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

Angular Impulse

Now that we have orientation, collisions require both a linear and angular response. This means we need an equation that gives us the impulse magnitude in terms of both linear and angular components.

From the previous section, Linear Impulse, we already know the linear impulse of the collision:

We need to find the angular component of this impulse. In the last section, Angular Velocity, we covered that the velocity of a point, P, at R distance away from the center of mass is given by the following equation:

We can find the total velocity (linear plus angular) by adding the rotational velocity to the Linear Velocity of the rigidbody at the center of mass. We also need to find the torque from the point of impact and collision normal divided by the inertia tensor. Knowing this, we can find the final equation for j:

We must also update the formula for tangential impulse to apply friction. To do so, we replace all instances of the collision normal n with the tangent vector t: