Quaternion

class gala.coordinates.Quaternion(wxyz)

Bases: object

Quaternions for 3D rotations.

This is largely thanks to Jake Vanderplas: https://jakevdp.github.io/blog/2012/11/24/simple-3d-visualization-in-matplotlib/

Parameters:

wxyz : array_like

A quaternion in vector representation. Order is assumed to be (w,x,y,z).

Attributes Summary

rotation_matrix	Compute the rotation matrix of the (normalized) quaternion.
v_theta	Return the (v, theta) equivalent of the (normalized) quaternion.

Methods Summary

from_v_theta(v, theta)	Create a quaternion from unit vector v and rotation angle theta.
random()	Randomly sample a Quaternion from a distribution uniform in 3D rotation angles.

Attributes Documentation

rotation_matrix

Compute the rotation matrix of the (normalized) quaternion.

Returns:

R : ndarray

A 3 by 3 rotation matrix (has shape (3,3)).

v_theta

Return the (v, theta) equivalent of the (normalized) quaternion.

Returns:

v : float

theta : float

Methods Documentation

classmethod from_v_theta(v, theta)

Create a quaternion from unit vector v and rotation angle theta.

Returns:

q : gala.coordinates.Quaternion

A Quaternion instance.

classmethod random()

Randomly sample a Quaternion from a distribution uniform in 3D rotation angles.

https://www-preview.ri.cmu.edu/pub_files/pub4/kuffner_james_2004_1/kuffner_james_2004_1.pdf

Returns:

q : gala.coordinates.Quaternion

A randomly sampled Quaternion instance.