Game Math and Physics Basics in 2D

• 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)

• 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