quaternions package

Submodules

quaternions.quaternion module

A module to hold and work with Quaternions Repo at: https://github.com/mjsobrep/quaternions

class quaternions.quaternion.Quaternion(w, x, y, z, norm_error=1e-08)

Bases: object

A class to hold and work with quaternions

w

The real component of the quaternion

x

The i component of the quaternion

y

The y component of the quaternion

z

The z component of the quaternion

norm_error

The maximum deviation from magnitude 1 for which a quaternion will be considered normalized

__init__(w, x, y, z, norm_error=1e-08)

Constructs a quaternion from individual components

Parameters:

• w (int,float) – The real component of the quaternion
• x (int,float) – The i component of the quaternion
• y (int,float) – The j component of the quaternion
• z (int,float) – The k component of the quaternion
• norm_error (float) – The maximum deviation from magnitude 1 for which a quaternion will be considered normalized

almost_equal(other, delta=1e-08)

Determines whether a quaternion is approximately equal to another using a naive comparison of the 4 values w, x, y, z

Parameters:

• other (Quaternion) – The quaternion with which to test equality
• delta (float) – The error range in which to define two quaternions equal

Returns:

static average(quats, init, threshold=0.01)

conjugate()

Return the conjugate of the quaternion.

Returns:The conjugate of the quaternion

distance(other)

Return the rotational distance between two quaternions.

Parameters:other (Quaternion) – The other Returns:The angular distance between two quaternions

dot(other)

Return the quaternion dot product

Parameters:other (Quaternion) – Quaternion with which to calculate the dot product Returns:The dot product of the two quaternions

classmethod from_axis_angle(axis, angle)

Constructs a quaternion from axis-angle measurements.

Parameters:

• axis – A list of three numbers representing the axis of rotation.
• angle – A single number representing the rotation about the axis in radians

Returns:

The constructed quaternion

classmethod from_euler(values, axes=['x', 'y', 'z'])

Constructs w quaternion using w 3 member list of Euler angles, along with w list defining their rotation sequence. Based off of this: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf

Parameters:

• values (list of numbers) – 3 member list giving the rotations of the Euler angles in radians
• axes (list of chars) – 3 member list specifying the order of rotations

Returns:

The constructed quaternion

classmethod from_matrix(matrix)

Generates a Quaternion from a rotation matrix

Parameters:matrix – A rotation matrix, a list of 3, 3 member lists of numbers Returns:The constructed quaternion

classmethod from_quaternion(quaternion)

Constructs a quaternion from another quaternion.

Parameters:quaternion (Quaternion) – The quaternion to copy Returns:The newly constructed quaternion

classmethod from_rotation_vector(vect)

Constructs a quaternion from a rotation vector.

Parameters:vect – A rotation vector with angle as the magnitude and vector for the vector. Returns:The constructed quaternion

classmethod from_translation(translation)

Generates a quaternion from a translation. Meant to be used along with the dual operator to generate dual quaternions

Parameters:

• translation – A list of three numbers representing the (x,y,z)
• translation –

Returns:

The quaternion created from the translation

get_euler()

Return an euler angle representation of the quaternion. Taken from [wikipedia](https://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles)

Returns:The list of euler angles x,y,z

get_rotation_matrix()

Return the rotation matrix which this quaternion is equivalent to

Returns:The rotation matrix which this quaternion is equivalent to as a list of three lists of three elements each

get_rotation_vector()

get_xyz_vector()

inverse()

Return the inverse of the quaternion. Specifically, this is the multiplicative inverse, such that multiplying the inverse of q by q yields the multiplicative identity.

Returns:The multiplicative inverse of the quaternion

norm()

Return the norm of the quaternion

Returns:The norm of the quaternion

unit()

Return the unit Quaternion

Returns:Unit quaternion

static vector_average(quats)

Module contents