Udemy
    •  
    •  
    •  
    •  
    •  
    •  
    •  
    •  
Subscribe
Turn what you know into an opportunity and reach millions around the world.
Learn More
Your cart is empty.
Keep shopping
Game Math and Physics Basics in 2D
Rating: 4.1 out of 5(22 ratings)
288 students

Game Math and Physics Basics in 2D

Learn Useful Computer Game Math
Created byT O
Last updated 8/2018
English

What you'll learn

  • 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!

Course content

2 sections • 79 lectures • 8h 9m total length

  • Displacements/distances along x7:22
  • Displacements/distances along y3:08
  • Unit vectors along each axis in 2D space3:47
  • Relative positions along coordinate axes3:47

    Investigate relative positions along coordinate axes, noting that there is no absolute origin, describe displacement from each object's perspective, and measure the single distance between objects.

  • World space vs. object space, part 16:15

    Explore world space versus object space in 2D game math by examining local coordinate systems, global origin, and how positions and relative measurements vary across objects.

  • World space vs. object space, part 24:49
  • Vector components in mathematical form12:00
  • Vector components in unity, 2 objects6:12
  • Displacements for tilted objects3:20
  • Displacements and scenes translations5:06
  • Z axis basics with physical model5:07
  • Effect of rotation on one object6:25
  • Vectors/vector components under rotations8:25
  • Vector components in unity, 3 objects7:30
  • Difference between distance and displacement vector length8:27
  • 0 magnitude displacements vs big distances5:58
  • Distance at tiny scales8:58
  • Angle basics in unity9:51
  • Magnitude and angle of displacement on unit circle9:57
  • Vectors from unit vectors11:23
  • Components from angles and length7:44

    Learn how a 2d position vector uses magnitude and angle to derive its x and y components from the origin, e.g., x = sqrt(3)/2, y = 1/2 at 30 degrees.

  • Unit vectors from math7:15
  • Vector addition for displacements, graphical rules7:39

    Explore graphical vector addition of displacements in 2d by tracing individual motion vectors along paths to obtain the resultant displacement.

  • Vector addition math9:07
  • Graphical vector subtraction8:00
  • Mathematical vector subtraction7:43
  • Midpoint of a segment5:25
  • Centroids of point distributions6:52
  • Weighted average, basic demo2:25
  • Weighted average, multiple objects, unity9:18
  • Simulation of coordinate translations, horizontal and vertical line segments4:56
  • Diagonal translations on coordinates4:06
  • 2D balance point, physical model4:40
  • Rotations and translations6:25
  • Constant speed in 2D, line segments6:28
  • Square roots in more detail3:01

    Learn to simplify square roots by factoring into a largest square and a factor, then distribute the root across factors; sqrt(24)=2 sqrt(6), sqrt(15) stays sqrt(15), sqrt(18)=3 sqrt(2).

  • Constant speed, diagonal movements5:44

    Explore constant speed motion along diagonal paths in 2d game math, using the distance formula and pythagorean theorem to show speed equals total distance divided by total time.

  • Constant velocity in 2D, horizontal and vertical7:58
  • Constant velocity, slanted segments6:41
  • Speed vs. velocity for line motions4:52

    Explore the difference between speed and velocity, with speed as distance over time and velocity as displacement over time. Compute velocity components and the speed magnitude using the Pythagorean theorem.

  • 0 velocity2:29
  • Average concepts6:32
  • Average speed in 2D, horizonital segments5:12
  • Average speed, slanted segments5:19
  • Average velocity in 2D, horizontal segments5:26
  • Calculations involving speed and velocity4:38
  • Average velocity for slanted movements7:05
  • Displacement vector from given velocity2:25
  • Desired velocity from object to object6:24
  • Constant acceleration changing speed6:30

    Explore constant acceleration and how speed grows or decelerates over time, starting from an initial speed and measured in meters per second and meters per second squared.

  • Visualizing acceleration7:04
  • Average acceleration3:31
  • Constant acceleration changing velocity3:06
  • Visualize acceleration6:58
  • Position vector7:28

    Compute the final position by adding the initial position to velocity multiplied by time. Use consistent units, such as meters and seconds; for example, (1,2) + (2,3)×2 = (5,8) meters.

  • Final velocity vector3:41

    Compute the final velocity vector as v_final = v_initial + a t, treating velocity and acceleration as vectors. Use a time-based example to confirm unit consistency with meters per second.

  • Basic vertical acceleration5:21
  • Physical introduction to forces5:38
  • Cancelling horizontal/vertical forces5:33
  • Cancelling slanted forces5:30
  • Cancelling four forces graphically4:51

    Visualize four force vectors and apply the graphical tip-to-tail method to sum them. The resultant is the zero vector, showing forces cancel in pairs.

  • Unbalanced forces7:49
  • Summation notation applied to forces4:00
  • Finding a missing vector graphically6:01

    Visualize balancing two force vectors in 2D by placing them tip-to-tail and adding a third vector to return to the start, confirming a zero net force with components.

  • Finding a missing force mathematically3:50

    Find a missing force vector by solving for its x and y components; x = -3, y = 0, then verify via component sums in newtons.

  • Finding a force in a given direction5:27
  • Force equals mass times acceleration7:35

    Explore the force-acceleration relationship F = ma, showing how mass and force determine acceleration and its vector form in newtons and meters per second squared.

  • Velocity from force11:37
  • Position vector from initial position, velocity and acceleration14:06
  • Projectile motion summary5:47
  • Projectile motion specific example4:02
  • Decomposing projectile motion into individual functions4:29

    Decompose projectile motion into independent x(t) and y(t) functions, showing how time governs horizontal and vertical components to define the trajectory.

  • Understanding x(t)5:28
  • Understanding y(t)7:44

Requirements

  • It's helpful to have the latest version of the Unity installed.
  • You should already know how to work with signed numbers.
  • You should already have seen the concept of a two dimensional coordinate space.

Description

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!


Who this course is for:

  • This is a course for those are interested in understanding the mathematics of 2D game development.
  • This is a course for those who are interested in understanding the basic physics of 2D game development.

Report abuse