Essential Mathematics for Games and Interactive Applications, 3rd Edition

Expert Guidance on the Math Needed for 3D Game Programming
Developed from the authors’ popular Game Developers Conference (GDC) tutorial, Essential Mathematics for Games and Interactive Applications, Third Edition illustrates the importance of mathematics in 3D programming. It shows you how to properly animate, simulate, and render scenes and discusses the mathematics behind the processes.

New to the Third Edition
Completely revised to fix errors and make the content flow better, this third edition reflects the increased use of shader graphics pipelines, such as in DirectX 11, OpenGL ES (GLES), and the OpenGL Core Profile. It also updates the material on real-time graphics with coverage of more realistic materials and lighting.

The Foundation for Successful 3D Programming
The book covers the low-level mathematical and geometric representations and algorithms that are the core of any game engine. It also explores all the stages of the rendering pipeline. The authors explain how to represent, transform, view, and animate geometry. They then focus on visual matters, specifically the representation, computation, and use of color. They also address randomness, intersecting geometric entities, and physical simulation.

An Introduction to Creating Real and Active Virtual Worlds
This updated book provides you with a conceptual understanding of the mathematics needed to create 3D games as well as a practical understanding of how these mathematical bases actually apply to games and graphics. It not only includes the theoretical mathematical background but also incorporates many examples of how the concepts are used to affect how a game looks and plays.

Web Resource
A supplementary website contains a collection of source code, supporting libraries, and interactive demonstrations that illustrate the concepts and enable you to experiment with animation and simulation applications. The site also includes slides and notes from the authors’ GDC tutorials.

Table of Contents

Chapter 1 Representing Real Numbers
Chapter 2 Vectors and Points
Chapter 3 Linear Transformations and Matrices
Chapter 4 Affine Transformations
Chapter 5 Orientation Representation
Chapter 6 Interpolation
Chapter 7 Viewing and Projection
Chapter 8 Geometry and Programmable Shading
Chapter 9 Lighting
Chapter 10 Rasterization
Chapter 11 Random Numbers
Chapter 12 Intersection Testing
Chapter 13 Rigid- Body Dynamics