Mathematics for 3D Game Programming and Computer Graphics, Third Edition 3rd Edition

by Eric Lengyel (Author)

108 ratings

ISBN-13: 978-1435458864

ISBN-10: 1435458869

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This updated third edition illustrates the mathematical concepts that a game developer needs to develop 3D computer graphics and game engines at the professional level. 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 Taylor series.

The third edition expands upon topics that include projections, shadows, physics, cloth simulation, and numerical methods. All of the illustrations have been updated, and the shader code has been updated to the latest high-level shading language specifications.

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Editorial Reviews

About the Author

Eric Lengyel is a veteran of the computer games industry with over 16 years of experience writing game engines. He has a PhD in Computer Science from the University of California at Davis and an MS in Mathematics from Virginia Tech. Eric is the founder of Terathon Software, where he currently leads ongoing development of the C4 Engine.

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Product details

Publisher ‏ : ‎ Cengage Learning PTR; 3rd edition (June 2, 2011)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 624 pages
ISBN-10 ‏ : ‎ 1435458869
ISBN-13 ‏ : ‎ 978-1435458864
Item Weight ‏ : ‎ 4.06 pounds
Dimensions ‏ : ‎ 7 x 1.5 x 9 inches

Best Sellers Rank: #220,633 in Books (See Top 100 in Books)
- #3 in DirectX Software Programming
- #5 in OpenGL Software Programming
- #96 in Game Programming

Customer Reviews:
108 ratings

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Eric Lengyel

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Eric Lengyel (Ph.D. computer science, M.S. mathematics) has been a game engine developer since the 1990s and has been writing about it almost as long. He spends most of his time working on the C4 Engine and the Slug Library, but sometimes takes a break to perform new research in geometric algebra. He lives in Lincoln, California.

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A. M. Hernandez

Awesome Coverage Of 3D Math. A Must Read for Graphics Programming.

Reviewed in the United States on April 28, 2014

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Mathematics for 3D Game Programming and Computer Graphics by Eric Lengyel is one of those books I have literally been eyeing for years and just never got around to reading. If you are not familiar, Eric Lengyel is the creator of the C4 Engine, and also the author of various game development books. He is well regarded in the community, so I assumed this was a must read title. After reading it, I still agree; it’s an excellent source of knowledge.

The book covers the basic stuff you would expect from a 3D math book: vectors, matrices, quaternions, intersections between various types of geometry, visibility, etc. Great, so the bases are covered. Lengyel goes a bit further, though, and discusses other topics that are very important in computer graphics. For example: lighting and shadowing, decals, curved surfaces, and physics (including fluid and cloth simulation). So a decent amount of topics are covered, but the chapters are still brief enough to finish each in one sitting.

While there are some implementation examples, the text is pretty light on the code. The code that is here is mostly based around OpenGL, however the concepts should still translate to DirectX. Not a huge issue. When needed, he does show code samples, but most of the copy is dedicated to math discussion and the equations.

Granted, some of the equations and proofs were dense and hard to follow. This was made worse by the fact that I was reading this on the Kindle, and the equations were made up of small images you couldn’t zoom in on. Having said that, I still understood most of the concepts, but there were a few times I felt overwhelmed. I can’t really fault the author for that, since his written explanations were all very clear and concise. It’s just some of the content is deep and complex, so be prepared.

All in all, I found this to be a great resource and you can never know enough math in this field. Unfortunately, I will still probably have to look up some of the equations online or in other books due to the low quality of the images in the e-book. But this is a minor complaint compared to the amount of information backed in this title. I would recommend this.

5 people found this helpful

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Patrick Rouse

The definitive guide for 3D math

Reviewed in the United States on January 16, 2012

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As a word of warning, do not purchase this book expecting it to teach you math fundamentals. If you do not have a background of at least algebra and trigonometry (and preferably a bit of calculus), you owe it to yourself to pick up another book and brush up on these fundamentals. While there are a few appendices covering a handful of topics, they are less about explaining the topic and more of reference pages.

Mathematics for 3D Game Programming and Computer Graphics is an excellent reference book for anyone doing 3D work. The topics are very to the point and few pages are wasted explaining basic math principles (hence the warning about having a decent math background). The book probably won't teach anyone who doesn't know they underlying principles but will be your go-to reference for any algorithm you implement.

The book starts with the reviews of the requisite vector, matrix, transformation (including rotations by quaternions) and basic geometry for a view frustum, but quickly dives into more advanced topics. Ray tracing is covered for all areas of use, from light maps to reflections. The lighting chapter covers texturing using several map types as well as lighting models with a very enjoyable discussion of specular reflection models.

Solid chapters on culling using bounding volumes and portal systems, shadowing and curve algorithms round out the first half of the book. The second half is devoted to the mathematics of physics, with chapters on basic collision detection, linear and rotational physics. The simulation of fluids and cloth (one of the more difficult physical models to accurately compute in a game) gets it's own chapter and it's a highlight for anyone implementing character clothing animation or a realistic water volume.

Every chapter has exercises (with and appendix of answers) to reinforce the material. The C++ and GLSL shader code is available on the books companion website ([...]) much of which forms the basis for the math classes of the authors own engine.

Anyone who needs a math reference book for 3D would do well to own this book. If you are writing your own engine, you owe it to yourself to pick up what will be the only math book you will need. While many technical books do not age well, this hardcover book will last through many late-night coding sessions both physically and with regard to the material within at a low price point. Never again will you have to scour through your old textbooks or search online for the algorithm you are trying to implement. The author has done the impossible; make a truly terrific math textbook.

51 people found this helpful

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Baffled in Palatine

Well written, good coverage of topic

Reviewed in the United States on May 30, 2018

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I've been away from math for too long - it's a tough read but mostly because I have become sloppy in my old age. I suspect the book is more intended for the reader who wants to look up a specific topic but I'm reading it from cover to cover just out of interest in this whole game engine thing. Also I refuse to move along until I"m sure I understand each proof. Probably my bucket book.

One person found this helpful

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Top reviews from other countries

N. Bwts

Love it

Reviewed in the United Kingdom on April 9, 2016

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I'm not a professional programmer rather an enthusiastic amateur. This is not a book for beginners.

Although there is a good review of linear algebra in the first part, some previous experience with linear algebra is essential to get the most out of this book in my opinion,

That said, I love this book. If you're looking for a good grounding in 3D graphics you cant go far wrong.

2 people found this helpful

Choudhry

Good, but dodgy print on some pages

Reviewed in the United Kingdom on April 19, 2021

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Great book, but some of the pages are slightly distorted

T. Pawlak

Highly recommended book

Reviewed in the United Kingdom on September 5, 2014

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I haven't read such a good book for ages.

The layout of the book is very clear and intuitive. You can easily find subjects you are looking for. Good graphics, examples and mathematical techniques make this book very useful for everyone who would like to learn more about 3D graphics and game programming.

Highly recommended.

One person found this helpful

The Oracle

... this product for my nephew who thinks it's absolutely fantastic. 10/10

Reviewed in the United Kingdom on November 24, 2015

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I bought this product for my nephew who thinks it's absolutely fantastic. 10/10.

One person found this helpful

PC Builder

Five Stars

Reviewed in the United Kingdom on August 13, 2016

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Well Recommender

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Mathematics for 3D Game Programming and Computer Graphics, Third Edition 3rd Edition

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Eric Lengyel

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