AffineTransformation#

class biotite.structure.AffineTransformation(center_translation, rotation, target_translation)[source]#

Bases: object

An affine transformation, consisting of translations and a rotation.

Parameters:
center_translationndarray, shape=(3,) or shape=(m,3), dtype=float

The translation vector for moving the centroid into the origin.

rotationndarray, shape=(3,3) or shape=(m,3,3), dtype=float

The rotation matrix.

target_translationndarray, shape=(m,3), dtype=float

The translation vector for moving the structure onto the fixed one.

Attributes:
center_translation, rotation, target_translationndarray

Same as the parameters. The dimensions are always expanded to (m,3) or (m,3,3), respectively.

apply(atoms)#

Apply this transformation on the given structure.

Parameters:
atomsAtomArray or AtomArrayStack or ndarray, shape(n,), dtype=float or ndarray, shape(m,n), dtype=float

The structure to apply the transformation on.

Returns:
transformedAtomArray or AtomArrayStack or ndarray, shape(n,), dtype=float or ndarray, shape(m,n), dtype=float

A copy of the atoms structure, with transformations applied. Only coordinates are returned, if coordinates were given in atoms.

Examples

>>> coord = np.arange(15).reshape(5,3)
>>> print(coord)
[[ 0  1  2]
 [ 3  4  5]
 [ 6  7  8]
 [ 9 10 11]
 [12 13 14]]
>>> # Rotates 90 degrees around the z-axis
>>> transform = AffineTransformation(
...     center_translation=np.array([0,0,0]),
...     rotation=np.array([
...         [0, -1,  0],
...         [1,  0,  0],
...         [0,  0,  1]
...     ]),
...     target_translation=np.array([0,0,0])
... )
>>> print(transform.apply(coord))
[[ -1.   0.   2.]
 [ -4.   3.   5.]
 [ -7.   6.   8.]
 [-10.   9.  11.]
 [-13.  12.  14.]]
as_matrix()#

Get the translations and rotation as a combined 4x4 transformation matrix.

Multiplying this matrix with coordinates in the form (x, y, z, 1) will apply the same transformation as apply() to coordinates in the form (x, y, z).

Returns:
transformation_matrixndarray, shape=(m,4,4), dtype=float

The transformation matrix. m is the number of models in the transformation.

Examples

>>> coord = np.arange(15).reshape(5,3)
>>> print(coord)
[[ 0  1  2]
 [ 3  4  5]
 [ 6  7  8]
 [ 9 10 11]
 [12 13 14]]
>>> # Rotates 90 degrees around the z-axis
>>> transform = AffineTransformation(
...     center_translation=np.array([0,0,0]),
...     rotation=np.array([
...         [0, -1,  0],
...         [1,  0,  0],
...         [0,  0,  1]
...     ]),
...     target_translation=np.array([0,0,0])
... )
>>> print(transform.apply(coord))
[[ -1.   0.   2.]
 [ -4.   3.   5.]
 [ -7.   6.   8.]
 [-10.   9.  11.]
 [-13.  12.  14.]]
>>> # Use a 4x4 matrix for transformation as alternative
>>> coord_4 = np.concatenate([coord, np.ones((len(coord), 1))], axis=-1)
>>> print(coord_4)
[[ 0.  1.  2.  1.]
 [ 3.  4.  5.  1.]
 [ 6.  7.  8.  1.]
 [ 9. 10. 11.  1.]
 [12. 13. 14.  1.]]
>>> print((transform.as_matrix()[0] @ coord_4.T).T)
[[ -1.   0.   2.   1.]
 [ -4.   3.   5.   1.]
 [ -7.   6.   8.   1.]
 [-10.   9.  11.   1.]
 [-13.  12.  14.   1.]]
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