Rotation Generator Types

Abstract rotation generators

A matrix $R$ is called skew-symmetric matrix if $R$ satisfies

\[\begin{aligned} R^\top &= -R. \end{aligned}\]

In Rotations.jl, there's an abstract type for skew-symmetric matrix, RotationGenerator{L}. Where L is a size of the skew-symmetric matrix.

Type hierarchy

julia> using Rotations, StaticArrays
julia> RotationGenerator <: StaticMatrix <: AbstractMatrixtrue
julia> subtypes(RotationGenerator{2})2-element Vector{Any}:
 Angle2dGenerator
 RotMatrixGenerator{2}
julia> subtypes(RotationGenerator{3})2-element Vector{Any}:
 RotMatrixGenerator{3}
 RotationVecGenerator

Overview of each type

For more information, see the sidebar page.

2D rotations

• RotMatrixGenerator2{T}
  • Skew symmetric matrix in 2 dimensional Euclidean space.
• Angle2dGenerator
  • Parametrized with one real number like Angle2d.

3D rotations

• RotMatrixGenerator3{T}
  • Skew symmetric matrix in 3 dimensional Euclidean space.
• RotationVecGenerator
  • Rotation generator around given axis. The length of axis vector represents its angle.