Mô tả

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.

Bạn sẽ học được gì

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.

Yêu cầu

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

Nội dung khoá học

7 sections

Introduction and Welcome

7 lectures
Welcome
04:00
Join the H3D Student Community
01:26
Contacting H3D
00:01
FAQs
00:14
How to Study This Course
00:22
Basic Trigonometry
02:01
Basic Trigonometry Quiz
10 questions

Bitwise Operations

15 lectures
Bits, Bytes and Binary
10:41
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

Location

8 lectures
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

Vectors

23 lectures
Introduction to Vectors Part 1
14:58
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

Intersections

16 lectures
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
19:52
Line-Plane Intersections, Projections and Reflections
18:14
Plane Reflections
13:19
Unity Specifics For Intersections
19:54
More Unity Specifics Part 1
13:58
More Unity Specifics Part 2
09:57

Affine Transformations

16 lectures
An Introduction to Matrices
08:26
Matrix Quiz
10 questions
Homogeneous Coordinates
05:28
Transformations
07:39
Matrices: Data Structures and Algorithms Part 1
19:26
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 Words

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

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