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}:
  - 0.410233 + 0.336623⋅i - 0.135209⋅j - 0.836727⋅k
julia> rand(DCM)DCM{Float64}:
 0.615988  -0.764296   0.190814
 0.762603   0.517841  -0.387656
 0.197473   0.384306   0.901839
julia> rand(EulerAngles)EulerAngles{Float64}:
  R(X) :  5.71524 rad  ( 327.459°)
  R(Z) :  4.94248 rad  ( 283.183°)
  R(Y) :  4.04504 rad  ( 231.764°)
julia> rand(EulerAngleAxis)EulerAngleAxis{Float64}:
  Euler angle : 2.25376 rad  (129.131°)
  Euler axis  : [-0.0254095, 0.387628, -0.921466]