2D Rotation Generator

RotMatrixGenerator2

example

julia> m = rand(2,2)2×2 Matrix{Float64}:
 0.596184  0.637158
 0.879545  0.550411
julia> s = RotMatrixGenerator{2}(m - m')2×2 RotMatrixGenerator2{Float64} with indices SOneTo(2)×SOneTo(2):
 0.0       -0.242387
 0.242387   0.0
julia> exp(s)2×2 RotMatrix2{Float64} with indices SOneTo(2)×SOneTo(2):
 0.970768  -0.24002
 0.24002    0.970768
julia> log(exp(s))2×2 RotMatrixGenerator2{Float64} with indices SOneTo(2)×SOneTo(2):
 0.0       -0.242387
 0.242387   0.0

Angle2dGenerator

example

julia> s = Angle2dGenerator(0.42)2×2 Angle2dGenerator{Float64} with indices SOneTo(2)×SOneTo(2)(0.42):
 0.0   -0.42
 0.42   0.0
julia> exp(s)2×2 Angle2d{Float64} with indices SOneTo(2)×SOneTo(2)(0.42):
 0.913089  -0.40776
 0.40776    0.913089
julia> log(exp(s))2×2 Angle2dGenerator{Float64} with indices SOneTo(2)×SOneTo(2)(0.42):
 0.0   -0.42
 0.42   0.0
julia> rotation_angle(exp(s))0.42
julia> rotation_angle(exp(2s))0.84
julia> rotation_angle(exp(2s)) / rotation_angle(exp(s))2.0