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  Consistent representations of and conversions between 3D rotations

Rowenhorst, D., Rollett, A., Rohrer, G., Groeber, M., Jackson, M., Konijnenberg, P. J., et al. (2015). Consistent representations of and conversions between 3D rotations. Modeling and Simulations in Materials Science and Engineering, 23(8): 083501. doi:10.1088/0965-0393/23/8/083501.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0028-954C-2 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0028-9554-E
Genre: Journal Article

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 Creators:
Rowenhorst, David1, Author
Rollett, Andrew2, Author
Rohrer, Gregory2, Author
Groeber, Mike3, Author
Jackson, Michael4, Author
Konijnenberg, Peter Joachim5, Author              
De Graef, Marc2, Author
Affiliations:
1The U.S. Naval Research Laboratory, 4555 Overlook Ave SW, Washington, DC 20375, USA, ou_persistent22              
2Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA, ou_persistent22              
3Air Force Research Laboratory, Materials & Manufacturing Directorate, Wright Patterson AFB, OH 45433, USA, ou_persistent22              
4BlueQuartz Software, 400 S. Pioneer Blvd, Springboro, OH 45066, USA, ou_persistent22              
5Microscopy and Diffraction, Microstructure Physics and Alloy Design, Max-Planck-Institut für Eisenforschung GmbH, Max Planck Society, ou_1863391              

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Free keywords: Tutorial
 Abstract: 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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Language(s): eng - English
 Dates: 2015-08-192015-10-05
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: DOI: 10.1088/0965-0393/23/8/083501
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Title: Modeling and Simulations in Materials Science and Engineering
Source Genre: Journal
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Publ. Info: -
Pages: 22 Volume / Issue: 23 (8) Sequence Number: 083501 Start / End Page: - Identifier: -