Rotations¶

class py123d.geometry.Quaternion[source]¶

Represents a quaternion for 3D rotations.

Examples

>>> import numpy as np
>>> from py123d.geometry import Quaternion
>>> quat = Quaternion(1.0, 0.0, 0.0, 0.0)
>>> quat.qw
1.0
>>> quat.qx
0.0
>>> quat.array
array([1.0, 0.0, 0.0, 0.0])
>>> quat.rotation_matrix
array([[1., 0., 0.],
       [0., 1., 0.],
       [0., 0., 1.]])

Public Data Attributes:

`qw`	The scalar component of the quaternion.
`qx`	The x component of the quaternion.
`qy`	The y component of the quaternion.
`qz`	The z component of the quaternion.
`array`	The numpy array of shape (4,) containing the quaternion [qw, qx, qy, qz], indexed by `QuaternionIndex`.
`pyquaternion`	The pyquaternion.Quaternion representation of the quaternion.
`euler_angles`	The `EulerAngles` representation of the quaternion.
`rotation_matrix`	Returns the 3x3 rotation matrix representation of the quaternion.

Inherited from ArrayMixin

`array`	The array representation of the geometric entity.
`shape`	Return the shape of the array.

Public Methods:

`from_array`(arr[, copy])	Constructs a Quaternion from a numpy array.
`from_rotation_matrix`(rotation_matrix)	Constructs a Quaternion from a 3x3 rotation matrix.
`from_euler_angles`(euler_angles)	Constructs a Quaternion from Euler angles.

Inherited from ArrayMixin

`from_array`(array[, copy])	Create an instance from a NumPy array.
`from_list`(values)	Create an instance from a list of values.
`tolist`()	Convert the array to a Python list.
`to_list`()	Convert the array to a Python list.
`copy`()	Return a copy of the object with a copied array.

__init__(qw, qx, qy, qz)[source]¶

Initialize Quaternion with components.

Parameters:

qw (float) – The scalar component of the quaternion.
qx (float) – The x component of the quaternion.
qy (float) – The y component of the quaternion.
qz (float) – The z component of the quaternion.

classmethod from_array(arr, copy=True)[source]¶

Constructs a Quaternion from a numpy array.

Parameters:

arr (ndarray[tuple[Any, ...], dtype[float64]]) – A 1D numpy array of shape (4,) containing the quaternion components [qw, qx, qy, qz].
copy (bool) – Whether to copy the array data, defaults to True.

Return type:

Quaternion

Returns:

A Quaternion instance.

classmethod from_rotation_matrix(rotation_matrix)[source]¶

Constructs a Quaternion from a 3x3 rotation matrix.

Parameters:: rotation_matrix (ndarray[tuple[Any, ...], dtype[float64]]) – A 3x3 numpy array representing the rotation matrix.
Return type:: Quaternion
Returns:: A Quaternion instance.

classmethod from_euler_angles(euler_angles)[source]¶

Constructs a Quaternion from Euler angles. NOTE: The rotation order is intrinsic Z-Y’-X’’ (yaw-pitch-roll).

Parameters:: euler_angles (EulerAngles) – An EulerAngles instance representing the Euler angles.
Return type:: Quaternion
Returns:: A Quaternion instance.

property qw: float¶: The scalar component of the quaternion.

property qx: float¶: The x component of the quaternion.

property qy: float¶: The y component of the quaternion.

property qz: float¶: The z component of the quaternion.

property array: ndarray[tuple[Any, ...], dtype[float64]]¶: The numpy array of shape (4,) containing the quaternion [qw, qx, qy, qz], indexed by QuaternionIndex.

property pyquaternion: Quaternion¶: The pyquaternion.Quaternion representation of the quaternion.

property euler_angles: EulerAngles¶: The EulerAngles representation of the quaternion.

property rotation_matrix: ndarray[tuple[Any, ...], dtype[float64]]¶: Returns the 3x3 rotation matrix representation of the quaternion.

copy()¶

Return a copy of the object with a copied array.

Return type:: ArrayMixin

classmethod from_list(values)¶

Create an instance from a list of values.

Return type:: Self
Parameters:: values (list)

property shape: tuple¶: Return the shape of the array.

to_list()¶

Convert the array to a Python list.

Return type:: list

tolist()¶

Convert the array to a Python list.

Return type:: list

class py123d.geometry.EulerAngles[source]¶

Class to represent 3D rotation using Euler angles (roll, pitch, yaw) in radians.

Examples

>>> import numpy as np
>>> from py123d.geometry import EulerAngles
>>> euler_angles = EulerAngles(roll=0.0, pitch=0.0, yaw=np.pi)
>>> euler_angles.roll
0.0
>>> euler_angles.yaw
3.141592653589793
>>> euler_angles.array
array([0.0, 0.0, 3.14159265])
>>> EulerAngles.from_rotation_matrix(euler_angles.rotation_matrix).yaw
3.141592653589793

Notes

The rotation order is intrinsic Z-Y’-X’’ (yaw-pitch-roll) [1].

References

Public Data Attributes:

`roll`	The roll (x-axis rotation) angle in radians.
`pitch`	The pitch (y-axis rotation) angle in radians.
`yaw`	The yaw (z-axis rotation) angle in radians.
`array`	Converts the EulerAngles instance to a numpy array of shape (3,), indexed by `EulerAnglesIndex`.
`quaternion`	The `Quaternion` representation of the Euler angles.
`rotation_matrix`	Returns the 3x3 rotation matrix representation of the Euler angles.

Inherited from ArrayMixin

`array`	The array representation of the geometric entity.
`shape`	Return the shape of the array.

Public Methods:

`from_array`(array[, copy])	Constructs a `EulerAngles` from a numpy array of shape (3,) representing, indexed by `EulerAnglesIndex`.
`from_rotation_matrix`(rotation_matrix)	Constructs a `EulerAngles` from a 3x3 rotation matrix.

Inherited from ArrayMixin

`from_array`(array[, copy])	Create an instance from a NumPy array.
`from_list`(values)	Create an instance from a list of values.
`tolist`()	Convert the array to a Python list.
`to_list`()	Convert the array to a Python list.
`copy`()	Return a copy of the object with a copied array.

__init__(roll, pitch, yaw)[source]¶

Initialize EulerAngles with roll, pitch, yaw angles in radians.

Parameters:

roll (float) – The roll (x-axis rotation) angle in radians.
pitch (float) – The pitch (y-axis rotation) angle in radians.
yaw (float) – The yaw (z-axis rotation) angle in radians.

classmethod from_array(array, copy=True)[source]¶

Constructs a EulerAngles from a numpy array of shape (3,) representing, indexed by EulerAnglesIndex.

Parameters:

array (ndarray[tuple[Any, ...], dtype[float64]]) – Array of shape (3,) representing the euler angles [roll, pitch, yaw].
copy (bool) – Whether to copy the input array. Defaults to True.

Return type:

EulerAngles

Returns:

A EulerAngles instance.

classmethod from_rotation_matrix(rotation_matrix)[source]¶

Constructs a EulerAngles from a 3x3 rotation matrix.

Parameters:: rotation_matrix (ndarray[tuple[Any, ...], dtype[float64]]) – A 3x3 numpy array representing the rotation matrix.
Return type:: EulerAngles
Returns:: A EulerAngles instance.

property roll: float¶: The roll (x-axis rotation) angle in radians.

property pitch: float¶: The pitch (y-axis rotation) angle in radians.

property yaw: float¶: The yaw (z-axis rotation) angle in radians.

property array: ndarray[tuple[Any, ...], dtype[float64]]¶: Converts the EulerAngles instance to a numpy array of shape (3,), indexed by EulerAnglesIndex.

property quaternion: Quaternion¶: The Quaternion representation of the Euler angles.

property rotation_matrix: ndarray[tuple[Any, ...], dtype[float64]]¶: Returns the 3x3 rotation matrix representation of the Euler angles.

copy()¶

Return a copy of the object with a copied array.

Return type:: ArrayMixin

classmethod from_list(values)¶

Create an instance from a list of values.

Return type:: Self
Parameters:: values (list)

property shape: tuple¶: Return the shape of the array.

to_list()¶

Convert the array to a Python list.

Return type:: list

tolist()¶

Convert the array to a Python list.

Return type:: list