sisl.Quaternion

class sisl.Quaternion

Bases: object

Quaternion object to enable easy rotational quantities.

Parameters:

*args – For 1 argument, it is the length 4 vector describing the quaternion. For 2 arguments, it is the angle, and vector.
rad – when passing two arguments, for angle and vector, the rad value decides which unit angle is in, for rad=True it is in radians. Otherwise it will be in degrees.

Examples

Construct a quaternion with angle 45°, all 3 are equivalent:

>>> q1 = Quaternion(45, [1, 2, 3], rad=False)
>>> q2 = Quaternion(np.pi/4, [1, 2, 3], rad=True)
>>> q3 = Quaternion([1, 2, 3], 45, rad=False)

If you have the full quaternion complex number, one can also instantiate it directly without having to consider angles:

>>> q = Quaternion([1, 2, 3, 4])

Methods

`angle`([in_rad])	Return the angle of this quaternion, in requested unit
`conj`()	Returns the conjugate of the quaternion
`copy`()	Return a copy of itself
`norm`()	Returns the norm of this quaternion
`rotate`(v)	Rotate a vector v by this quaternion

Attributes

`degree`	Returns the angle associated with this quaternion (in degrees)
`radian`	Returns the angle associated with this quaternion (in radians)

angle(in_rad=True)[source]

Return the angle of this quaternion, in requested unit

Returns the conjugate of the quaternion

Return a copy of itself

Returns the norm of this quaternion

Rotate a vector v by this quaternion

This rotation method uses the fast method which can be expressed as:

\[\mathbf v' = \mathbf q \mathbf v \mathbf q ^*\]

But using a faster approach (more numerically stable), we can use this relation:

\[\begin{split}\mathbf t = 2\mathbf q \cross \mathbf v \\ \mathbf v' = \mathbf v + q_w \mathbf t + \mathbf q \cross \mathbf t\end{split}\]

property degree: float: Returns the angle associated with this quaternion (in degrees)

property radian: float: Returns the angle associated with this quaternion (in radians)