WikiSysop: Created page with "== Citation == Urzhumtseva, Ludmila / Urzhumtsev, Alexandre. py_convrot: rotation conventions, to understand and to apply. 2019. Journal of Applied Crystallography, Vol. 52, No. 4, p. 869-881 == Abstract == Rotation is a core crystallographic operation. Two sets of Cartesian coordinates of each point of a rotated object, those before and after rotation, are linearly related, and the coefficients of these linear combinations can be represented in matrix form. This 3 3..."

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Created page with "== Citation == Urzhumtseva, Ludmila / Urzhumtsev, Alexandre. py_convrot: rotation conventions, to understand and to apply. 2019. Journal of Applied Crystallography, Vol. 52, No. 4, p. 869-881 == Abstract == Rotation is a core crystallographic operation. Two sets of Cartesian coordinates of each point of a rotated object, those before and after rotation, are linearly related, and the coefficients of these linear combinations can be represented in matrix form. This 3 3..."

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== Citation ==

Urzhumtseva, Ludmila / Urzhumtsev, Alexandre. py_convrot: rotation conventions, to understand and to apply. 2019. Journal of Applied Crystallography, Vol. 52, No. 4, p. 869-881

== Abstract ==

Rotation is a core crystallographic operation. Two sets of Cartesian coordinates
of each point of a rotated object, those before and after rotation, are linearly
related, and the coefficients of these linear combinations can be represented in
matrix form. This 3 3 matrix is unique for all points and thus describes
unambiguously a particular rotation. However, its nine elements are mutually
dependent and are not interpretable in a straightforward way. To describe
rotations by independent and comprehensible parameters, crystallographic
software usually refers to Euler or to polar angles. In crystallography and cryoelectron
microscopy, there exists a large choice of conventions, making direct
comparison of rotation parameters difficult and sometimes confusing. The
program py_convrot, written in Python, is a converter of parameters describing
rotations. In particular, it deals with all possible choices of polar angles and with
all kinds of Euler angles, including all choices of rotation axes and rotation
directions. Using a menu, a user can build their own rotation parameterization;
its action can be viewed with an interactive graphical tool, Demo. The tables in
this article and the extended help pages of the program describe details of these
parameterizations and the decomposition of rotation matrices into all types of
parameters. The program allows orthogonalization conventions and symmetry
operations to be taken into account. This makes the program and its supporting
materials both an illustrative teaching material, especially for non-specialists in
mathematics and computing, and a tool for practical use.

== Keywords ==

== Links ==

https://journals.iucr.org/j/issues/2019/04/00/gj5227/index.html

== Related software ==

== Related methods ==

== Comments ==

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