Rotation

class compas.geometry.Rotation

Bases: Transformation

Class representing a rotation transformation.

The class contains methods for converting rotation matrices to axis-angle representations, Euler angles, quaternion and basis vectors.

Parameters:

matrixlist[list[float]], optional

A 4x4 matrix (or similar) representing a rotation.

checkbool, optional

If True, the provided matrix will be checked for validity.

namestr, optional

The name of the transformation.

Raises:

ValueError

If check is True and the provided transformation matrix is not a rotation.

Examples

>>> from compas.geometry import Frame
>>> f1 = Frame([0, 0, 0], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> R = Rotation.from_frame(f1)
>>> args = False, "xyz"
>>> alpha, beta, gamma = R.euler_angles(*args)
>>> xaxis, yaxis, zaxis = [1, 0, 0], [0, 1, 0], [0, 0, 1]
>>> Rx = Rotation.from_axis_and_angle(xaxis, alpha)
>>> Ry = Rotation.from_axis_and_angle(yaxis, beta)
>>> Rz = Rotation.from_axis_and_angle(zaxis, gamma)
>>> f2 = Frame.worldXY()
>>> f1 == f2.transformed(Rx * Ry * Rz)
True

Attributes:

quaternioncompas.geometry.Quaternion, read-only

The quaternion from the rotation.

axis_and_angletuple[compas.geometry.Vector, float], read-only

The axis and the angle of the rotation.

axis_angle_vectorcompas.geometry.Vector, read-only

The axis-angle vector of the rotation.

basis_vectorstuple[compas.geometry.Vector, compas.geometry.Vector], read-only

The basis vectors of the rotation.

Methods

euler_angles	Returns Euler angles from the rotation according to specified axis sequence and rotation type.
from_axis_and_angle	Construct a rotation transformation from a rotation axis and an angle and an optional point of rotation.
from_axis_angle_vector	Construct a rotation transformation from an axis-angle vector.
from_basis_vectors	Construct a rotation transformation from basis vectors (= orthonormal vectors).
from_euler_angles	Construct a rotation transformation from Euler angles.
from_frame	Construct a rotation transformationn from world XY to frame.
from_quaternion	Construct a rotation transformation` from quaternion coefficients.

Inherited Methods

ToString	Converts the instance to a string.
concatenate	Concatenate another transformation to this transformation.
concatenated	Concatenate two transformations into one Transformation.
copy	Returns a copy of the transformation.
decomposed	Decompose the Transformation into its components.
from_change_of_basis	Construct a change of basis transformation between two frames.
from_frame_to_frame	Construct a transformation between two frames.
from_json	Construct an object of this type from a JSON file.
from_jsonstring	Construct an object of this type from a JSON string.
from_list	Creates a transformation from a list of 16 numbers.
from_matrix	Creates a transformation from a list[list[float]] object.
inverse	Returns the inverse transformation.
invert	Invert this transformation.
inverted	Returns the inverse transformation.
sha256	Compute a hash of the data for comparison during version control using the sha256 algorithm.
to_json	Convert an object to its native data representation and save it to a JSON file.
to_jsonstring	Convert an object to its native data representation and save it to a JSON string.
transpose	Transpose the matrix of this transformation.
transposed	Create a transposed copy of this transformation.
validate_data	Validate the data against the object's data schema.