Rotation Types

Abstract rotations

A matrix $R$ is called rotation matrix if $R$ satisfies

\[\begin{aligned} R^\top &= R^{-1}, & \det(R)&=1. \end{aligned}\]

In Rotations.jl, there's an abstract type for rotations matrix, Rotation{L}. Where L is a size of the rotation matrix.

Type hierarchy

julia> using Rotations, StaticArrays
julia> Rotation <: StaticMatrix <: AbstractMatrixtrue
julia> subtypes(Rotation{2})2-element Vector{Any}:
 Angle2d
 RotMatrix{2}
julia> subtypes(Rotation{3})27-element Vector{Any}:
 AngleAxis
 MRP
 QuatRotation
 RodriguesParam
 RotMatrix{3}
 RotX
 RotXY
 RotXYX
 RotXYZ
 RotXZ
 ⋮
 RotYZY
 RotZ
 RotZX
 RotZXY
 RotZXZ
 RotZY
 RotZYX
 RotZYZ
 RotationVec

Overview of each type

For more information, see the sidebar page.

2D rotations

• RotMatrix2{T}
  • Rotation matrix in 2 dimensional Euclidean space.
• Angle2d
  • Parametrized with rotational angle.

3D rotations

• RotMatrix3{T}
  • Rotation matrix in 3 dimensional Euclidean space.
• RotX, RotYZ, RotXYZ and etc.
  • Euler angles.
• AngleAxis
  • Rotation around given axis and angle.
• RotationVec
  • Rotation around given axis. The length of axis vector represents its angle.
• QuatRotation
  • A 3D rotation parameterized by a unit quaternion.
• MRP
  • A 3D rotation encoded by the stereographic projection of a unit quaternion.