Misorientation-Angle Distribution of Randomly Oriented Symmetric Objects

The problem of the distribution of the misorientation angle for symmetric randomly oriented objects is solved. It concerns, in particular, the crystallites in polycrystalline materials. The solution is the reference point for materials with nonrandom orientation distribution of crystallites and no correlations between the orientations of the neighbouring grains. The method applied is based on Rodrigues parametrization of rotations. The results for all point-symmetry groups are given.