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}:
  + 0.106873 - 0.186806⋅i + 0.967335⋅j - 0.133955⋅k
julia> rand(DCM)DCM{Float64}:
 0.443569   0.890368    0.10243
 0.819486  -0.4492      0.355896
 0.36289   -0.0739241  -0.928895
julia> rand(EulerAngles)EulerAngles{Float64}:
  R(Y) :  0.640155 rad  ( 36.6782°)
  R(X) :  5.20521  rad  ( 298.236°)
  R(Z) :  4.0819   rad  ( 233.876°)
julia> rand(EulerAngleAxis)EulerAngleAxis{Float64}:
  Euler angle : 2.30403 rad  (132.011°)
  Euler axis  : [0.311194, 0.719553, -0.620808]