exp(Rotations.UnitQuaternion(0, π, 0, 0)) gives incorrect result

[bzinberg]

julia> exp(Rotations.UnitQuaternion(0, π, 0, 0))
3×3 UnitQuaternion{Float64} with indices SOneTo(3)×SOneTo(3)(0.540302, 0.841471, 0.0, 0.0):
 1.0   0.0        0.0     
 0.0  -0.416147  -0.909297
 0.0   0.909297  -0.416147

I would expect the result UnitQuaternion(-1.0, 0, 0, 0).

This issue might end up being superseded by a fix to #30.

[hyrodium]

We need to introduce skew-symmetric matrix type(#30) to solve this issue cleanly, but we can do the following for now:

julia> exp(Rotations.UnitQuaternion(0, π, 0, 0, false))
3×3 UnitQuaternion{Float64} with indices SOneTo(3)×SOneTo(3)(-1.0, 1.22465e-16, 0.0, 0.0):
 1.0   0.0          0.0
 0.0   1.0          2.44929e-16
 0.0  -2.44929e-16  1.0

The false means "do not normalize". This seems a dirty solution because it is not unit quaternion.

[hyrodium]

julia> using Rotations

julia> exp(RotationVecGenerator(π,0,0))
3×3 RotationVec{Float64} with indices SOneTo(3)×SOneTo(3)(3.14159, 0.0, 0.0):
 1.0   0.0           0.0
 0.0  -1.0          -1.22465e-16
 0.0   1.22465e-16  -1.0

julia> exp(RotationVecGenerator(2π,0,0))
3×3 RotationVec{Float64} with indices SOneTo(3)×SOneTo(3)(6.28319, 0.0, 0.0):
 1.0   0.0          0.0
 0.0   1.0          2.44929e-16
 0.0  -2.44929e-16  1.0