Mathematics for 3D Game Programming and Computer Graphics, Third Edition 3rd Edition
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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.
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.
Top international reviews
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.
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.
Mi sembra più adatto come testo universitario di approfondimento che come manuale di auto-apprendimento.
detail knowledge of polynomials, calculus.
It doesn't gives complete justification of cubic,quartic polynomials as well as intersection method are not explained in detail difficult for beginner to understand how formula derived without proper justification.