JavascriptReallyWorks / Linear-algebra-for-game-developers

Linear Algebra For Game Developers

Notes from Linear Algebra for Game Developers Part 1

Vector examples:

• position
• velocity
• direction
• acceleration
• ...

Important:

• keep track of units
  • velocity is in meters/second or in pixels/frame
• remember the context of the vector
  • (0, 1) is a velocity or a direction?
  • Same vector, different meanings

Example: (3, 5, 2) is a position in meters

1. east (3 methers east from the origin)
2. up (z axis)
3. north

Negative numbers represent opposite directions (west, down south).

Vector addition

(0,1,4) + (3,-2,5) = (0+3, 1-2, 4+5) = (3,-1,9)

Addition is a component-wise operation.

Useful for: physics integration

loop:
    position += velocity
    velocity += acceleration

Vector subtraction

Useful for getting a vector that points from one position to another.

Distance vector = destination - origin

V1 = rifleman position
V2 = robot position
v3 = laser beam = V2 - V1