Gibbs / Rodrigues parameter representation for rotations

Search IconIcon to open search

Parent: Orientation parametrisations
See also: Rotation error representation

Source: Markley 2014

From unit quaternions : Image.png

From euler-axis-angle-representation : unknown_filename.2.png

To unit quaternions : 

 unknown_filename.1.png

unknown_filename.png

  • Plane of the figure contains identity quaternion , origin
  • The circle is a cross section of the quaternion sphere S^3
  • The upper horizontal axis is the 3D Gibbs vector hyperplane (tangent at the identity quaternion)

[+] q and -q map to the same Gibbs vector, therefore there is a 1:1 mapping of rotations between quaternions and the Gibbs parameter [-] the Gibbs vector is infinite for 180 degree rotations (q.w = q4 = 0? - [ ] )

  • therefore not good for global orientation representations,
  • but good for representation of small rotations