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

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.

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_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_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_frame_to_frame(frame_from, frame_to)

Computes a transformation between two frames.

from_json(filepath)

Construct an object from serialized data contained in a JSON file.

from_jsonstring(string)

Construct an object from serialized data contained in a JSON string.

from_list(numbers)

Creates a Transformation from a list of 16 numbers.

from_matrix(matrix)

Creates a Transformation from a 4x4 matrix-like object.

from_quaternion(quaternion)

Calculates a Rotation from quaternion coefficients.

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[, pretty])

Serialize the data representation of an object to a JSON file.

to_jsonstring([pretty])

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).