Mathematics for Game Developers

Course Preview

A fundamental understanding of mathematics is critical in every occupation and nowhere is it more important than in games development. In this course you will build your own C# classes to work with the geometrical constructs of 2D and 3D space that will develop your understanding of positioning and moving game objects. In short you will be build your own maths library to replicate Unity’s Vector2, Vector3 and Matrix4x4 and some Mathf methods.

Learn how to program and work with: 2D and 3D Space, Points, Vectors, Matrices, Mapping from one coordinate system to another, Positioning Objects, Navigation ,Angles and Interpolation.

Course Information

Estimated Time: 15 Hours, 69 Lectures

Difficulty: Beginner

Categories:

Course Instructor

Penny de Byl Penny de Byl Author

I’m a full stack developer of most things computer sciency and academic with a true passion for teaching.  I’ve been teaching others about games development, programming, computer graphics, animation and web design for over 25 years in universities in Australia and Europe at the full professor level. I’ve also consulted for Unity, SAE, the Australian Institute of Entertainment and Wikitude. My best selling textbooks including Holistic Game Development with Unity are used in over 100 institutions world-wide. My graduates work at companies like Apple, Ubisoft, LinkedIn and Deloitte Digital.

 

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Introduction and Welcome

Maths Welcome
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Join the H3D Student Community
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FAQs
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How to Study This Course
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Basic Trigonometry
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Basic Trigonometry Quiz
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Bitwise Operations

Bits, Bytes and Binary
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Binary Quiz
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Bit Flags & Bitwise Operators
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Turning Bit Flags Off
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Bit Masks
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Bit Mask Challenge Solution
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Bit Shifting
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Bit Shift Quiz
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Bit Toggling and Unity Specifics
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Bitboards
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Putting Bitboards Into Practice Part 1
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Putting Bitboards Into Practice Part 2
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Putting Bitboards Into Practice Part 3
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Bitboard Quiz
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Bitwise Operator Hacks
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Location

Cartesian Coordinates & Points
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Plotting Points, A Simple Data Structure
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Drawing Lines: Solution
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Graph Lines Challenge
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Practice Locating 2D Points on a Cartesian plane
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Calculating Distance Part 1
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Points Quiz
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Calculating Distance Part 2
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Vectors

Introduction To Vectors Part 1
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Introduction To Vectors Part 2
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Vectors Quiz
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Vectors Moving to a Point
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Vectors and Points Quiz
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Vector Normal Form
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Calculating Vector Normals Quiz
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Dot Product
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Derivation of Vector Angle Calculation
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Dot Product Quiz
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Rotations
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Cross Product
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Cross Product Quiz
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2D LookAt Challenge
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Dot Cross Challenge
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Challenge Solutions
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Turn Angle and Distance Quiz
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Recreate Rotate and Translate Challenge Part 1
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Recreate Rotate and Translate Challenge Part 2
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Moving from 2D to 3D
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3D Points Quiz
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3D Vector Mathmatics Quiz
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Exploring Rotation in 3D
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Intersections

Lines, Line Segments and Rays Part 1
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Lines, Line Segments and Rays Part 2
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Lines Quiz
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Planes
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Planes Points Quiz
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Another Line Constructor
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Intersection of Two Line Segments
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Improving Line Intersection
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Line Intersection Quiz
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Line-Line Intersection Challenge
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Line-Plane Intersections
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Line-Plane Intersections, Projections and Reflections
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Plane Reflections
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Unity specifics for Intersections
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More Unity Specifics Part 1
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More Unity Specifics Part 2
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Affine Transformations

An Introduction to Matrices
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Matrix Quiz
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Homogeneous Coordinates
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Transformations
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Matrices: Data Structures and Algorithms Part 1
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Matrices: Data Structures and Algorithms Part 2
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Translation
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Scaling
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Rotation
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Affine Transformations
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Shear and Reflect Challenge
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Quaternions
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Quaternion Quiz
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Programming Quaternion Rotations
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Extracting the Rotation Axis and Angle
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Rotating With Quaternions
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Final Words

Final Version of Maths Scripts
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Final Words Maths
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