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}:
  + 0.905542 - 0.11916⋅i + 0.380625⋅j + 0.144635⋅k
julia> rand(DCM)DCM{Float64}:
  0.424574   0.399741  0.812369
 -0.776948   0.621536  0.100223
 -0.464853  -0.673721  0.574466
julia> rand(EulerAngles)EulerAngles{Float64}:
  R(Z) :  3.64319 rad  ( 208.739°)
  R(Y) :  2.10039 rad  ( 120.344°)
  R(X) :  5.11474 rad  ( 293.053°)
julia> rand(EulerAngleAxis)EulerAngleAxis{Float64}:
  Euler angle : 2.24746 rad  (128.77°)
  Euler axis  : [0.0634468, -0.974105, 0.217013]