Game Math and Physics Basics in 2D from Udemy

1. Friends, please take the time to review the curriculum carefully before buying so you can see exactly whether this is the right course for you. Please do not join until you have completed this step.

2. Please watch the free preview videos so you can see whether the presentation style works for you. Please remember I am just one person, and I make my videos often after I have been working for many hours already. Please do not join until you have completed this step.

3. If something needs fixing, please let me know. Again, I'm just one person and not a big team of people. I will try to fix it as quickly as possible. Thank you.

Course Overview:

1. This course is for those who already know how to make a simple 2D project in unity. I'm assuming you can figure out how to do this. Please remember, however, that using Unity is NOT the main objective of this course.

2. This course focuses only on two dimensional math and physics concepts related to game programming.

3. In some of the videos you see how to use unity.

4. In some of the videos I use physical demonstrations to illustrate mathematical concepts related to game development.

5. In some of the videos I write by hand on paper because this is faster than writing on the computer screen.

6. You should be mentally prepared to work with square roots, vectors and units of various kinds like m/s and m/s^2 and kg.

7. I draw a lot in this course to illustrate various vector concepts. In other words, I use a variety of teaching methods.

8. There are a variety of exercises placed throughout the videos. Please try to complete every exercise. Practice, of the right kind, counts. :)

9. These videos focus primarily on understanding the concepts of vectors, distances, angles, transformations, speeds, velocities, accelerations, forces, and related concepts.

10. You should already be able to solve basic linear equations like 2+4+x=10 and you should understand how to compare numbers with ratios, as in 10kg/2kg. I do, however, still explain these too.

11. Please be sure to read the curriculum with meticulous care before enrolling so you can be sure this is truly the right course for you.

12. If you are already a great physics/math expert, please do not join this course. It will not help you.

13. For the hearing-impaired, closed-captions are added automatically. I do not have control over those, so they might not be perfect.

14. Thank you for reading, and see you inside.

What's inside

Learning objectives

Describe unit vectors
Describe vectors in general
Describe scalars
Describe distance
Describe speed
Describe velocity
Understand coordinate transformations
Describe world space
Describe object space
Describe forces
Describe acceleration
Describe displacement
Describe the z axis in unity vividly
Describe rotations
Work with square roots as needed

Describe vector components
Describe magnitudes
Describe motion on a circle
Understand angles
Add vectors
Subtract vectors
Multiple vectors by scalars
Find unit vectors
Find vectors of a desired magnitude and direction
Understand weighted averages
Describe average speed
Describe average velocity
And many others!
Show more
Show less

Describe unit vectors
Describe vectors in general
Describe scalars
Describe distance
Describe speed
Describe velocity
Understand coordinate transformations
Describe world space
Describe object space
Describe forces
Describe acceleration
Describe displacement
Describe the z axis in unity vividly
Describe rotations
Work with square roots as needed
Describe vector components
Describe magnitudes
Describe motion on a circle
Understand angles
Add vectors
Subtract vectors
Multiple vectors by scalars
Find unit vectors
Find vectors of a desired magnitude and direction
Understand weighted averages
Describe average speed
Describe average velocity
And many others!
Show more
Show less

Syllabus

2D coordinate and vector concepts

Displacements/distances along x

Displacements/distances along y

Unit vectors along each axis in 2D space

Relative positions along coordinate axes

World space vs. object space, part 1

World space vs. object space, part 2

Vector components in mathematical form

Vector components in unity, 2 objects

Displacements for tilted objects

Displacements and scenes translations

Z axis basics with physical model

Effect of rotation on one object

Vectors/vector components under rotations

Vector components in unity, 3 objects

Difference between distance and displacement vector length

0 magnitude displacements vs big distances

Distance at tiny scales

Angle basics in unity

Magnitude and angle of displacement on unit circle

Vectors from unit vectors

Components from angles and length

Unit vectors from math

Vector addition for displacements, graphical rules

Vector addition math

Graphical vector subtraction

Mathematical vector subtraction

Midpoint of a segment

Centroids of point distributions

Weighted average, basic demo

Weighted average, multiple objects, unity

Simulation of coordinate translations, horizontal and vertical line segments

Diagonal translations on coordinates

2D balance point, physical model

Rotations and translations

Constant speed in 2D, line segments

Square roots in more detail

Constant speed, diagonal movements

Constant velocity in 2D, horizontal and vertical

Constant velocity, slanted segments

Speed vs. velocity for line motions

0 velocity

Average concepts

Average speed in 2D, horizonital segments

Average speed, slanted segments

Average velocity in 2D, horizontal segments

Calculations involving speed and velocity

Average velocity for slanted movements

Displacement vector from given velocity

Desired velocity from object to object

Constant acceleration changing speed

Visualizing acceleration

Average acceleration

Constant acceleration changing velocity

Visualize acceleration

Position vector

Final velocity vector

Basic vertical acceleration

Physical introduction to forces

Cancelling horizontal/vertical forces

Cancelling slanted forces

Cancelling four forces graphically

Unbalanced forces

Summation notation applied to forces

Finding a missing vector graphically

Finding a missing force mathematically

Finding a force in a given direction

Force equals mass times acceleration

Velocity from force

Position vector from initial position, velocity and acceleration

Projectile motion summary

Projectile motion specific example

Decomposing projectile motion into individual functions

Understanding x(t)

Understanding y(t)

Other Ideas

Dot product basics

Scalar projections with dot products

Projecting velocity components with dot products along x and y axes

Projecting velocity components along slanted vectors

Course Summary

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Game Math and Physics Basics in 2D with these activities:

Review Vector Math Fundamentals

Show steps

Solidify your understanding of vector math, which is crucial for grasping the concepts taught in this course.

Show steps

Review basic vector operations like addition, subtraction, and scalar multiplication.
Practice solving problems involving vector components and magnitudes.
Familiarize yourself with coordinate systems and transformations.

Review 'Essential Mathematics for Games and Interactive Applications'

Show steps

Supplement your learning with a comprehensive book on game mathematics to gain a deeper understanding of the underlying principles.

View Essential Mathematics for Games and Interactive... on Amazon

Show steps

Read the chapters related to vectors, matrices, and transformations.
Work through the examples and exercises provided in the book.
Relate the concepts learned in the book to the topics covered in the course.

Practice Vector Calculations in Unity

Show steps

Reinforce your understanding of vector calculations by implementing them in Unity.

Show steps

Create a new Unity project and import necessary assets.
Write scripts to perform vector addition, subtraction, and normalization.
Visualize the results of the calculations using Unity's scene view.
Experiment with different vector values and observe the changes in the scene.

Four other activities

Expand to see all activities and additional details

Show all seven activities

Create a Vector Visualization Tool

Show steps

Solidify your understanding of vectors by creating a tool that visually represents vector operations.

Show steps

Design a user interface for inputting vector components and selecting operations.
Implement the vector operations using Unity's scripting language.
Display the resulting vector in the scene view using lines or arrows.
Add features to visualize vector magnitude, angle, and components.

Implement Simple 2D Physics

Show steps

Apply your knowledge of game math and physics to create a simple 2D physics engine.

Show steps

Create a new Unity project and set up the 2D environment.
Implement basic physics concepts like gravity, friction, and collision detection.
Create a simple game with objects that interact with the physics engine.
Experiment with different physics parameters and observe the effects on the game.

Review 'Real-Time Collision Detection'

Show steps

Expand your knowledge of collision detection techniques, which are crucial for creating realistic game physics.

View Real Time Collision Detection on Amazon

Show steps

Read the chapters related to bounding volume hierarchies and collision queries.
Implement some of the collision detection algorithms in Unity.
Compare the performance of different algorithms and choose the most suitable one for your game.

Follow Advanced Unity Physics Tutorials

Show steps

Refine your skills by following advanced tutorials on Unity's physics engine.

Show steps

Search for tutorials on topics like ragdoll physics, inverse kinematics, and procedural animation.
Follow the tutorials step-by-step and implement the techniques in your own projects.
Experiment with different parameters and settings to achieve desired results.

Career center

Learners who complete Game Math and Physics Basics in 2D will develop knowledge and skills that may be useful to these careers:

Game Developer

A game developer brings video game concepts to life. This involves coding the gameplay mechanics, implementing game physics, and ensuring smooth and engaging player experiences. This course focusing on two dimensional math and physics concepts related to game programming helps build a foundation for manipulating game objects, creating realistic movement, and designing challenging and fun game mechanics. Expertise in vector math, coordinate transformations, and physics principles like forces and acceleration, covered in this course, are essential for any aspiring game developer. This course may be useful to those interested in the underlying mathematical and physical principles that drive game development.

See salaries and explore the career path for Game Developer

Physics Programmer

A physics programmer specializes in creating realistic and accurate simulations of physical phenomena within games or other applications. The physics programmer works to implement the game physics. This course, with its focus on two dimensional math and physics concepts related to game programming, provides a solid groundwork for understanding and implementing physics engines. It includes description of forces, acceleration, and motion, is beneficial for accurately simulating physical interactions. Anyone interested in creating believable physics-based interactions should consider this course.

See salaries and explore the career path for Physics Programmer

Gameplay Programmer

Gameplay programmers are responsible for implementing the interactive elements of a game, such as character movement, combat systems, and puzzle mechanics. The gameplay programmer role requires a strong understanding of game math and physics. This course helps gameplay programmers, especially the sections on vectors, coordinate transformations, and motion, build a foundation to design fun and engaging player experiences. Course modules covering topics like vector addition, subtraction, and average velocity may be particularly useful.

See salaries and explore the career path for Gameplay Programmer

Animator

Animators create the illusion of movement through a sequence of images, whether for cartoons, video games, or films. Animators should know how to manipulate objects in two dimensional space. This course focusing on two dimensional math and physics concepts related to game programming may help build a foundation for creating realistic and believable movement. The course sections on vectors, angles, and transformations build a foundation for animating characters and objects.

See salaries and explore the career path for Animator

Motion Graphics Designer

Motion graphics designers create animated visual content for a variety of media, including commercials, websites, and video games. A motion graphics designer often uses math and physics principles to create realistic and engaging animations. This course focusing on two dimensional math and physics concepts related to game programming may help build a solid understanding of vector math, transformations, and motion. The course covers topics like rotations, speed, velocity, and acceleration, all of which are essential for creating compelling motion graphics.

See salaries and explore the career path for Motion Graphics Designer

Augmented Reality Developer

An augmented reality developer creates applications that overlay computer-generated images onto the real world via devices like smartphones or headsets. As an augmented reality developer, understanding how to manipulate and transform virtual objects in relation to the user's environment is extremely pivotal. This course focusing on two dimensional math and physics concepts related to game programming may help build an understanding of coordinate systems, vector math, and transformations. These skills are essential for creating seamless and intuitive augmented reality experiences.

See salaries and explore the career path for Augmented Reality Developer

Virtual Reality Developer

Virtual reality developers create immersive digital environments and experiences. The virtual reality developer needs a strong grasp of spatial reasoning and object manipulation in three dimensional space. While this course focuses on 2D concepts, it helps build a strong foundation in vector math, coordinate systems, and transformations that can be extended into 3D virtual reality development. The course is helpful in visualizing coordinate transformations, vectors, and other quantities.

See salaries and explore the career path for Virtual Reality Developer

Simulation Engineer

A simulation engineer develops software to model and simulate real-world systems for purposes such as training, analysis, or prediction. The simulation engineer benefits from understanding how to model real-world systems using mathematical and physical principles. This course may give these engineers a foundation in vector math, coordinate transformations, and physics concepts like forces and acceleration. The course sections on motion, velocity, and acceleration may be particularly relevant for anyone interested in realistic simulations. Simulation engineers typically require an advanced degree.

See salaries and explore the career path for Simulation Engineer

Robotics Engineer

Robotics engineers design, build, and program robots for a variety of applications, from manufacturing to exploration. This course may give a robotics engineer a basic toolkit of knowledge for controlling robot movement and interactions within a two dimensional space. The sections on vectors, coordinate transformations, and forces are beneficial for calculating robot trajectories and ensuring accurate movements. Understanding unit vectors may be helpful for controlling movement. Robotics engineers typically require an advanced degree.

See salaries and explore the career path for Robotics Engineer

Science Teacher

Science teachers educate students on scientific principles. This course may help science teachers who want to communicate concepts in physics. Familiarity with forces and motion may be relevant. The course may be useful to teachers who use game development.

See salaries and explore the career path for Science Teacher

Data Visualization Specialist

Data visualization specialists translate complex datasets into visual representations that are easier to understand. While this course focuses on game math and physics, the fundamental principles of vector math, coordinate systems, and transformations taught in this course may be useful for representing data points and relationships visually. A data visualization specialist will find the course on rotations helpful. The course may be useful for those who want to represent two dimensional data.

See salaries and explore the career path for Data Visualization Specialist

Math Teacher

Math teachers educate students on mathematical concepts and problem-solving skills. Often, math teachers explain the concepts behind vector math and coordinate systems. This course may provide teachers with additional insights into the practical applications of these concepts in game development. A math teacher may use this course as a source of examples. The course on unit vectors and vector addition may be particularly relevant.

See salaries and explore the career path for Math Teacher

Tools Programmer

Tools programmers develop software that streamlines the game development process for other team members, such as artists and designers. This often involves creating custom editors or scripts to automate tasks. This course may aid a tools programmer to understand the math behind certain transformations or calculations that the tools need to perform. Familiarity with vectors, angles, and coordinate systems may be useful as a tools programmer seeks to create efficient and user-friendly tools. A tools programmer should also know how to represent two dimensional space.

See salaries and explore the career path for Tools Programmer

Instructional Designer

Instructional designers create learning experiences. An instructional designer typically blends pedagogy with multimedia practice. This course may provide instructional designers with an expanded toolset to create instructional materials. The modules which display graphical concepts and the modules which display physical concepts will assist in communicating concepts with a diverse array of students. It may be useful to those looking to apply new methods to instruction.

See salaries and explore the career path for Instructional Designer

Data Scientist

Data scientists analyze and interpret complex data to identify trends, patterns, and insights. This course may not be immediately relevant to traditional data science tasks. However, the foundations of data science often include vector math. The course may be useful to understand the underlying math behind data analysis techniques. Data scientists typically require an advanced degree.

See salaries and explore the career path for Data Scientist

Game Math and Physics Basics in 2D

What's inside

Learning objectives

Syllabus

Save this course

Activities

Career center

Reading list

Share

Similar courses