Transformation

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

Bases: compas.base.Base

The Transformation represents a 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 of list of float, optional) – The 4x4 transformation matrix.

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

`__init__`([matrix])	Construct a transformation from a 4x4 transformation matrix.
`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_euler_angles`(euler_angles[, static, …])	Construct a transformation from a rotation represented by Euler angles.
`from_frame`(frame)	Computes a 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 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).

Transformation

COMPAS