Essential Mathematics for Games and Interactive Applications provides the expert insights on the mathematics essential for 3D game and interactive applications development. Based on the authors' well-received tutorial from the Game Developers Conference (GDC), it emphasizes the critical role of mathematics in 3D programming. It guides you through the proper techniques for animating, simulating, and rendering scenes while delving into the mathematical principles that underlie these processes.
Building on their tutorials, this book provides the fundamental mathematics required for advanced 3D graphics and interactive physical simulations. It starts with numeric representation, linear algebra, and matrix manipulation, then broadens to include topics like texture filtering, interpolation, animation, randomness, and basic game physics. This resource emphasizes the critical aspects of 3D game development relevant to programmers and offers optimization tips throughout.
In addition to fundamental mathematical and geometric representations along with algorithms that form the backbone of any game engine, this book also covers every phase of the rendering pipeline, detailing how to represent, transform, view, and animate geometry. The authors also delve into visual elements, focusing on color representation, computation, and application. Other topics include randomness, geometric entity intersections, and physical simulations.
The third edition of this book features completely revised chapters on lighting and graphics, along with comprehensive updates across all content to enhance clarity and accessibility. It has been thoroughly updated to correct previous errors and enhance content coherence. It reflects the growing prominence of shader graphics pipelines, including DirectX 11, OpenGL ES (GLES), and the OpenGL core profile. Additionally, it provides updated information on real-time graphics with an emphasis on more realistic materials and lighting techniques.
In short, this book equips you with a conceptual framework for the mathematics required in 3D game creation, while also demonstrating its practical application in games and graphics. It provides not just the theoretical foundations of mathematics, but also numerous examples illustrating how these concepts influence game aesthetics and mechanics.
BTW, an accompanying website features a variety of source code, supporting libraries, and interactive demonstrations that exemplify the concepts discussed in this book, allowing you to engage with animation and simulation applications. Moreover, this website also offers 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
Book Example Codes
Download URLs
| Format | Download | Size |
| Essential Mathematics for Games and Interactive Applications, Third Edition | ||
 |
12.4 MB | |