#### 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

## Point and plane

We have seen the plane equation before; a point is on a plane if the result of the plane equation is 0. To find the point on the plane closest to a test point, we must project the test point onto the normal of the plane. We then subtract this new vector from the test point to get the closest point:

We are going to implement two functions. The first function will test whether a point is on the surface of a plane using the plane equation. The second function will find the point on a plane closest to a given test point.

### How to do it…

Perform the following steps to implement point tests for a plane:

1. Declare `PointOnPlane` and `ClosestPoint` in `Geometry3D.h`:

```bool PointOnPlane(const Point& point, const Plane& plane);
Point ClosestPoint(const Plane& plane, const Point& point);```
2. Implement `PointOnPlane` in `Geometry3D.cpp`:

```bool PointOnPlane(const Point& point, const Plane& plane) {
float dot = Dot(point, plane.normal);
// To make this more robust, use...```