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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.
- Sales Rank: #100923 in Books
- Brand: Brand: Course Technology PTR
- Published on: 2011-06-02
- Original language: English
- Number of items: 1
- Dimensions: 9.00" h x 7.00" w x 1.50" l, 4.03 pounds
- Binding: Hardcover
- 576 pages
- Used Book in Good Condition
Review
Preface. 1. The Rendering Pipeline. 2. Vectors. 3. Matrices. 4. Transforms. 5. 3D Engine Geometry. 6. Ray Tracing. 7. Illumination. 8. Visibility Determination. 9. Collision Detection. 10. Polygonal Techniques. 11. Shadows. 12. Linear Physics. 13. Rotational Physics. 14. Fluid Simulation. 15. Numerical Methods. 16. Curves and Surfaces. Appendix A: Complex Numbers. Appendix B: Trigonometry Reference. Appendix C: Coordinate Systems. Appendix D: Taylor Series. Appendix E: Answers to Exercises.
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.
Most helpful customer reviews
33 of 33 people found the following review helpful.
The definitive guide for 3D math
By Patrick Rouse
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.
30 of 31 people found the following review helpful.
Essential reference for any 3D graphics work.
By Frank Kane
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!
47 of 55 people found the following review helpful.
Math majors rejoice
By GameMaker
To be honest, while I find this book to be a decent reference, I find it to be pretty inaccessible in terms of sitting down and reading through it in an attempt to learn the concepts. As a non-math major (I'm actually an engineer and software developer) these math concepts are by no means beyond me. But rather than simply being presented with equation after equation, proof after proof, what I find a lot more valuable is more discussion on the usage of these equations. Specifically I'd like to see examples, diagrams, and code, and there is precious little of any of that in this book.
In other words, this book is very much like what you expect to find in a very dry upper devision college math text for the consumption of math majors who are used to such things. But for a non math major just trying to make use of these concepts in order to get the job done and make games? eh, not so much.
Still, I do think this book is useful as a reference when I want to look up an equation as there are a ton of them crammed into this book, but for me, I just don't find this book to be very good as a learning tool.
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