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}:
  + 0.892535 - 0.0221365⋅i - 0.312915⋅j - 0.323999⋅k
julia> rand(DCM)DCM{Float64}:
  0.0546606  0.698451  -0.713567
 -0.755929   0.49585    0.42744
  0.652368   0.516042   0.555082
julia> rand(EulerAngles)EulerAngles{Float64}:
  R(Y) :  1.4104  rad  ( 80.8098°)
  R(Z) :  1.32875 rad  ( 76.1319°)
  R(Y) :  2.014   rad  ( 115.394°)
julia> rand(EulerAngleAxis)EulerAngleAxis{Float64}:
  Euler angle : 2.00792 rad  (115.046°)
  Euler axis  : [0.589844, 0.437571, 0.678686]