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Three‐dimensional texture visualization approaches: theoretical analysis and examples
Author(s) -
Callahan Patrick G.,
Echlin McLean,
Pollock Tresa M.,
Singh Saransh,
De Graef Marc
Publication year - 2017
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576717001157
Subject(s) - stereographic projection , euler's formula , orientation (vector space) , visualization , euler angles , point (geometry) , homogeneous space , texture (cosmology) , computer science , set (abstract data type) , tessellation (computer graphics) , planar , space (punctuation) , computer graphics (images) , geometry , mathematics , artificial intelligence , mathematical analysis , image (mathematics) , programming language , operating system
Crystallographic textures are commonly represented in terms of Euler angle triplets and contour plots of planar sections through Euler space. In this paper, the basic theory is provided for the creation of alternative orientation representations using three‐dimensional visualizations. The use of homochoric, cubochoric, Rodrigues and stereographic orientation representations is discussed, and illustrations are provided of fundamental zones for all rotational point‐group symmetries. A connection is made to the more traditional Euler space representations. An extensive set of three‐dimensional visualizations in both standard and anaglyph movies is available.