Journal
MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING
Volume 23, Issue 8, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0965-0393/23/8/083501
Keywords
3D rotation; quaternion; crystallography
Funding
- Naval Research Laboratory
- Office of Naval Research [N0001414WX20779]
- National Science Foundation [DMR 1435544]
- Air Force Office of Scientific Research, MURI [FA9550-12-1-0458]
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In materials science the orientation of a crystal lattice is described by means of a rotation relative to an external reference frame. A number of rotation representations are in use, including Euler angles, rotation matrices, unit quaternions, Rodrigues-Frank vectors and homochoric vectors. Each representation has distinct advantages and disadvantages with respect to the ease of use for calculations and data visualization. It is therefore convenient to be able to easily convert from one representation to another. However, historically, each representation has been implemented using a set of often tacit conventions; separate research groups would implement different sets of conventions, thereby making the comparison of methods and results difficult and confusing. This tutorial article aims to resolve these ambiguities and provide a consistent set of conventions and conversions between common rotational representations, complete with worked examples and a discussion of the trade-offs necessary to resolve all ambiguities. Additionally, an open source Fortran-90 library of conversion routines for the different representations is made available to the community.
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