pyrobopath.toolpath.path.transform.Rotation#

class pyrobopath.toolpath.path.transform.Rotation(orient: List[float] | Tuple[float, float, float, float] | ndarray[Tuple[Literal[4]], dtype[floating]] | quaternion | None = None)[source]#

Bases: object

A rotation class that implements spatial rotations on members of the group SO3 (Special Orthogonal)

This class internally represents a rotation as a numpy-quaternion. The aim is to make interpolation as fast as possible – as this is used a lot throughout pyrobopath

Class method constructors facilitate constructing rotations with common SO3 parameterizations (i.e. axis rotations, quaternions, homogeneous transformations, Euler angles.)

Parameters:

orient (Quat) – The rotational component as {w, x, y, z} (default: [1, 0, 0, 0])

Methods

Quaternion

Construct a new SO(3) rotation instance from Quaternion

Rx

Construct a new SO(3) rotation from X-axis rotation

Ry

Construct a new SO(3) rotation from Y-axis rotation

Rz

Construct a new SO(3) rotation from Z-axis rotation

almost_equal

copy

interp

Interpolate between SO(3) instances

inv

Find the inverse transformation of the SE(3) instance

Attributes

matrix

The 3x3 rotation matrix

quat

Get the rotation as a quaternion
classmethod Quaternion(w: float, x: float, y: float, z: float) → Rotation[source]#

Construct a new SO(3) rotation instance from Quaternion

q = [w, x, y, z]

Parameters:

  • w (float) – the real component

  • x (float) – the x component of the imaginary vector

  • y (float) – the y component of the imaginary vector

  • z (float) – the z component of the imaginary vector

Returns:

SE(3) rotation

Return type:

Pose instance

classmethod Rx(theta: float) → Rotation[source]#

Construct a new SO(3) rotation from X-axis rotation

Parameters:

θ (float or array_like) – rotation angle about the X-axis

Returns:

SE(3) rotation

Return type:

SE3 instance

classmethod Ry(theta: float) → Rotation[source]#

Construct a new SO(3) rotation from Y-axis rotation

Parameters:

θ (float or array_like) – rotation angle about the Y-axis

Returns:

SE(3) rotation

Return type:

SE3 instance

classmethod Rz(theta: float) → Rotation[source]#

Construct a new SO(3) rotation from Z-axis rotation

Parameters:

θ (float or array_like) – rotation angle about the Z-axis

Returns:

SE(3) rotation

Return type:

SE3 instance

interp(other: Rotation, s: float) → Rotation[source]#

Interpolate between SO(3) instances

Parameters:

  • other (SO3) – the ending orientation at s = 1.0

  • s (float) – the interpolation variable s in [0, 1]

Returns:

the SO(3) instances interpolated at value s

Return type:

SO(3)

inv() → Rotation[source]#

Find the inverse transformation of the SE(3) instance

Returns:

SE(3) inverse

Return type:

SE3

property matrix: ndarray[Tuple[Literal[3], Literal[3]], dtype[floating]]#

The 3x3 rotation matrix

Returns:

An array view of the 3x3 rotation matrix

Return type:

R3x3

property quat: quaternion#

Get the rotation as a quaternion

Returns:

The rotation as a quaternion

Return type:

quat.quaternion