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This completely updated second edition illustrates the mathematical concepts that a game programmer would need to develop a professional-quality 3D engine. Although the book is geared toward applications in game development, many of the topics appeal to general interests in 3D graphics. 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 game 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.

Key Features

* Includes four new chapters: the graphics pipeline, the stencil shadow rendering technique, curves & surfaces, and numerical methods

* Concentrates on key mathematical topics for programming 3D game engines

* Discusses applications in the context of the OpenGL architecture due to its cross-platform nature and long-standing industry acceptance. Sample rendering code is presented using ARB vertex programs and fragment programs

* Selected topics include quaternions, homogeneous coordinates, ray tracing, bump mapping, portal systems, polygonal techniques, shadows, and physics

* Includes exercise sets for use as a textbook

New to This Edition

The following are selected revisions in the second edition:

* A new preliminary chapter that provides a review of the 3D rendering pipeline

* A new chapter containing an advanced discussion of the stencil shadow rendering technique

* A new chapter covering various numerical methods pertinent to 3D graphics programming, including numerical solutions to linear systems, numerical eigenvalue determination, and numerical integration

* A new chapter covering curves and surfaces, including Bézier curves and B-splines

* New discussions of texture filtering, mipmapping, and infinite projection matrices

* Updated lighting method implementations and collision detection techniques

* Additional exercises in all chapters

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