Transformation

class compas.geometry.Transformation

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:

matrixlist[list[float]], optional

The 4x4 transformation matrix.

namestr, optional

The name of the transformation.

Attributes:

scalecompas.geometry.Scale, read-only

The scale component of the transformation matrix.

shearcompas.geometry.Shear, read-only

The shear component of the transformation matrix.

rotationcompas.geometry.Rotation, read-only

The rotation component of the transformation matrix.

translationcompas.geometry.Translation, read-only

The translation component of the transformation matrix.

projectioncompas.geometry.Projection, read-only

The projection component of the transformation matrix.

translation_vectorcompas.geometry.Vector, read-only

The translation component of the transformation matrix as a translation vector.

basis_vectorstuple[compas.geometry.Vector, compas.geometry.Vector], read-only

The basis vectors from the rotation component of the transformation matrix.

listlist[float], read-only

Flattens the 4x4 transformation matrix into a list of 16 numbers.

determinantfloat, 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

ToString	Converts the instance to a string.
from_json	Construct an object of this type from a JSON file.
from_jsonstring	Construct an object of this type from a JSON string.
sha256	Compute a hash of the data for comparison during version control using the sha256 algorithm.
to_json	Convert an object to its native data representation and save it to a JSON file.
to_jsonstring	Convert an object to its native data representation and save it to a JSON string.
validate_data	Validate the data against the object's data schema.