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}:
  + 0.525721 + 0.331211⋅i + 0.0472393⋅j + 0.782103⋅k
julia> rand(DCM)DCM{Float64}:
  0.914219    0.126734   0.384892
 -0.0950651  -0.856247   0.507743
  0.393911   -0.500778  -0.77075
julia> rand(EulerAngles)EulerAngles{Float64}:
  R(X) :  3.75207 rad  ( 214.978°)
  R(Y) :  3.25544 rad  ( 186.523°)
  R(Z) :  2.8572  rad  ( 163.705°)
julia> rand(EulerAngleAxis)EulerAngleAxis{Float64}:
  Euler angle : 1.76824 rad  (101.313°)
  Euler axis  : [0.269311, -0.897076, -0.350322]