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2D Collision Detection for
Game Programmers
Focus on Point Collisions
By Steven Vaerten

2D Collision Detection for Game Programmers:
Focus on Point Collisions.
Copyright © 2018 (MMXVIII) by Steven Vaerten, all rights reserved.
No part of this book may be reproduced, stored in a retrieval system, or transmitted by
any means, electronic, mechanical, photocopying, recording, or otherwise, without out
written permission from the author. No patent liability is assumed with respect to the
use of the information contained herein. Although every precaution has been taken in
the preparation of this book, the publisher and the author assume no responsibility for
errors or omissions, and no liability is assumed for damages resulting from the use of
the information contained herein.
ISBN: 9781980354970
First printing: March 2018.
Disclaimer
Every effort has been made to make this book as complete and as accurate as possible,
but no warranty or fitness is implied. The information provided is on an “as is” basis.
The author and the publisher shall have neither liability nor responsibility to any
person or entity with respect to any loss or damages arising from the information
contained in this book.
Corrections and Comments
Corrections and comments may be sent to the author, Steven Vaerten, at
CollisionDetectionAlgorithms@gmail.com. Please clearly define the book title, section
number, and line item in question with a description of the comment or correction.

To Cayce Williams
Thank you for the motivation
that made this series possible

Table of Contents
1 INTRODUCTION
1.1 Who Should Read This Book
1.2 Why I Wrote This Book
1.3 About the Author
1.4 Build A Sandbox
1.5 Efficiency
1.6 Designing Algorithms
2 MATHEMATICS FOR COLLISION DETECTION
2.1 Vectors
2.1.1 Vector Magnitude (Length)
2.1.2 Unit Vectors
2.1.3 Normal (Perpendicular) Vectors
2.1.4 Vector Addition
2.1.5 Vector Subtraction
2.1.6 Vector Negation
2.1.7 Scalar Multiplication
2.1.8 Scalar Division
2.1.9 Dot (Inner) Product
2.1.10 Perpendicular (Cross) Product
2.1.11 Projection
2.1.12 Vector Slope
2.1.13 Creating a Vector from an Angle
2.1.14 Angle of a Vector
2.1.15 The Angle Between Vectors
2.1.16 Rotating a Vector
2.1.17 Classifying a Vector
2.2 Algebraic Formulas
2.2.1 Distance Formula
2.2.2 The Quadratic Formula
3 COLLISION OBJECTS
3.1 Points
3.2 Lines
3.3 Horizontal Lines (HLine)
3.4 Vertical Lines (VLine)
3.5 Rays
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