Rotation

class compas.geometry.Rotation(matrix=None)[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

>>> 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`([static, axes])	Returns Euler angles from the `Rotation` according to specified axis sequence and rotation type.
`from_axis_and_angle`(axis, angle[, point])	Calculates a `Rotation` from a rotation axis and an angle and an optional point of rotation.
`from_axis_angle_vector`(axis_angle_vector[, …])	Calculates a `Rotation` from an axis-angle vector.
`from_basis_vectors`(xaxis, yaxis)	Creates a `Rotation` from basis vectors (= orthonormal vectors).
`from_euler_angles`(euler_angles[, static, axes])	Calculates a `Rotation` from Euler angles.
`from_frame`(frame)	Computes the rotational transformation from world XY to frame.
`from_quaternion`(quaternion)	Calculates a `Rotation` from quaternion coefficients.

Inherited Methods

`concatenate`(other)	Concatenate another transformation to this transformation.
`concatenated`(other)	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`(frame_from, frame_to)	Computes a change of basis transformation between two frames.
`from_data`(data)	Creates a `Transformation` from a data dict.
`from_frame_to_frame`(frame_from, frame_to)	Computes a transformation between two frames.
`from_json`(filepath)	Construct an object from serialised data contained in a JSON file.
`from_list`(numbers)	Creates a `Transformation` from a list of 16 numbers.
`from_matrix`(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`(filepath)	Serialize the data representation of an object to a JSON file.
`transpose`()	Transpose the matrix of this transformation.
`transposed`()	Create a transposed copy of this transformation.
`validate_data`()	Validate the data of this object against its data schema (self.DATASCHEMA).
`validate_json`()	Validate the data loaded from a JSON representation of the data of this object against its data schema (self.DATASCHEMA).

Rotation

COMPAS