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Game Physics Cookbook

You're reading from Game Physics Cookbook Discover over 100 easy-to-follow recipes to help you implement efficient game physics and collision detection in your games

Product type Paperback

Published in Mar 2017

Publisher Packt

ISBN-13 9781787123663

Length 480 pages

Edition 1st Edition

Languages

C++

Tools

Unity

Concepts

Game Design

Author (1):

Gabor Szauer

View More author details

Table of Contents (19) Chapters

Preface

1. Vectors FREE CHAPTER

2. Matrices

3. Matrix Transformations

4. 2D Primitive Shapes

5. 2D Collisions

6. 2D Optimizations

7. 3D Primitive Shapes

8. 3D Point Tests

9. 3D Shape Intersections

10. 3D Line Intersections

11. Triangles and Meshes

12. Models and Scenes

13. Camera and Frustum

14. Constraint Solving

15. Manifolds and Impulses

16. Springs and Joints

A. Advanced Topics

Index

Rotation matrices

Rotation about any axis is a linear transformation. Any linear transformation can be expressed using a matrix. To represent a three-dimensional rotation we need a 3 X 3 or a 4 X 4 matrix. In this section, we are going to derive a matrix that represents rotation around the Z-Axis by some angle theta. This matrix will be used to transform a vector into a rotated version of that vector, .The new vector will be the result of rotating the original vector around the Z-Axis. After we derive the matrix which rotates around the Z-Axis, rotation matrices for the X-Axis and Y-Axis will be discussed as well.

is the result of rotation vector by some angle around the Z-Axis. We can represent this rotation in terms of matrix Z; this can be expressed with the following formula:

The definition of this rotation matrix, Z, is given. We will go into detail about how to derive this matrix in the How it works section:

To use the rotation matrix, simply plug in the numbers for theta and evaluate...

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Authors (1)

Gabor Szauer

Gabor Szauer

Gabor Szauer has been making games since 2010. He graduated from Full Sail University in 2010 with a bachelor's degree in game development. Gabor maintains an active Twitter presence, and maintains a programming-oriented game development blog. Gabor's previously published books are Game Physics Programming Cookbook and Lua Quick Start Guide, both published by Packt.

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