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}:
  + 0.106085 + 0.510503⋅i + 0.834236⋅j + 0.179394⋅k
julia> rand(DCM)DCM{Float64}:
 -0.0711744  -0.609939  -0.789245
 -0.677702   -0.551007   0.486941
 -0.731884    0.569531  -0.374139
julia> rand(EulerAngles)EulerAngles{Float64}:
  R(Y) :  2.74985  rad  ( 157.555°)
  R(X) :  5.43651  rad  ( 311.489°)
  R(Y) :  0.340472 rad  ( 19.5076°)
julia> rand(EulerAngleAxis)EulerAngleAxis{Float64}:
  Euler angle : 1.78048 rad  (102.014°)
  Euler axis  : [0.285541, -0.929013, -0.235374]
julia> rand(CRP)CRP{Float64}:
  X : + 31.0924
  Y : - 6.88569
  Z : - 29.8073
julia> rand(MRP)MRP{Float64}:
  X : - 0.2703
  Y : - 0.157447
  Z : - 0.361578