Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Journal Article

Consistent representations of and conversions between 3D rotations


Konijnenberg,  Peter Joachim
Microscopy and Diffraction, Microstructure Physics and Alloy Design, Max-Planck-Institut für Eisenforschung GmbH, Max Planck Society;

External Resource
No external resources are shared
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available

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.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0028-954C-2
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.