MaThematics For Computer Games Development Using Unity

Mathematics For Computer Games Development Using Unity
Last updated 8/2022
MP4 | Video: h264, 1280×720 | Audio: AAC, 44.1 KHz

A Beginner’s Guide to Essential Mathematics, Data Structures and Algorithms used in Game Programming applied in Unity

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

Section 1: Introduction and Welcome

Lecture 1 Welcome

Lecture 2 Join the H3D Student Community

Lecture 3 Contacting H3D

Lecture 4 FAQs

Lecture 5 How to Study This Course

Lecture 6 Basic Trigonometry

Section 2: Bitwise Operations

Lecture 7 Bits, Bytes and Binary

Lecture 8 Bit Flags & Bitwise Operators

Lecture 9 Turning Bit Flags Off

Lecture 10 Bit Masks

Lecture 11 Bit Mask Challenge Solution

Lecture 12 Bit Shifting

Lecture 13 Bit Toggling and Unity Specifics

Lecture 14 Bitboards

Lecture 18 Other Bitwise Operation Hacks

Section 3: Location

Lecture 20 Plotting Points: A Simple Data Structure

Lecture 21 Drawing Lines: Solution

Lecture 22 Graph Line Challenge

Section 4: Vectors

Lecture 28 Vectors: Moving to a Point

Lecture 29 Vector Normal Form

Lecture 30 Dot Product

Lecture 31 Derivation of Vector Angle Calculation

Lecture 32 Rotations

Lecture 33 Cross Product

Lecture 34 2D LookAt Challenge

Lecture 35 Dot Cross Challenge

Lecture 36 Challenge Solutions

Lecture 39 Moving from 2D to 3D

Lecture 40 Exploring Rotation in 3D

Section 5: Intersections

Lecture 43 Planes

Lecture 44 Another Line Constructor

Lecture 45 Intersection of Two Line Segments

Lecture 46 Improving Line Intersection

Lecture 47 Line-Line Intersection Challenge

Lecture 48 Line-Plane Intersections

Lecture 49 Line-Plane Intersections, Projections and Reflections

Lecture 50 Plane Reflections

Lecture 51 Unity Specifics For Intersections

Section 6: Affine Transformations

Lecture 54 An Introduction to Matrices

Lecture 55 Homogeneous Coordinates

Lecture 56 Transformations

Lecture 59 Translation

Lecture 60 Scaling

Lecture 61 Rotation

Lecture 62 Affine Transformations

Lecture 63 Shear and Reflect Challenge

Lecture 64 Quaternions

Lecture 65 Programming Quaternion Rotations

Lecture 66 Extracting the Rotation Axis and Angle

Lecture 67 Quaternion Rotations

Section 7: Final Words

Lecture 68 Final Maths Library Code

Lecture 69 Some Final Words from Penny

Lecture 70 Where to now?

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.