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Vectors (Vectors (Basics (A vector is a list of numbers [ 20 13 ],…
Vectors
Vectors
Basics
A vector is a list of numbers
[ 20 13 ]
Abstract numbers in many dimensions
[-2+5]
[3 - 2]
Tail at coordinate 0,0 (
origin
) vector value at fx. (2, 3)
Arrows pointing in space :arrow_lower_left: :arrow_upper_left:
Basis vectors
^i = vector in x direction
^j = vector in y direction
Basic functions and concepts
Multiplication
2 [4 2] = [8 4]
Scaling
the vector
Addition
Vector direction
Span
= the entire possible outcome of
adding two vectors
Think of a vector as:
[scalar-x
vector-x scalar-y
vector-y]
Matrices
Linear transformations
(moving vector)
Input :arrow_right: Function :arrow_right: Output
Origin vectors moves, the rest will follow
Compute the new position
Basis vectors movement
Componsition
More vector operations at once.
Fx rotation and shear
Calculation
Calculation of X. NB! Read backwards
Calculation of Y
3D vector transformation
