Book Image

Game Physics Cookbook

By : Gabor Szauer
Book Image

Game Physics Cookbook

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 (27 chapters)
Game Physics Cookbook
Credits
About the Author
Acknowledgements
About the Reviewer
Acknowledgements
www.PacktPub.com
Customer Feedback
Preface
Index

Operations on a 4x4 matrix


We know how to find the minor, cofactor, and determinant of 2 X 2 and 3 X 3 matrices. In this section, we're going to implement those functions for a 4 X 4 matrix. We begin with the matrix of minors. The process for finding the minor of element i, j in a 4 X 4 matrix is the same as it was for a 3 X 3 matrix. We eliminate row i and column j of the matrix, the determinant of the resulting 3 X 3 matrix is the minor for element i, j.

Next, we find the cofactor. To find the cofactor we just follow the same formula we did for the 3 X 3 matrix:

To get the cofactor of element i, j, we take the minor of that element and multiply it by . Finally, we have to find the determinant of the matrix. Again, we do this by following the same formula we used for the 3 X 3 matrix:

To find the determinant, we loop through any row of the matrix and sum up the result of multiplying each of the elements in the row by their respective cofactor. You only need to loop through one row, and which...