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}:
  - 0.68818 + 0.194146⋅i + 0.644524⋅j + 0.270749⋅k
julia> rand(DCM)DCM{Float64}:
 -0.445756  -0.342946  -0.826855
 -0.835573  -0.171954   0.521775
 -0.321122   0.923482  -0.209907
julia> rand(EulerAngles)EulerAngles{Float64}:
  R(Z) :  0.165174 rad  ( 9.46376°)
  R(X) :  3.57263  rad  ( 204.697°)
  R(Y) :  4.71154  rad  ( 269.951°)
julia> rand(EulerAngleAxis)EulerAngleAxis{Float64}:
  Euler angle : 1.8008 rad  (103.178°)
  Euler axis  : [-0.794215, 0.0019806, 0.607634]