3D Rotation Generator

RotMatrixGenerator3

example

julia> m = rand(3,3)3×3 Matrix{Float64}:
 0.294519  0.831364  0.276749
 0.268923  0.200404  0.00559627
 0.499669  0.873583  0.487837
julia> s = RotMatrixGenerator{3}(m - m')3×3 RotMatrixGenerator3{Float64} with indices SOneTo(3)×SOneTo(3):
  0.0       0.562441  -0.222919
 -0.562441  0.0       -0.867987
  0.222919  0.867987   0.0
julia> exp(s)3×3 RotMatrix3{Float64} with indices SOneTo(3)×SOneTo(3):
  0.833432   0.375174  -0.405754
 -0.551275   0.5132    -0.657816
 -0.0385623  0.771926   0.634541

RotationVecGenerator

example

julia> s = RotationVecGenerator(0.1,0.2,0.3)3×3 RotationVecGenerator{Float64} with indices SOneTo(3)×SOneTo(3)(0.1, 0.2, 0.3):
  0.0  -0.3   0.2
  0.3   0.0  -0.1
 -0.2   0.1   0.0
julia> exp(s)3×3 RotationVec{Float64} with indices SOneTo(3)×SOneTo(3)(0.1, 0.2, 0.3):
  0.935755  -0.283165   0.210192
  0.302933   0.950581  -0.0680313
 -0.18054    0.127335   0.97529
julia> log(exp(s))3×3 RotationVecGenerator{Float64} with indices SOneTo(3)×SOneTo(3)(0.1, 0.2, 0.3):
  0.0  -0.3   0.2
  0.3   0.0  -0.1
 -0.2   0.1   0.0
julia> rotation_angle(exp(s))0.37416573867739417
julia> rotation_angle(exp(2s))0.7483314773547883
julia> rotation_angle(exp(2s)) / rotation_angle(exp(s))2.0