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Abstract
Spherical geometry of quaternions is employed to characterize the Bingham distribution on the 3-dimensional sphere S^sup 3^ [subset of] R^sup 4^ as being uniquely composed of a bipolar, a circular and a spherical component. A new parametrization of its dispersion parameters provides a classification of patterns of crystallographic preferred orientations (CPO, or textures). It is shown that the Bingham distribution can represent most types of ideal CPO patterns; in particular single component, fiber and surface textures are represented by rotationally invariant bipolar, circular and spherical distributions, respectively. Pole figures of given crystal directions are derived by the spherical Radon transform of the Bingham probability density function of rotations, which are displayed for general and special cases.[PUBLICATION ABSTRACT]