Four-dimensional objects.

In a simplified sense, quaternions are an extension of the concept of complex numbers, represented by \(a + bi + cj + dk\) where \(i\), \(j\), and \(k\) are quaternion units and \(i^2 = j^2 = k^2 = ijk = -1\). For further reference see the Wikipedia article.

Unit quaternions are efficient objects for representing rotations, and hence orientations.


von_mises(x, alpha[, reference])

A vastly simplified Von Mises-Fisher distribution calculation.

get_proper_groups(Gl, Gr)

Return the appropriate groups for the asymmetric domain calculation.

get_distinguished_points(s1[, s2])

Return points symmetrically equivalent to identity with respect to s1 and s2.

get_point_group(space_group_number[, proper])

Map a space group number to its (proper) point group.



Basic quaternion object.


Transformations of three-dimensional space, leaving the origin in place.

Misorientation(data[, symmetry])

Misorientation object.

Orientation(data[, symmetry])

Orientations represent misorientations away from a reference of identity and have only one associated symmetry.


A set of Rotation which are the normals of an orientation region.


The set of rotations comprising a point group.