Table of Contents
Textures and Microstructures
Volume 19 (1992), Issue 4, Pages 197-202

“Normal” Orientation Distributions

Laboratory of Metallurgy of Polycrystalline Materials (LM2P), University of Metz, ile du Saulcy, Metz–Cedex 01 57045, France

Received 10 January 1992

Copyright © 1992 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Analogues of the normal distribution in Euclidean space for orientations represented by Rodrigues parameters are discussed. It is emphasized that different characterizations of the normal distribution in Euclidean space lead to different distributions in other spaces, none of which is mathematically superior to any other one. Particular analogues of the normal distribution are the Bingham distribution on S+4 for the purposes of mathematical statistics, and the Brownian motion distribution on S+4 in terms of probability theory and stochastic processes. It is reminded of the fact that a simple analogue of the central limit theorem in Euclidean space does not exist for the hyperspheres SP and projective hyperplanes HP1=S+4.