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Title: Applications of the Clifford torus to material textures
This paper introduces a new 2D representation of the orientation distribution function for an arbitrary material texture. The approach is based on the isometric square torus mapping of the Clifford torus, which allows for points on the unit quaternion hypersphere (each corresponding to a 3D orientation) to be represented in a periodic 2D square map. The combination of three such orthogonal mappings into a single RGB (red–green–blue) image provides a compact periodic representation of any set of orientations. Square torus representations of five different orientation sampling methods are compared and analyzed in terms of the Rieszsenergies that quantify the uniformity of the samplings. The effect of crystallographic symmetry on the square torus map is analyzed in terms of the Rodrigues fundamental zones for the rotational symmetry groups. The paper concludes with example representations of important texture components in cubic and hexagonal materials. The new RGB representation provides a convenient and compact way of generating training data for the automated analysis of material textures by means of neural networks.  more » « less
Award ID(s):
2203378
PAR ID:
10529570
Author(s) / Creator(s):
Publisher / Repository:
International Union for Crystallography
Date Published:
Journal Name:
Journal of Applied Crystallography
Volume:
57
Issue:
3
ISSN:
1600-5767
Page Range / eLocation ID:
638 to 648
Subject(s) / Keyword(s):
orientation distribution functions texture symmetry quaternions Clifford torus
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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