Rotation

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

Bases: compas.geometry.transformations.transformation.Transformation

Create a rotation transformation.

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

Parameters: matrix (4x4 matrix-like, optional) – A 4x4 matrix (or similar) representing a 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

Attributes

`axis_and_angle`	Returns the axis and the angle of the `Rotation`.
`axis_angle_vector`	Returns the axis-angle vector of the `Rotation`.
`basis_vectors`	Returns the basis vectors of the `Rotation`.
`quaternion`	Returns the Quaternion from the `Rotation`.

Inherited Attributes

`DATASCHEMA`	The schema of the data of this object.
`JSONSCHEMA`	The schema of the JSON representation of the data of this object.
`JSONSCHEMANAME`
`data`	Return a `Transformation` object's to a data dict.
`determinant`	The determinant of the matrix of the transformation.
`dtype`	The type of the object in the form of a '2-level' import and a class name.
`guid`	The globally unique identifier of the object.
`jsondefinitions`	Reusable schema definitions.
`jsonstring`	The representation of the object data in JSON format.
`jsonvalidator`	JSON schema validator for draft 7.
`list`	Flattens the 4x4 transformation matrix into a list of 16 numbers.
`name`	The name of the object.
`projection`	The projection component of the transformation matrix.
`rotation`	The rotation component of the transformation matrix.
`scale`	The scale component of the transformation matrix.
`shear`	The shear component of the transformation matrix.
`translation`	The translation component of the transformation matrix.
`translation_vector`

Methods

`euler_angles`	Returns Euler angles from the `Rotation` according to specified axis sequence and rotation type.
`from_axis_and_angle`	Calculates a `Rotation` from a rotation axis and an angle and an optional point of rotation.
`from_axis_angle_vector`	Calculates a `Rotation` from an axis-angle vector.
`from_basis_vectors`	Creates a `Rotation` from basis vectors (= orthonormal vectors).
`from_euler_angles`	Calculates a `Rotation` from Euler angles.
`from_frame`	Computes the rotational transformation from world XY to frame.
`from_quaternion`	Calculates a `Rotation` 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 `Scale`, `Shear`, `Rotation`, `Translation` and `Projection` components.
`from_change_of_basis`	Computes a change of basis transformation between two frames.
`from_data`	Creates a `Transformation` from a data dict.
`from_frame_to_frame`	Computes 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 4x4 matrix-like object.
`inverse`	Returns the inverse transformation.
`invert`	Invert this transformation.
`inverted`	Returns the inverse transformation.
`to_data`	Convert a `Transformation` object to a data dict.
`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 (self.DATASCHEMA).
`validate_json`	Validate the object's data against its json schema (self.JSONSCHEMA).

Rotation

COMPAS