**Mathematics for Computer Games Development using Unity**

English | MP4 | AVC 1280×720 | AAC 44KHz 2ch | 15 Hours | 8.71 GB

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

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 and 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 to 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 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.

**Table of Contents**

**Introduction and Welcome**

1 Welcome

2 FAQs

3 How to Study This Course

4 Basic Trigonometry

**Bitwise Operations**

5 Bits, Bytes and Binary

6 Bit Flags & Bitwise Operators

7 Turning Bit Flags Off

8 Bit Masks

9 Bit Mask Challenge Solution

10 Bit Shifting

11 Bit Toggling and Unity Specifics

12 Bitboards

13 Putting Bitboards Into Practice Part 1

14 Putting Bitboards Into Practice Part 2

15 Putting Bitboards Into Practice Part 3

16 Other Bitwise Operation Hacks

**Location**

17 Cartesian Coordinates & Points

18 Plotting Points: A Simple Data Structure

19 Drawing Lines: Solution

20 Graph Line Challenge

21 Practice Locating 2D Points on a Cartesian Plane

22 Calculating Distance Part 1

23 Calculating Distance Part 2

**Vectors**

24 Introduction to Vectors Part 1

25 Introduction to Vectors Part 2

26 Vectors: Moving to a Point

27 Vector Normal Form

28 Dot Product

29 Derivation of Vector Angle Calculation

30 Rotations

31 Cross Product

32 2D LookAt Challenge

33 Dot Cross Challenge

34 Challenge Solutions

35 Recreate Rotate and Translate Challenge Part 1

36 Recreate Rotate and Translate Challenge Part 2

37 Moving from 2D to 3D

38 Exploring Rotation in 3D

**Intersections**

39 Lines, Line Segments and Rays Part 1

40 Lines, Line Segments and Rays Part 2

41 Planes

42 Another Line Constructor

43 Intersection of Two Line Segments

44 Improving Line Intersection

45 Line-Line Intersection Challenge

46 Line-Plane Intersections

47 Line-Plane Intersections, Projections and Reflections

48 Plane Reflections

49 Unity Specifics For Intersections

50 More Unity Specifics Part 1

51 More Unity Specifics Part 2

**Affine Transformations**

52 An Introduction to Matrices

53 Homogeneous Coordinates

54 Transformations

55 Matrices: Data Structures and Algorithms Part 1

56 Matrices: Data Structures and Algorithms Part 2

57 Translation

58 Scaling

59 Rotation

60 Affine Transformations

61 Shear and Reflect Challenge

62 Quaternions

63 Programming Quaternion Rotations

64 Extracting the Rotation Axis and Angle

65 Quaternion Rotations

**Final Words**

66 Final Maths Library Code

67 Some Final Words from Penny

68 Where to now?

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