#### 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
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
Advanced Topics
Index

## Plane

A plane is a flat surface that extents infinitely in all directions. A plane has a direction, which is expressed differently based on how we represent a plane. There are three common ways to represent a plane:

• Three points (not on a straight line)

• A normal and a point on the plane

• A normal and the distance from origin

For our plane implementation we will use the third representation, a normal, and a distance from origin:

Assuming the normal of the plane is of unit length, we can use the following formula to find the distance of any point (X) from origin along the normal of the plane:

```Dot(X, plane.Normal) = PointDistance
// Not plane distance from origin! ^```

By subtracting the distance of the plane from the distance of the point, we can check if a point is on the plane:

```Dot(X, plane.Normal) - plane.Distance = 0; // Plane Equation
// ^ Will always equal 0 if point is on the plane```

This is called the plane equation. The preceding equation will return the following:

• `0` if the point is on the plane...