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
About the Author
About the Reviewer
Customer Feedback

Determinant of a 3x3 matrix

We can find the determinant of any matrix through Laplace Expansion. We will be using this method to find the determinant of 3 X 3 and higher order matrices. We also used this method to find the determinant of 2 X 2 matrices; we just expanded the method by hand for that function to avoid looping:

To follow the formula, we loop through the first row of the matrix and multiply each element with the respective element of the cofactor matrix. Then, we sum up the result of each multiplication. The resulting sum is the determinant of the matrix.

Using the first row is an arbitrary choice. You can do this equation on any row of the matrix and get the same result.

Getting ready

In order to implement this in code, first find the cofactor of the input matrix. Once we have a cofactor matrix, sum the result of looping through the first row and multiply each element by the same element in the cofactor matrix.

How to do it…

Follow these steps to implement a function which returns...