#### 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!
Game Physics Cookbook
Credits
Acknowledgements
Acknowledgements
www.PacktPub.com
Customer Feedback
Preface
Free Chapter
Vectors
Matrices
Matrix Transformations
2D Primitive Shapes
2D Collisions
2D Optimizations
3D Primitive Shapes
3D Point Tests
3D Shape Intersections
3D Line Intersections
Triangles and Meshes
Models and Scenes
Camera and Frustum
Constraint Solving
Manifolds and Impulses
Springs and Joints
Index

## Robustness of the Separating Axis Theorem

Currently, there is a flaw in our SAT implementation. You can see this flaw in action by testing two triangles that lay on the same plane. Let's assume that we run the SAT test with the following triangles:

• T1: (-2, -1, 0), (-3, 0, 0), (-1, 0, 0)

• T2: (2, 1, 0), (3, 0, 0), (1, 0, 0)

These two triangles will report a false positive. Visualizing them, they look like this:

Why does this happen? When we compute the cross products of the edges of the triangles, the cross product of parallel vectors is the zero vector. When edges or face normals are parallel, we end up with an invalid axis to test.

We are going to implement a new function, `SatCrossEdge`. This function will detect if the cross product of two edges is 0. If that is the case, the function will use an axis perpendicular to the first edge to try to get a new test axis. If no such test axis exists, then the two edges being tested must be on a line. If the edges are on a line, we return...