Coordinate Systems (2d)

• origin is the top-left corner of the screen
  • y values increase downward
• identify points through (x, y) pairs
  • these are position vectors

Unit Vectors

vectors with magnitudes of 1 (direction vectors, normals)

• useful for keeping track of direction
• normalization: reducing a vectors length to one while preserving its direction
  • a.normalized()
• normals: unit vectors aligned perpendicular to a surface
  • used for lighting, collision

Vector operations

• member access
  • vector.x, vector.y
• adding
  • corresponding components added
• scalar multiplication
  • does not change direction, changes magnitude (scale)
• dot product
  • operation on two vectors that returns a scalar
  • useful with unit vectors
    • can tell us the angle between
    • dot product of unit vector and any point in space is the distance from the point to the plane
• cross product
  • operation on two vectors that returns a vector with a direction perpendicular to both
• reflect

Practical Applications

• Movement
  • vectors can represent any quantity:
    • position
    • velocity: change in position per unit of time
    • acceleration
    • force
  • next_position = position + velocity
  • direction_to_point_A = A_position - target_position