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Eric Lengyel
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Mathematics for 3D Game Programming and Computer Graphics, Second Edition 2nd Edition

by Eric Lengyel (Author)
4.1 4.1 out of 5 stars 24 ratings
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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.
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  1. ISBN-10
    1584502770
  2. ISBN-13
    978-1584502777
  3. Edition
    2nd
  4. Publisher
    Cengage Learning
  5. Publication date
    November 17, 2003
  6. Language
    English
  7. Dimensions
    7.5 x 1.5 x 9.5 inches
  8. Print length
    576 pages
  9. See all details
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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.

Product details

  • Publisher ‏ : ‎ Cengage Learning; 2nd edition (November 17, 2003)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 576 pages
  • ISBN-10 ‏ : ‎ 1584502770
  • ISBN-13 ‏ : ‎ 978-1584502777
  • Item Weight ‏ : ‎ 2.57 pounds
  • Dimensions ‏ : ‎ 7.5 x 1.5 x 9.5 inches
  • Customer Reviews:
    4.1 4.1 out of 5 stars 24 ratings

About the author

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Eric Lengyel

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.

Customer reviews

4.1 out of 5 stars
24 global ratings

Top reviews from the United States

Marcin Heniborg
5.0 out of 5 stars I strongly recomend for the ones that want to seriously go into game development!
Reviewed in the United States on February 6, 2010
Verified Purchase
When I received this book I couldn't wait to start reading it. I didn't finish it yet but so far all explanations, mathematical rules are so clear and understandable. It's incredible to model world with usage of equations and numbers. Don't hesitate! Get it. Enjoy.
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5.0 out of 5 stars Five Stars
Reviewed in the United States on February 12, 2017
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much better than i thought
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123
3.0 out of 5 stars A good reference
Reviewed in the United States on October 29, 2012
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I was disappointed that this book is more of a reference and not something that used exercises and examples to facilitate learning.

-2 stars for being a hammer when I needed a screwdriver? Perhaps. But then maybe I'm taking off 2 stars because the title and description do not make it clear that this is a reference.

However if you are looking for a reference, this is definitely the book for you! I own a few 3d game engine math books and have done an in depth comparison. This is a very complete reference.

I would also like to add that this book is EXTREMELY TOUGH. I was very impressed with the toughness of the binding, thickness of pages and quality of print. All in all this is probably one of the highest quality books I have owned, from a physical standpoint.
9 people found this helpful
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Matthew K. Minerd
5.0 out of 5 stars An Essential Source for Robust 3D Graphics Engine Design
Reviewed in the United States on November 21, 2004
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.
10 people found this helpful
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Laval
2.0 out of 5 stars One of the books a regret
Reviewed in the United States on March 31, 2013
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This book is poorly written. Mathematics, whatever the area of application, is something to be understood, not a bunch of formulas to be known. This explains just about nothing and just gives a bunch formulas with little good examples of their proper use.
8 people found this helpful
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Tristan Lorach
4.0 out of 5 stars Not available for Kindle PC !?!
Reviewed in the United States on April 26, 2010
Verified Purchase
Disapointing : this ebook doesn't seem to be allowed for Kindle PC.
I was interested to be able to check the book on my desktop machine at work at the same time I would read it from my Kindle...
One person found this helpful
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Frank Kane
5.0 out of 5 stars Essential reference for any 3D graphics work.
Reviewed in the United States on June 30, 2004
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!
33 people found this helpful
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Top reviews from other countries

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Frank Geppert
5.0 out of 5 stars Gut strukturiertes und umfangreiches Werk
Reviewed in Germany on July 4, 2008
Verified Purchase
Dieses Buch des Autors Eric Lengyel, der auch die sehr leistungsstarke C4 Engine programmiert, startet so, wie man eine Mathematik-Veranstaltung an der Universität präsentiert bekommt: Es beginnt aufbauend auf den Schulkenntnissen von Mathematik, beschreibt nochmal Vektoren und Matrizen und wendet dieses Wissen auch sofort an.

Einige eingestreute Annahmen und Beweise sind kurz gehalten und damit nicht immer vollständig, dadurch wird aber nicht vom tatsächlichen Inhalt abgelenkt.

Am Ende eines jeden Kapitels gibt es nochmal eine zusammenfassende Darstellung der anwendbaren Formeln, die erarbeitet wurden. Damit könnte man diese Stellen auch als ein Nachschlagewerk nutzen.

Es gibt evtl. andere Werke, die noch Einsteigerfreundlicher geschrieben sind, aber durch die langen Erklärungen weniger Wissen vermitteln. Dieses Buch ist etwas kompakter, lässt scheinbar nichts aus und bietet damit deutlich mehr Inhalt.
5 people found this helpful
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