Rodrigues parameterization for orientation and misorientation distributions

The Rodrigues parameterization of rotations offers an intuitively simple space which enables visualization of the geometric configuration of orientations and misorientations. Recent efforts have concentrated on promoting the use of Rodrigues vectors for orientation parameterization. In the present work a procedure for determining the boundaries of the asymmetric domains for orientations and misorientations in Rodrigues space is given for all crystal symmetries, and the complete description of these zones is presented. The geometric properties of the Rodrigues space are described in detail and important relations useful in crystallographic texture analysis are derived. It is demonstrated that the special properties and geometry of the Rodrigues space facilitate analysis of texture function reproduction from pole figures and of texture evolution in plastic deformation of polycrystals.