Book Image

Game Physics Cookbook

By : Gabor Szauer
Book Image

Game Physics Cookbook

By: Gabor Szauer

Overview of this book

Physics is really important for game programmers who want to add realism and functionality to their games. Collision detection in particular is a problem that affects all game developers, regardless of the platform, engine, or toolkit they use. This book will teach you the concepts and formulas behind collision detection. You will also be taught how to build a simple physics engine, where Rigid Body physics is the main focus, and learn about intersection algorithms for primitive shapes. You’ll begin by building a strong foundation in mathematics that will be used throughout the book. We’ll guide you through implementing 2D and 3D primitives and show you how to perform effective collision tests for them. We then pivot to one of the harder areas of game development—collision detection and resolution. Further on, you will learn what a Physics engine is, how to set up a game window, and how to implement rendering. We’ll explore advanced physics topics such as constraint solving. You’ll also find out how to implement a rudimentary physics engine, which you can use to build an Angry Birds type of game or a more advanced game. By the end of the book, you will have implemented all primitive and some advanced collision tests, and you will be able to read on geometry and linear Algebra formulas to take forward to your own games!
Table of Contents (27 chapters)
Game Physics Cookbook
Credits
About the Author
Acknowledgements
About the Reviewer
Acknowledgements
www.PacktPub.com
Customer Feedback
Preface
Index

Separating Axis Theorem


The Separating Axis Theorem (SAT) can be used to determine if two arbitrary shapes intersect. Both shapes being tested must be convex. The SAT works by looking for at least one axis of separation between two objects. If no axis of separation exists, the objects are colliding. An axis of separation can be represented by any arbitrary plane:

The first step in the SAT is to find an axis that we want to test for separation. In the example image above, the two oriented bounding boxes can havewo possible axes of separation. The X axis (1, 0) or the Y axis (0, 1) can separate these boxes.

Once we have figured out the axis of potential separation, we project both shapes onto the axis being tested. This projection results in a set of points. The minimum and maximum points of this projection create an Interval. An interval is like a line; in the above image you can see four intervals, one on the X axis for both objects and one on the Y axis for both objects:

Once we know the interval...