#### 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

## Manifold for spheres

In order to resolve collisions between objects that have volume, we need to learn more about the nature of the mentioned collisions. This additional information is known as a Collision Manifold. A typical collision manifold usually contains the following things:

• The collision normal

• The penetration distance

• A set of contact points

Additionally, a manifold might also contain the following things:

• Pointers to the colliding objects

• The relative velocity of the collision

• Nature of the collision (no collision, colliding, penetrating)

Let's assume that we have two colliding objects, A and B. The collision normal of the manifold between the two, tells us what direction each object needs to move in to resolve the collision. If A moves in the negative direction of the normal and B moves in the positive direction, the objects will no longer intersect.

The penetration distance of the manifold is half of the total length of penetration. Each object needs to move by the penetration distance...