Transformation

class compas.geometry.Transformation(matrix=None)[source]

Bases: Data

Class representing a general 4x4 transformation matrix.

It is the base class for transformations like Rotation, Translation, Scale, Reflection, Projection and Shear.

The class allows to concatenate Transformations by multiplication, to calculate the inverse transformation and to decompose a transformation into its components of rotation, translation, scale, shear, and perspective. The matrix follows the row-major order, such that translation components x, y, z are in the right column of the matrix, i.e. M[0][3], M[1][3], M[2][3] = x, y, z.

Parameters

matrix (list[list[float]], optional) – The 4x4 transformation matrix.

Attributes

scale (compas.geometry.Scale, read-only) – The scale component of the transformation matrix.
shear (compas.geometry.Shear, read-only) – The shear component of the transformation matrix.
rotation (compas.geometry.Rotation, read-only) – The rotation component of the transformation matrix.
translation (compas.geometry.Translation, read-only) – The translation component of the transformation matrix.
projection (compas.geometry.Projection, read-only) – The projection component of the transformation matrix.
translation_vector (compas.geometry.Vector, read-only) – The translation component of the transformation matrix as a translation vector.
basis_vectors (tuple[compas.geometry.Vector, compas.geometry.Vector], read-only) – The basis vectors from the rotation component of the transformation matrix.
list (list[float], read-only) – Flattens the 4x4 transformation matrix into a list of 16 numbers.
determinant (float, read-only) – The determinant of the matrix of the transformation.

Examples

>>> from compas.geometry import Frame
>>> f1 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
>>> T = Transformation.from_frame(f1)
>>> Sc, Sh, R, Tl, P = T.decomposed()
>>> Tinv = T.inverse()

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_euler_angles`	Construct a transformation from a rotation represented by Euler angles.
`from_frame`	Construct a transformation from world XY to frame.
`from_frame_to_frame`	Construct a transformation between two frames.
`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.
`transpose`	Transpose the matrix of this transformation.
`transposed`	Create a transposed copy of this transformation.

Inherited Methods

`from_data`	Construct an object of this type from the provided data.
`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.
`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.
`validate_data`	Validate the object's data against its data schema.
`validate_json`	Validate the object's data against its json schema.

Transformation

COMPAS