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Название: Essential Mathematics for Games and Interactive Applications, Second Edition: A Programmer's Guide
Авторы: Verth J., Bishop L.
As a novice game programming hobbyist, I've written applications using the DirectX SDK to render 3D visuals without really understanding what's happening behind the scenes. Applying a transformation matrix to a model and illuminating it with a spotlight just seemed to be magic beyond my understanding. This book has delivered enough information to get a good foundation in the understanding of the mathematics involved to bring points and images into a visual representation to the screen while going even further to discuss collision detection, interpolation, and rigid body dynamics.
If the reader wanted to develop a 3D application on a platform with no native support or SDK, there's enough material in this book to give the reader a core background to develop a software solution. Even though portions of the graphics pipeline are automatically handled by an SDK or hardware, the concepts are presented so the reader is taken every step of the way.
The reader should know algebra (of course), trigonometry, and calculus if they want to get something out of it. A history of linear algebra also helps, but it isn't necessary since the chapter on matrices that goes over the essential operations. The later chapters on collision detection and physics start getting more math-heavy. Having previously read a couple other books in the Morgan Kaufmann series: Real Time Collision Detection and Game Physics, I was expecting the discussions to be very similar; however, the reader would only get a basic understanding of the topics and would greatly benefit from continuing their reading into the aforementioned books.
Overall, I enjoyed this book very much and it gets my approval for anyone wanting to get into game programming and 3D simulation. The author also provides many resources and accompanies the book with a CD of precompiled visual examples that should better solidify the user's understanding. As previously mentioned, Real Time Collision Detection and Game Physics make fantastic supplements to this book.