3D Rotation Matrix

An $3 \times 3$ rotation matrix storing the rotation. This is a simple wrapper for a StaticArrays SMatrix{3,3,T}. A rotation matrix $R$ should have the property $I = R R^\top$, but this isn't enforced by the constructor. On the other hand, all the types below are guaranteed to be "proper" rotations for all input parameters (equivalently: parity conserving, in $SO(3)$, $\det(R) = 1$, or a rotation without reflection).

RotMatrix3

example

julia> t = 1.21.2
julia> m1 = [cos(t) -sin(t) 0;sin(t) cos(t) 0;0 0 1]3×3 Matrix{Float64}:
 0.362358  -0.932039  0.0
 0.932039   0.362358  0.0
 0.0        0.0       1.0
julia> RotMatrix{3}(m1)  # construct from matrix3×3 RotMatrix3{Float64} with indices SOneTo(3)×SOneTo(3):
 0.362358  -0.932039  0.0
 0.932039   0.362358  0.0
 0.0        0.0       1.0
julia> m2 = RotZ(t)  # Other rotation type3×3 RotZ{Float64} with indices SOneTo(3)×SOneTo(3)(1.2):
 0.362358  -0.932039  0.0
 0.932039   0.362358  0.0
 0.0        0.0       1.0
julia> RotMatrix{3}(m2)  # convert m2 to RotMatrix3×3 RotMatrix3{Float64} with indices SOneTo(3)×SOneTo(3):
 0.362358  -0.932039  0.0
 0.932039   0.362358  0.0
 0.0        0.0       1.0
julia> RotMatrix(m2)  # Type parameter can be omitted.3×3 RotMatrix3{Float64} with indices SOneTo(3)×SOneTo(3):
 0.362358  -0.932039  0.0
 0.932039   0.362358  0.0
 0.0        0.0       1.0