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)

Return the angle of this quaternion, in requested unit

Parameters:

in_rad (bool)

Return type:

float

conj()

Returns the conjugate of the quaternion

Return type:

Quaternion

copy()

Return a copy of itself

Return type:

Quaternion

norm()

Returns the norm of this quaternion

Return type:

float

rotate(v)

Rotate a vector v by this quaternion

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

$${\mathbf{v}}^{\prime }=\mathbf{q}\mathbf{v}{\mathbf{q}}^{\ast }$$

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

$$\begin{array}{r}\mathbf{t}=2\mathbf{q}\text{cross}\mathbf{v}\\ {\mathbf{v}}^{\prime }=\mathbf{v}+q_w\mathbf{t}+\mathbf{q}\text{cross}\mathbf{t}\end{array}$$

Return type:

ndarray

property degree: float

Returns the angle associated with this quaternion (in degrees)

property radian: float

Returns the angle associated with this quaternion (in radians)