Starting on a fairly basic level in areas such as vector geometry and linear algebra, and then developed into more advanced topics in 3D game programming such as illumination and visibility determination. Key Features * Includes four new chapters: the graphics pipeline, 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 the nature of cross-platform and the old industrial acceptance. Example rendering code is presented using the program ARB vertex and fragment programs The selected topics * including Quaternions, homogeneous coordinates, ray tracing, bump mapping, portal systems, polygonal techniques, shadows, and physics * Includes set of exercises to be used as a textbook New to This Edition Here is a revision selected in the second edition: * A new early chapter gives a review of the 3D rendering pipeline * A new chapter contains further discussion of the stencil shadow rendering technique * A new chapter covering various numerical methods related to 3D graphics programming, including numerical solutions for linear systems, numerical eigenvalue determination, and numerical integration * A new chapter that includes curves and surfaces, including curve B? Er and B-splines * New discussions on texture filtering, mipmapping, and an infinite projection matrix * Updated lighting implementation of collision detection methods and techniques * Additional exercises in all chapters