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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

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Product type Paperback
Published in Mar 2017
Publisher Packt
ISBN-13 9781787123663
Length 480 pages
Edition 1st Edition
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Author (1):
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Gabor Szauer Gabor Szauer
Author Profile Icon Gabor Szauer
Gabor Szauer
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Toc

Table of Contents (19) Chapters Close

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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