3D Rotation Generator

RotMatrixGenerator3

example

julia> m = rand(3,3)3×3 Matrix{Float64}:
 0.44178    0.902747   0.616936
 0.435129   0.113867   0.461802
 0.0912659  0.0400408  0.831451
julia> s = RotMatrixGenerator{3}(m - m')3×3 RotMatrixGenerator3{Float64} with indices SOneTo(3)×SOneTo(3):
  0.0        0.467618  0.52567
 -0.467618   0.0       0.421761
 -0.52567   -0.421761  0.0
julia> exp(s)3×3 RotMatrix3{Float64} with indices SOneTo(3)×SOneTo(3):
  0.766072   0.312137  0.561875
 -0.521688   0.812597  0.259861
 -0.375466  -0.492196  0.785346

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