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Game Physics Cookbook

Game Physics Cookbook

By : Gabor Szauer
4.3 (4)
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Game Physics Cookbook

Game Physics Cookbook

4.3 (4)
By: Gabor Szauer

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 (19 chapters)
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18
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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