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Development Game Development Math

Mathematics for Computer Games Development using Unity

A Beginner's Guide to Essential Mathematics, Data Structures and Algorithms used in Game Programming applied in Unity
Highest Rated
Rating: 4.7 out of 54.7 (1,137 ratings)
10,418 students
Created by Penny de Byl, Penny @Holistic3D.com
Last updated 11/2020
English
English [Auto]
30-Day Money-Back Guarantee

What you'll learn

  • How to use bitwise operations to optimise processing and storage in games.
  • Everything there is to know about vector mathematics and how to navigate in 2D and 3D space.
  • The principles and practice behind collision detection with lines, line segments and ray casting.
  • The beauty of affine transformations and the fundamentals in transforming game objects.
  • What a quaternion is and how it is used to rotate game objects.
  • How to build a mathematics library in C# from scratch.
Curated for the Udemy for Business collection

Course content

7 sections • 69 lectures • 15h 6m total length

  • Preview04:00
  • Preview01:26
  • FAQs
    00:25
  • How to Study This Course
    00:22
  • Basic Trigonometry
    02:01
  • Basic Trigonometry Quiz
    10 questions

  • Preview10:41
  • Binary Quiz
    10 questions
  • Bit Flags & Bitwise Operators
    19:02
  • Turning Bit Flags Off
    13:57
  • Bit Masks
    13:07
  • Bit Mask Challenge Solution
    14:50
  • Bit Shifting
    10:56
  • Bit Shift Quiz
    10 questions
  • Bit Toggling and Unity Specifics
    17:05
  • Bitboards
    10:31
  • Putting Bitboards Into Practice Part 1
    19:31
  • Putting Bitboards Into Practice Part 2
    17:56
  • Putting Bitboards Into Practice Part 3
    08:21
  • Bitboard Quiz
    5 questions
  • Other Bitwise Operation Hacks
    01:34

  • Cartesian Coordinates & Points
    18:28
  • Plotting Points: A Simple Data Structure
    17:08
  • Drawing Lines: Solution
    15:03
  • Graph Line Challenge
    16:05
  • Practice Locating 2D Points on a Cartesian Plane
    18:30
  • Calculating Distance Part 1
    19:42
  • Points Quiz
    10 questions
  • Calculating Distance Part 2
    21:45

  • Preview14:58
  • Introduction to Vectors Part 2
    16:13
  • Vectors Quiz
    25 questions
  • Vectors: Moving to a Point
    16:47
  • Vectors and Points Quiz
    9 questions
  • Vector Normal Form
    19:01
  • Calculating Vector Normals Quiz
    10 questions
  • Dot Product
    16:51
  • Derivation of Vector Angle Calculation
    00:27
  • Dot Product Quiz
    10 questions
  • Rotations
    09:33
  • Cross Product
    17:20
  • Cross Product Quiz
    10 questions
  • 2D LookAt Challenge
    10:20
  • Dot Cross Challenge
    19:25
  • Challenge Solutions
    06:38
  • Turn Angle and Distance Quiz
    5 questions
  • Recreate Rotate and Translate Challenge Part 1
    19:58
  • Recreate Rotate and Translate Challenge Part 2
    06:22
  • Moving from 2D to 3D
    19:43
  • 3D Points Quiz
    10 questions
  • 3D Vector Mathematics Quiz
    20 questions
  • Exploring Rotation in 3D
    13:19

  • Lines, Line Segments and Rays Part 1
    18:56
  • Lines, Line Segments and Rays Part 2
    13:37
  • Lines Quiz
    10 questions
  • Planes
    18:58
  • Planes Points Quiz
    10 questions
  • Another Line Constructor
    01:50
  • Intersection of Two Line Segments
    19:59
  • Improving Line Intersection
    14:42
  • Line Intersection Quiz
    7 questions
  • Line-Line Intersection Challenge
    11:55
  • Line-Plane Intersections
    19:58
  • Line-Plane Intersections, Projections and Reflections
    18:14
  • Plane Reflections
    13:19
  • Unity Specifics For Intersections
    19:54
  • Preview13:58
  • More Unity Specifics Part 2
    09:57

  • An Introduction to Matrices
    08:26
  • Matrix Quiz
    10 questions
  • Homogeneous Coordinates
    05:28
  • Transformations
    07:39
  • Preview19:26
  • Matrices: Data Structures and Algorithms Part 2
    14:10
  • Translation
    19:44
  • Scaling
    13:08
  • Rotation
    16:51
  • Affine Transformations
    17:21
  • Shear and Reflect Challenge
    11:28
  • Quaternions
    17:55
  • Quaternion Quiz
    5 questions
  • Programming Quaternion Rotations
    19:41
  • Extracting the Rotation Axis and Angle
    10:52
  • Quaternion Rotations
    16:41

  • Final Maths Library Code
    00:03
  • Some Final Words from Penny
    01:51
  • Where to now?
    11:16

Requirements

  • Familiarity with the Unity Game Engine
  • Confidence in programming with C#
  • Mathematics skills to high school level (basic trigonometry and algebra).

Description

Did you know computer games use mathematics to perform every single task, from rendering to animation and physics to AI?  Mathematics is everywhere.  A fundamental understanding of mathematics is critical in every occupation and nowhere is it more important than in games development. It underpins all primary operations performed by a game engine.  You can't even move a character across the screen without it.  Keen to learn more and build up your knowledge in mathematics to improve your game development skills?  Then this course is for you.

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 build your own maths library to replicate some of Unity's Vector2, Vector3, Matrix4x4 and some Mathf methods.  Throughout, we will be using the Unity Game Engine to help emphasise the mathematics concepts.

Join Dr Penny de Byl as she introduces game development mathematics using her internationally acclaimed holistic teaching style and expertise from over 25 years of teaching, research and work in games and computer graphics. Through-out the course you will follow along with hands-on workshops designed to teach you the vital mathematical techniques used in programming computer game mechanics and visuals.

During the course we will be building a game that not only uses the code we've written to move 2D and 3D objects around on the screen, but to play the game you will have to use your knowledge of points and vectors to solve puzzles that will reinforce your learning.  You will also build numerous mini projects to apply mathematical concepts and see how they work in games environments.

Learn how to program and work with:

  • Bitwise Operations, Bit Packing and Bitboards

  • 2D and 3D Space

  • Points

  • Vectors

  • Matrices

  • Mapping from one coordinate system to another

  • Positioning Objects

  • Navigation

  • Angles

  • Interpolation

  • Quaternions

What students are saying about this course:

  • Brilliant course. Might be the most helpful course I've found on Udemy so far. Penny is an amazing instructor. Even by the end of the first section learned super valuable information that I can apply to my games.

  • Early in the program but already learned enough to make the purchase price worthwhile.

  • As always, the professor delivers a great, clear course on a badly needed subject to learn. She is so knowledgeable and can impart her knowledge to her students. I recommend all her courses and her YouTube channel.

Who this course is for:

  • Beginner game development students who want to be able to understand the mathematics behind game engines.
  • Skilled programmers keen to move into 2D and 3D game development spaces.
  • Game development enthusiasts who want a deeper understanding of how mathematics is applied in games.
  • Anyone with an appreciation of mathematics who wants to investigate how it is applied in computer game environments.

Featured review

David Fu
David Fu
11 courses
5 reviews
Rating: 5.0 out of 5a year ago
Amazing course. Thank you for breaking down Quaternions into such easy to understand bits and pieces. I just have one small quibble. In section 6, module 61: Shear and Reflect Challenge, it's quite dependant on the previous few transformation so it would be nice to have the code you need as the base to attempt the challenge. Once again, you are an oasis of reputable and dependable educational content in the desert of what I can only politely refer to as "semi-qualified" content creators.

Instructors

Penny de Byl
International Award Winning Professor & Best Selling Author
Penny de Byl
  • 4.6 Instructor Rating
  • 16,680 Reviews
  • 106,722 Students
  • 22 Courses

Hi, I'm Dr Penny de Byl.  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.

I have an honours degree in computer graphics and a Ph.D. in artificial intelligence for games characters.  Over the course of my career I've won numerous awards for teaching excellence at the state, national and international levels including the Australian Learning and Teaching Council's Excellence in Teaching Award and the Unity Mobile Game Curriculum Competition. My approach to teaching computer science and related fields is project-based giving you hands-on workshops you can immediately get your teeth into.

I want you to leave my virtual classroom fully armed with a toolkit of skills for life-long learning.  I'm excited to now be focussing my efforts full-time on Udemy to bring my years of knowledge and experience to those eager to learn about technology.


Penny @Holistic3D.com
Academic, Author & Game Development Enthusiast
Penny @Holistic3D.com
  • 4.6 Instructor Rating
  • 16,680 Reviews
  • 106,722 Students
  • 22 Courses

Hi, I'm Dr Penny de Byl.  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 and SAE. 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.

I have an honours degree in computer graphics and a Ph.D. in artificial intelligence for games characters.  Over the course of my career I've won numerous awards for teaching excellence at the state, national and international levels including the Australian Learning and Teaching Council's Excellence in Teaching Award and the Unity Mobile Game Curriculum Competition. My approach to teaching computer science and related fields is project-based giving you hands-on workshops you can immediately get your teeth into.

I want you to leave my virtual classroom fully armed with a toolkit of skills for life-long learning.  I'm excited to now be focussing my efforts full-time on Udemy to bring my years of knowledge and experience to those eager to learn about technology.

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