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}:
  - 0.854712 + 0.405105⋅i - 0.255352⋅j - 0.200382⋅k
julia> rand(DCM)DCM{Float64}:
  0.645408   0.488087   0.587555
 -0.663082  -0.0238294  0.748167
  0.379171  -0.87247    0.308262
julia> rand(EulerAngles)EulerAngles{Float64}:
  R(Y) :  5.35912  rad  ( 307.055°)
  R(X) :  3.50237  rad  ( 200.671°)
  R(Y) :  0.328937 rad  ( 18.8467°)
julia> rand(EulerAngleAxis)EulerAngleAxis{Float64}:
  Euler angle : 2.15477 rad  (123.459°)
  Euler axis  : [-0.721742, 0.005374, -0.692142]