Table of Contents
Textures and Microstructures
Volume 10, Issue 1, Pages 77-96

On the Normal Distribution in the Orientation Space

1Zentralinstitut für Kernforschung Rossendorf, DDR, PF 19, Dresden 8051, Germany
2Institut de Mathématiques, 7 rue René Descartes, Strasbourg 67000, France

Received 15 March 1988

Copyright © 1988 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.


The properties of model distributions used in texture analysis up to now are discussed. The normal distribution in the G-space (recently investigated by T. I. Savjolova) is analysed. Its connection with the central limit theorem of probability theory is demonstrated in a mathematically simplified manner. An analytically closed approximative expression (with very high precision for halfwidths of practical interest) for the normal distribution is derived. Possible correlations between forms of texture components and mechanisms of texture development are mentioned.