3D Rotation Generator

RotMatrixGenerator3

example

julia> m = rand(3,3)3×3 Matrix{Float64}:
 0.838406  0.29884   0.447385
 0.930052  0.940084  0.993462
 0.920853  0.908114  0.372662
julia> s = RotMatrixGenerator{3}(m - m')3×3 RotMatrixGenerator3{Float64} with indices SOneTo(3)×SOneTo(3):
 0.0       -0.631212  -0.473468
 0.631212   0.0        0.085348
 0.473468  -0.085348   0.0
julia> exp(s)3×3 RotMatrix3{Float64} with indices SOneTo(3)×SOneTo(3):
 0.704701  -0.547836  -0.450857
 0.586169   0.807571  -0.0650824
 0.399753  -0.218415   0.89022

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