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}:
  - 0.521199 - 0.4494⋅i - 0.688986⋅j - 0.227354⋅k
julia> rand(DCM)DCM{Float64}:
 -0.0566015  0.965869  -0.252771
 -0.193968   0.237715   0.951771
  0.979374   0.102901   0.173893
julia> rand(EulerAngles)EulerAngles{Float64}:
  R(Y) :  6.07682  rad  ( 348.176°)
  R(Z) :  1.3211   rad  ( 75.6935°)
  R(Y) :  0.858694 rad  ( 49.1995°)
julia> rand(EulerAngleAxis)EulerAngleAxis{Float64}:
  Euler angle : 2.56912 rad  (147.2°)
  Euler axis  : [-0.291155, -0.297709, -0.909174]