Dear Ralf,
There is a
very nice paper from Hirsch and Lücke (Description and Presentations Methods for Textures, in Textures and Microstructures 8 (1988), 131 - 151), which describes several different types
of textures and their representation.
The problem with the beta fibre is that is, that the path is not fixed in the Euler space, it connects only the intensity maxima in the ODF sections along the fibre.
Is it possible to plot beta fibres with MTEX? For other fibres such as alpha or gamma it is rather easy, since 2 angles are fixed (and you described already how to plot them). Unfortunatelly for beta fibres it is not so easy, since alle 3 Euler Angles change.
Thank you