# quaternion#

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.

Functions

 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.

Classes

 Quaternion([data]) Basic quaternion object. Rotation(data) 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. Symmetry(data) The set of rotations comprising a point group.