Special Euclidean Groups¶

class py123d.geometry.PoseSE2[source]¶

Class to represents a 2D pose as SE2 (x, y, yaw).

Examples

>>> from py123d.geometry import PoseSE2
>>> pose = PoseSE2(x=1.0, y=2.0, yaw=0.5)
>>> print(pose.x, pose.y, pose.yaw)
1.0 2.0 0.5
>>> print(pose.rotation_matrix)
[[ 0.87758256 -0.47942554]
 [ 0.47942554  0.87758256]]

Public Data Attributes:

`x`	The x-coordinate of the pose.
`y`	The y-coordinate of the pose.
`yaw`	The yaw angle of the pose.
`array`	Pose as numpy array of shape (3,), indexed by `PoseSE2Index`.
`pose_se2`	Returns self to match interface of other pose classes.
`point_2d`	The `Point2D` of the pose, i.e. the translation part.
`vector_2d`	The `Vector2D` translation component of the SE2 pose.
`rotation_matrix`	The 2x2 rotation matrix representation of the pose.
`transformation_matrix`	The 3x3 transformation matrix representation of the pose.
`shapely_point`	The Shapely point representation of the pose.

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 PoseSE2 from a numpy array.
`from_transformation_matrix`(transformation_matrix)	Constructs a PoseSE2 from a 3x3 transformation matrix.
`from_R_t`(rotation, translation)	Constructs a `PoseSE2` from a rotation and a translation.
`identity`()	Constructs an identity PoseSE2.

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__(x, y, yaw)[source]¶

Init PoseSE2 with x, y, yaw coordinates.

Parameters:

x (float) – The x-coordinate.
y (float) – The y-coordinate.
yaw (float) – The yaw angle in radians.

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

Constructs a PoseSE2 from a numpy array.

Parameters:

array (ndarray[tuple[Any, ...], dtype[float64]]) – Array of shape (3,) representing the state [x, y, yaw], indexed by PoseSE2Index.
copy (bool) – Whether to copy the input array. Defaults to True.

Return type:

PoseSE2

Returns:

A PoseSE2 instance.

classmethod from_transformation_matrix(transformation_matrix)[source]¶

Constructs a PoseSE2 from a 3x3 transformation matrix.

Parameters:: transformation_matrix (ndarray[tuple[Any, ...], dtype[float64]]) – A 3x3 numpy array representing the transformation matrix.
Return type:: PoseSE2
Returns:: A PoseSE2 instance.

classmethod from_R_t(rotation, translation)[source]¶

Constructs a PoseSE2 from a rotation and a translation.

Parameters:

rotation (Union[ndarray[tuple[Any, ...], dtype[float64]], float]) – Any implemented representation of a SO2 rotation: - (2, 2) rotation matrix as numpy array, - (1,) numpy array representing the yaw angle in radians.
translation (Union[ndarray[tuple[Any, ...], dtype[float64]], Point2D, Vector2D]) – The translation component: - (2,) numpy array indexed by Vector2DIndex, - Vector2D instance, - Point2D is also accepted for convenience.

Return type:

PoseSE2

Returns:

A PoseSE2 instance.

classmethod identity()[source]¶

Constructs an identity PoseSE2.

Return type:: PoseSE2
Returns:: An identity PoseSE2 instance.

property x: float¶: The x-coordinate of the pose.

property y: float¶: The y-coordinate of the pose.

property yaw: float¶: The yaw angle of the pose.

property array: ndarray[tuple[Any, ...], dtype[float64]]¶: Pose as numpy array of shape (3,), indexed by PoseSE2Index.

property pose_se2: PoseSE2¶: Returns self to match interface of other pose classes.

property point_2d: Point2D¶: The Point2D of the pose, i.e. the translation part.

property vector_2d: Vector2D¶: The Vector2D translation component of the SE2 pose.

property rotation_matrix: ndarray[tuple[Any, ...], dtype[float64]]¶: The 2x2 rotation matrix representation of the pose.

property transformation_matrix: ndarray[tuple[Any, ...], dtype[float64]]¶: The 3x3 transformation matrix representation of the pose.

property shapely_point: Point¶: The Shapely point representation of the pose.

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.PoseSE3[source]¶

Class representing a pose in SE3 space.

Examples

>>> from py123d.geometry import PoseSE3
>>> pose = PoseSE3(x=1.0, y=2.0, z=3.0, qw=1.0, qx=0.0, qy=0.0, qz=0.0)
>>> pose.point_3d
Point3D(array=[1. 2. 3.])
>>> pose.transformation_matrix
array([[1., 0., 0., 1.],
       [0., 1., 0., 2.],
       [0., 0., 1., 3.],
       [0., 0., 0., 1.]])
>>> PoseSE3.from_transformation_matrix(pose.transformation_matrix) == pose
True
>>> print(pose.yaw, pose.pitch, pose.roll)
0.0 0.0 0.0

Public Data Attributes:

`x`	The x-coordinate of the pose.
`y`	The y-coordinate of the pose.
`z`	The z-coordinate of the pose.
`qw`	The w-coordinate of the quaternion, representing the scalar part.
`qx`	The x-coordinate of the quaternion, representing the first component of the vector part.
`qy`	The y-coordinate of the quaternion, representing the second component of the vector part.
`qz`	The z-coordinate of the quaternion, representing the third component of the vector part.
`array`	The numpy array representation of the pose with shape (7,), indexed by `PoseSE3Index`
`pose_se3`	The `PoseSE3` itself.
`pose_se2`	The `PoseSE2` representation of the SE3 pose.
`point_3d`	The `Point3D` representation of the SE3 pose, i.e. the translation part.
`point_2d`	The `Point2D` representation of the SE3 pose, i.e. the translation part.
`vector_3d`	The `Vector3D` translation component of the SE3 pose.
`vector_2d`	The `Vector2D` 2D translation component (x, y) of the SE3 pose.
`shapely_point`	The Shapely point representation, of the translation part of the SE3 pose.
`quaternion`	The `Quaternion` representation of the state's orientation.
`euler_angles`	The `EulerAngles` representation of the state's orientation.
`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.
`rotation_matrix`	Returns the 3x3 rotation matrix representation of the state's orientation.
`transformation_matrix`	Returns the 4x4 transformation matrix representation of the state.
`inverse`	Returns the inverse of the SE3 pose.

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 `PoseSE3` from a numpy array of shape (7,), indexed by `PoseSE3Index`.
`from_transformation_matrix`(transformation_matrix)	Constructs a `PoseSE3` from a 4x4 transformation matrix.
`from_R_t`(rotation, translation)	Constructs a `PoseSE3` from arbitrary rotation and translation representations.
`identity`()	Constructs an identity `PoseSE3`.

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__(x, y, z, qw, qx, qy, qz)[source]¶

Initialize PoseSE3 with x, y, z, qw, qx, qy, qz coordinates.

Parameters:

x (float) – The x-coordinate.
y (float) – The y-coordinate.
z (float) – The z-coordinate.
qw (float) – The w-coordinate of the quaternion, representing the scalar part.
qx (float) – The x-coordinate of the quaternion, representing the first component of the vector part.
qy (float) – The y-coordinate of the quaternion, representing the second component of the vector part.
qz (float) – The z-coordinate of the quaternion, representing the third component of the vector part.

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

Constructs a PoseSE3 from a numpy array of shape (7,), indexed by PoseSE3Index.

Parameters:

array (ndarray[tuple[Any, ...], dtype[float64]]) – Array of shape (7,) representing the state [x, y, z, qw, qx, qy, qz].
copy (bool) – Whether to copy the input array. Defaults to True.

Return type:

PoseSE3

Returns:

A PoseSE3 instance.

classmethod from_transformation_matrix(transformation_matrix)[source]¶

Constructs a PoseSE3 from a 4x4 transformation matrix.

Parameters:: transformation_matrix (ndarray[tuple[Any, ...], dtype[float64]]) – A 4x4 numpy array representing the transformation matrix.
Return type:: PoseSE3
Returns:: A PoseSE3 instance.

classmethod from_R_t(rotation, translation)[source]¶

Constructs a PoseSE3 from arbitrary rotation and translation representations.

Parameters:

rotation (Union[ndarray[tuple[Any, ...], dtype[float64]], Quaternion, EulerAngles]) – Any implemented representation of a SO3 rotation: - (3, 3) rotation matrix as numpy array, - (4,) quaternion array indexed by QuaternionIndex, - (3,) euler angles indexed by EulerAnglesIndex, - Quaternion instance, - EulerAngles instance.
translation (Union[ndarray[tuple[Any, ...], dtype[float64]], Point3D, Vector3D]) – The translation component:, - (3,) numpy array indexed by Vector3DIndex, - Vector3D instance, - Point3D is also accepted for convenience. :return: A PoseSE3 instance.

Return type:

PoseSE3

classmethod identity()[source]¶

Constructs an identity PoseSE3.

Return type:: PoseSE3
Returns:: An identity PoseSE3 instance.

property x: float¶: The x-coordinate of the pose.

property y: float¶: The y-coordinate of the pose.

property z: float¶: The z-coordinate of the pose.

property qw: float¶: The w-coordinate of the quaternion, representing the scalar part.

property qx: float¶: The x-coordinate of the quaternion, representing the first component of the vector part.

property qy: float¶: The y-coordinate of the quaternion, representing the second component of the vector part.

property qz: float¶: The z-coordinate of the quaternion, representing the third component of the vector part.

property array: ndarray[tuple[Any, ...], dtype[float64]]¶: The numpy array representation of the pose with shape (7,), indexed by PoseSE3Index

property pose_se3: PoseSE3¶: The PoseSE3 itself.

property pose_se2: PoseSE2¶: The PoseSE2 representation of the SE3 pose.

property point_3d: Point3D¶: The Point3D representation of the SE3 pose, i.e. the translation part.

property point_2d: Point2D¶: The Point2D representation of the SE3 pose, i.e. the translation part.

property vector_3d: Vector3D¶: The Vector3D translation component of the SE3 pose.

property vector_2d: Vector2D¶: The Vector2D 2D translation component (x, y) of the SE3 pose.

property shapely_point: Point¶: The Shapely point representation, of the translation part of the SE3 pose.

property quaternion: Quaternion¶: The Quaternion representation of the state’s orientation.

property euler_angles: EulerAngles¶: The EulerAngles representation of the state’s orientation.

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 rotation_matrix: ndarray[tuple[Any, ...], dtype[float64]]¶: Returns the 3x3 rotation matrix representation of the state’s orientation.

property transformation_matrix: ndarray[tuple[Any, ...], dtype[float64]]¶: Returns the 4x4 transformation matrix representation of the state.

property inverse: PoseSE3¶: Returns the inverse of the SE3 pose.

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