Mathematics of Game Development. A Collection of Applied Lessons

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Credits
Introduction
1. Unity Fundamentals
	Why Unity?
	Downloading and Installing Unity
	The Unity Interface
	GameObjects and Components
	Primitive Shapes
	Navigating the Scene and Manipulating GameObjects
	Saving
	Activity: Falling Balls and Animal House
	Challenges
2. Programming Fundamentals
	Why Programming?
	Purpose of Writing Code
	Editors
	Visual Studio
	Programming Languages and Syntax
	C#
	Create a C# Script
	Edit a C# Script
	Run a C# Script
	Variables and Data Types
	Conditional Statements and Boolean Operators
	Variable Scope
	Mathematical Operators
	Overloading Operators
	Access Modifiers
	Property Visibility
	Alternative Solutions
	Functions
	Activity: Bouncy Box
	Challenges
	Summary
3. Position of Game Objects in 2D | Points on a Coordinate Plane
	Introduction
	The Math
	Positioning Objects in Games
	Pivot Points
	Activity: Platformer
	Challenges
	Achievements
	Exercises
4. Distance | Right Triangles, Pythagorean Theorem, and the Distance Formula
	Introduction
	Activity: Bombs Away
	Challenges
	Achievements
	Exercises
5. Field of View | Pi and Finding Angles Using SIN, COS, TAN
	Introduction
	The Math
	Activity: Avoid Detection
	Challenges
	Achievements
	Exercises
6. Simulating Physics in a Virtual World | Matrices and Vectors
	Introduction
	The Math
	Rules for Matrix Mathematics
		Operations with Position Vectors
	Activity: Critters
	Challenges
	Achievements
	Exercises
7. Sinusoidal Functions | Sine and Cosine
	Introduction
	The Math
		Special Right Triangles
		Rethinking Sine and Cosine
		Horizontal and Vertical Projections
		Values of Sine and Cosine
		Sinusoidal Functions
	Activity: Headbob
	Challenges
	Achievements
	Exercises
8. Directionality | Dot Product
	Introduction
	The Math
		Multiplying Matrices
		Multiplying Vectors (Dot Product)
	Activity: Speed Racer
	Challenges
	Achievements
	Exercises
9. Orthogonal Directionality | Cross Product
	Introduction
	The Math
		ijk Notation
		Multiplying Vectors (Cross Product)
		Using Cross Product to Find Area
		The Normal
	Achievements
	Exercises
10. Reflections | Vector Projection and Reflection
	Introduction
	The Math
	Activity: The Octagon
	Challenges
	Achievements
	Exercises
Conclusion
Answers to Exercises
Index