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Rotations

3D rotations made easy in Julia

Documentation

The documentation is still work in progress. For more information, see also

(TBW) comments are left in areas that have not yet been documented. Feel free to open pull requests and improve this document!

Installation

pkg> add Rotations

First example

julia> using Rotations
       
       # 3D Rotation by Euler Angles
julia> R_euler = RotXYZ(1,2,3)
       
       # Get an angle and an axis of the rotation3×3 RotXYZ{Float64} with indices SOneTo(3)×SOneTo(3)(1.0, 2.0, 3.0):
  0.411982   0.0587266   0.909297
 -0.681243  -0.642873    0.350175
  0.605127  -0.763718   -0.224845
julia> rotation_angle(R_euler), rotation_axis(R_euler)
       
       # Convert the rotation to unit quaternion(2.386003742640557, [-0.8122105149361277, 0.22178973672199065, -0.5395585159294407])
julia> R_quat = QuatRotation(R_euler)
       
       # Get quaternion parameters of the rotation3×3 QuatRotation{Float64} with indices SOneTo(3)×SOneTo(3)(QuaternionF64(0.368871, -0.754934, 0.206149, -0.501509)):
  0.411982   0.0587266   0.909297
 -0.681243  -0.642873    0.350175
  0.605127  -0.763718   -0.224845
julia> Rotations.params(R_quat)
       
       # Convert the rotation to MRP (Modified Rodrigues Parameters)4-element StaticArraysCore.SVector{4, Float64} with indices SOneTo(4):
  0.36887135771328977
 -0.7549338012644524
  0.20614922602687769
 -0.5015090964037221
julia> R_mrp = MRP(R_euler)3×3 MRP{Float64} with indices SOneTo(3)×SOneTo(3)(-0.551501, 0.150598, -0.366367):
  0.411982   0.0587266   0.909297
 -0.681243  -0.642873    0.350175
  0.605127  -0.763718   -0.224845
julia> Rotations.params(R_mrp)
       
       # Get parameters of the MRP3-element StaticArraysCore.SVector{3, Float64} with indices SOneTo(3):
 -0.551500911324184
  0.1505979541943602
 -0.3663668565916208
julia> Rotations.params(R_mrp)
       
       # Also supports 2D rotation3-element StaticArraysCore.SVector{3, Float64} with indices SOneTo(3):
 -0.551500911324184
  0.1505979541943602
 -0.3663668565916208
julia> R_2d = Angle2d(π/6)
       
       # Also supports some differentiation2×2 Angle2d{Float64} with indices SOneTo(2)×SOneTo(2)(0.523599):
 0.866025  -0.5
 0.5        0.866025
julia> Rotations.jacobian(RotMatrix, R_quat)9×4 StaticArraysCore.SMatrix{9, 4, Float64, 36} with indices SOneTo(9)×SOneTo(4):
  0.433806  -0.887829   -0.582158   1.41624
 -0.500436  -0.616288   -1.22899    0.0544439
 -0.858727  -0.0893562  -0.987236  -0.902914
  0.959693   0.500968   -1.53408   -0.678839
  1.21202    0.539215    0.677354   0.358205
 -0.94644   -0.415371   -0.688138  -0.353725
 -0.258529   0.369901    0.362841  -0.597826
  1.25153   -0.209024   -1.1474     0.763531
  0.903621   1.17038    -0.319595  -1.22854