- Hardcover: 624 pages
- Publisher: Cengage Learning PTR; 3rd edition (June 2, 2011)
- Language: English
- ISBN-10: 1435458869
- ISBN-13: 978-1435458864
- Product Dimensions: 7.6 x 1.7 x 9.4 inches
- Shipping Weight: 4 pounds
- Average Customer Review: 56 customer reviews
- Amazon Best Sellers Rank: #544,317 in Books (See Top 100 in Books)
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Mathematics for 3D Game Programming and Computer Graphics, Third Edition 3rd Edition
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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.
Top customer reviews
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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.
I also want to give the book a huge plus for showing how to use Quaternions for vector rotation in the chapter(4) on vector transforms. If you want to avoid the evil "gimbal lock event" from jamming your model's rotation, this is the best way to program your model to turn.
There are 16 chapters and 2 appendices that can give you a solid understanding of how to be a great computer modeler. In 530 pages you have everything you need to make your birds look real and fly in flocks, make your rail car rise up and accelerate down the track, or animate a rock warrior in battle and make him explode or dissolve convincingly.
To make use of the mathematics contained here you will probably need a GPU to run your animations and you will need to program in OpenCL or CUDA to get the animations running quickly in DirectX or OpenGL .
This is about two college semesters of study contained between the covers, but if you want to be great you have to get serious about knowing your craft.
-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.
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