Rotation

class compas.geometry.Rotation(matrix=None, check=True)[source]

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

matrix (list[list[float]], optional) – A 4x4 matrix (or similar) representing a rotation.

Attributes

quaternion (compas.geometry.Quaternion, read-only) – The quaternion from the rotation.
axis_and_angle (tuple[compas.geometry.Vector, float], read-only) – The axis and the angle of the rotation.
axis_angle_vector (compas.geometry.Vector, read-only) – The axis-angle vector of the rotation.
basis_vectors (tuple[compas.geometry.Vector, compas.geometry.Vector], read-only) – The basis vectors of the rotation.

Raises

ValueError – If the default constructor is used, 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

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

`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_data`	Construct an object of this type from the provided data.
`from_frame_to_frame`	Construct a transformation between two frames.
`from_json`	Construct an object from serialized data contained in a JSON file.
`from_jsonstring`	Construct an object from serialized data contained in 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.
`to_data`	Convert an object to its native data representation.
`to_json`	Serialize the data representation of an object to a JSON file.
`to_jsonstring`	Serialize the data representation of an object to a JSON string.
`transpose`	Transpose the matrix of this transformation.
`transposed`	Create a transposed copy of this transformation.
`validate_data`	Validate the object's data against its data schema.
`validate_json`	Validate the object's data against its json schema.

Rotation

COMPAS