Graphical representations of orientations and ODFs by Rodrigues vectors
Peter Mark Neumann · Steel Research · 1991
The most commonly used representation of orientations in the space of the Euler angles has two serious deficiencies: 1) The invariant volume element has a singularity at ϕ = 0.2) In the case of cubic symmetry the common representation has a threefold ambiguity. Both disadvantages can be avoided by using the representation by Rodrigues vectors which is the geodesic projection of the quaternion representation and is characterized by mathematical simplicity. Especially, all symmetry induced subspaces are bounded by piecewise plane surfaces, and all fibre textures are represented by straight lines. With the help of examples it is demonstrated that the graphical appearance of real textures is simpler in the Rodrigues representation.