Mathematics for 3D Game Programming and Computer Graphics [Hardcover]

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 (www.mathfor3dgameprogramming.com) 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.

This book is just what I have been looking for: something that presents and cogently explains the math that is most useful for implementing 2d and 3d computer graphics. If the Kindle edition did not have the problems it has, I would give it 5 stars. However, it gets a poor rating for two reasons. One, the diagrams are too small! Other Kindle documents allow the reader to scale images, but not this one. Two, and this is just INEXCUSABLE: The Kindle edition, but not the print edition, has errors that make the equations and proofs worthless. I can't quote examples exactly because special characters don't show up properly, but here's a description of three examples:

1. print p. 13, Theorem 2.2
Kindle uses improper notation in (c), and an ill-formed expression in (d).

2. print p. 14, fig 2.1: "The triangle inequality states that [equation]"
Kindle reverses the inequality in the equation.

3. print p. 15,
"Definition 2.3. The dot product of two n-dimensional vectors P and Q, written as ..."
Kindle leaves out a crucial character in the "written as" formula.

The graphics alone make this a quality book. I use it in conjunction with my University level programming book to be one step ahead of the Professor.