Dave Yu · Rating 5 out of 5]

Excellent reference for 3D math. Most of the math in the book focuses on applications in real-time graphics and gameplay (there are sections on collision detection and physics). This, along with Real Time Rendering by Akenine-Moller and Haines and Real Time Collision Detection by Ericson are probably the best modern references for gameplay/graphics/physics math.

[Taneli · Rating 4 out of 5]

A definite must read for anyone interested in 3D programming. First chapters discuss the basic mathematical concepts used in the rest of the book in detail. Rest of the chapters are dedicated to discussing how these concepts are used in rendering and physics calculations.

[Lorenzo Marsicano]

I've skipped some part of it, but it was an awesome resource to get back into some trigonometry and linear algebra with some practical application to 3D graphic programming.

[Dante Ding · Rating 4 out of 5]

Not used to read, used to check

[Exo · Rating 2 out of 5]

A good reference. That's about it. It's very "cut and paste theorems from wikipedia" styled and rarely has worked examples. A lot of content, but lacks the experienced narrative voice (not an attack on Lengyel, it just tends to lack depth. Lengyel is experienced, by all means, yes). It really isn't a bad book, but I, personally, learn by example.

[Adam · Rating 5 out of 5]

Amazing book, a really great introduction to the 3D math world of computer game programming.

[Samson · Rating 4 out of 5]

Very good book

[Admir · Rating 5 out of 5]

I use it as a good reference book. It covers almost every topic of mathematics in game development.