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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

Product type Paperback

Published in Mar 2017

Publisher Packt

ISBN-13 9781787123663

Length 480 pages

Edition 1st Edition

Languages

C++

Tools

Unity

Concepts

Game Design

Author (1):

Gabor Szauer

View More author details

Table of Contents (19) Chapters

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

Multiplication

Like a vector, there are many ways to multiply a matrix. In this chapter we will cover multiplying matrices by a scalar or by another matrix. Scalar multiplication is component wise. Given a matrix M and a scalar s, scalar multiplication is defined as follows:

We can also multiply a matrix by another matrix. Two matrices, A and B, can be multiplied together only if the number of columns in A matches the number of rows in B. That is, two matrices can only be multiplied together if their inner dimensions match.

When multiplying two matrices together, the dimension of the resulting matrix will match the outer dimensions of the matrices being multiplied. If A is an matrix and B is an matrix, the product of AB will be an matrix. We can find each element of the matrix AB with the following formula:

This operation concatenates the transformations represented by the two matrices into one matrix. Matrix multiplication is not cumulative. . However, matrix multiplication is associative...

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Authors (1)

Gabor Szauer

Gabor Szauer

Gabor Szauer has been making games since 2010. He graduated from Full Sail University in 2010 with a bachelor's degree in game development. Gabor maintains an active Twitter presence, and maintains a programming-oriented game development blog. Gabor's previously published books are Game Physics Programming Cookbook and Lua Quick Start Guide, both published by Packt.

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