Random rotations

Sometimes it is necessary to generate random rotations. For example, if you are testing a stochastic system numerically, you need to perform a Monte Carlo simulation sampling the initial conditions. ReferenceFrameRotations.jl defines rand function for all rotation representations, which samples a random rotation uniformly in SO(3).

julia> rand(Quaternion)Quaternion{Float64}:
  + 0.826 + 0.39732⋅i - 0.318209⋅j - 0.242083⋅k
julia> rand(DCM)DCM{Float64}:
  0.0614045  0.551877   0.831662
  0.587651   0.653519  -0.477052
 -0.806781   0.51802   -0.284182
julia> rand(EulerAngles)EulerAngles{Float64}:
  R(X) :  6.18009 rad  ( 354.093°)
  R(Y) :  4.18932 rad  ( 240.03°)
  R(X) :  5.46073 rad  ( 312.877°)
julia> rand(EulerAngleAxis)EulerAngleAxis{Float64}:
  Euler angle : 1.38224 rad  (79.1963°)
  Euler axis  : [-0.144305, -0.395613, -0.90701]