The Ultimate Math Guide for 3D Game Development

This book provides the essential math needed to describe, simulate, and render a 3D world and includes: Fundamentals of coordinate spaces, vectors, and matrices are covered in the first several chapters.This material falls properly in the realm of linear algebra, but it is integral for setting the stage for actually creating games. It is also one of the main driving factors called out by reviewers of the previous book as a must have. Systems of equations are not central to game development but rather the geometric interpretation of linear algebra operations. Orientation in three dimensions is a topic that is critical for 3D simulations but not covered in any depth in traditional books, perhaps with the exception of advanced dynamics. This book devotes an entire chapter to this subject, covering the major methods for describing orientation and rate of rotation.The quality of the coverage on this important topic is a unique feature of the book. Graphics cannot be left out of any book about game development. Fundamentals of graphics are covered: the transformation pipeline, the Blinn-Phong lighting model, texture mapping, etc. Since the entire book itself not as a book on graphics, but is a supplement to those sources, focus is particularly on those mathematical elements that, from experience, tend to cause beginners the most confusion or are not clarified sufficiently, such as field of view and aspect ratio, thmapping. Also offered are some context about how real-time hacks like the ubiquitous Blinn-Phong model fit into the wider world of computer graphics. A toolbox of geometric primitives and tests completes the coverage of the fundamentals. These two chapters establish some fundamentals such as barycentric coordinates, and also serve as a useful reference. Introductions to calculus and dynamics are packed into two chapters. Responding to reviewers of the previous book, we have included a big-picture introduction to these subjects. The book covers the most essential elements, especially geared towards what is useful in game development dynamics. The coverage of mechanics also describes how rigid body simulation is done with a computer rendering equation, and bump. Parametric curves are highly useful in rendering and simulation, but the only what is absolutely necessary in order to grasp the most important concepts.