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}:
  + 0.547234 - 0.612486⋅i - 0.251102⋅j + 0.512195⋅k
julia> rand(DCM)DCM{Float64}:
  0.637532  -0.733323  0.236199
  0.251131   0.487644  0.836144
 -0.728345  -0.473751  0.495049
julia> rand(EulerAngles)EulerAngles{Float64}:
  R(Y) :  1.53143   rad  ( 87.7445°)
  R(X) :  0.0587999 rad  ( 3.36898°)
  R(Z) :  5.39348   rad  ( 309.024°)
julia> rand(EulerAngleAxis)EulerAngleAxis{Float64}:
  Euler angle : 2.79025 rad  (159.869°)
  Euler axis  : [0.433002, 0.700645, -0.567103]
julia> rand(CRP)CRP{Float64}:
  X : - 4.35337
  Y : + 2.40669
  Z : + 0.924787
julia> rand(MRP)MRP{Float64}:
  X : + 1.11253
  Y : + 0.459671
  Z : + 0.692937