Figure 1 :
r
transformation from O reference frame to

r
in

O
reference frame
Rotation: The three variables vector
α
that defines the rotation matrix can be expressed as (α,

n
), where

n
is a unit vector along the rotation axis and α the rotated angle around this direction, so that any rotation is finally described in terms of three angles: θ & ϕ that describe the unit vector

n
and α and this can be expressed as a 3D rotation matrix R(
α
).