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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.
