Transformation

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

Bases: compas.data.data.Data

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()

Attributes

DATASCHEMA	The schema of the data of this object.
JSONSCHEMANAME
basis_vectors	The basis vectors from the rotation component of the transformation matrix.
data	Return a Transformation object's to a data dict.
determinant	The determinant of the matrix of the transformation.
list	Flattens the 4x4 transformation matrix into a list of 16 numbers.
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

Inherited Attributes

JSONSCHEMA	The schema of the JSON representation of the data of this object.
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.
name	The name of the object.

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

Inherited Methods

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_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 (self.DATASCHEMA).
validate_json	Validate the object's data against its json schema (self.JSONSCHEMA).