pillow_affine package¶

Submodules¶

pillow_affine.matrix module¶

pillow_affine.matrix.shearing_matrix(angle, clockwise=False)¶

Creates an affine horizontal shearing matrix in the form

\[\begin{split}\mathrm{\mathbf{S}} = \begin{pmatrix} 1 & - \sin \varphi & 0 \\ 0 & \cos \varphi & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} = \begin{pmatrix} a & b & c \\ d & e & f \\ 0 & 0 & 1 \\ \end{pmatrix}\end{split}\]

Parameters

angle (float) – Angle \(\varphi\) in degrees.
clockwise (bool) – If True, the shearing will be performed clockwise. Defaults to False.

Return type

Tuple[float, float, float, float, float, float]

Returns

Parameters \(a\), \(b\), \(c\), \(d\), \(e\), \(f\).

pillow_affine.matrix.rotation_matrix(angle, clockwise=False)¶

Creates an affine rotation matrix in the form

\[\begin{split}\mathrm{\mathbf{R}} = \begin{pmatrix} \cos \varphi & - \sin \varphi & 0 \\ \sin \varphi & \cos \varphi & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} = \begin{pmatrix} a & b & c \\ d & e & f \\ 0 & 0 & 1 \\ \end{pmatrix}\end{split}\]

Parameters

angle (float) – Angle \(\varphi\) in degrees.
clockwise (bool) – If True, the rotation will be performed clockwise. Defaults to False.

Return type

Tuple[float, float, float, float, float, float]

Returns

Parameters \(a\), \(b\), \(c\), \(d\), \(e\), \(f\).

pillow_affine.matrix.scaling_matrix(factor)¶

Creates an affine scaling matrix in the form

\[\begin{split}\mathrm{\mathbf{C}} = \begin{pmatrix} c_\text{horz} & & 0 \\ 0 & c_\text{vert} & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} = \begin{pmatrix} a & b & c \\ d & e & f \\ 0 & 0 & 1 \\ \end{pmatrix}\end{split}\]

Parameters: factor (Union[float, Tuple[float, float]]) – Horizontal and vertical scaling factors (\(c_\text{horz}\), \(c_\text{vert}\)). If scalar, the same factor is used for both directions.
Return type: Tuple[float, float, float, float, float, float]
Returns: Parameters \(a\), \(b\), \(c\), \(d\), \(e\), \(f\).

pillow_affine.matrix.translation_matrix(translation, inverse=False)¶

Creates an affine scaling matrix in the form

\[\begin{split}\mathrm{\mathbf{T}} = \begin{pmatrix} 1 & 0 & t_\text{horz} \\ 0 & 1 & t_\text{vert} \\ 0 & 0 & 1 \\ \end{pmatrix} = \begin{pmatrix} a & b & c \\ d & e & f \\ 0 & 0 & 1 \\ \end{pmatrix}\end{split}\]

Parameters

translation (Tuple[float, float]) – Horizontal and vertical translation. (\(t_\text{horz}\), \(t_\text{vert}\))
inverse (bool) – If True, the translation will be performed in the opposite direction. Defaults to False.

Return type

Tuple[float, float, float, float, float, float]

Returns

Parameters \(a\), \(b\), \(c\), \(d\), \(e\), \(f\).

pillow_affine.transforms module¶

class pillow_affine.transforms.AffineTransform¶

Bases: abc.ABC

ABC for all affine transformations.

extract_transform_params(size, expand=False)¶

Extracts the transformation parameters that need to be passed to Image.transform() for the affine transformation. An simple call might look like:

from PIL import Image
from pillow_affine import transforms


image = Image.open(...)
transform = transforms.Rotate(30.0)

transform_params = transform.extract_transform_params(image.size)
transformed_image = image.transform(*transform_params)

Parameters

size (Tuple[int, int]) – Image size (width, height).
expand (bool) – If True, expands the canvas to hold the complete transformed motif. Defaults to False.

Note

If you use the expand flag the motif is centered on the canvas and thus any final translation is removed.

Return type

Tuple[Tuple[int, int], int, Tuple[float, float, float, float, float, float]]

Returns

size, method, and data parameters for Image.transform()

.

class pillow_affine.transforms.Shear(angle, clockwise=False, center=None)¶

Bases: pillow_affine.transforms.ElementaryTransform

Affine horizontal shearing transformation.

Parameters

angle (float) – Shearing angle in degrees.
clockwise (bool) – If True, the shearing will be performed clockwise. Defaults to False.
center (Optional[Tuple[float, float]]) – Optional center of the shearing. Defaults to the center of the image.

class pillow_affine.transforms.Rotate(angle, clockwise=False, center=None)¶

Bases: pillow_affine.transforms.ElementaryTransform

Affine rotation transformation.

Parameters

angle (float) – Rotation angle in degrees.
clockwise (bool) – If True, the rotation will be performed clockwise. Defaults to False.
center (Optional[Tuple[float, float]]) – Optional center of the rotation. Defaults to the center of the image.

class pillow_affine.transforms.Scale(factor, center=None)¶

Bases: pillow_affine.transforms.ElementaryTransform

Affine scaling transformation

Parameters

factor (Union[float, Tuple[float, float]]) – Horizontal and vertical scaling factors. If scalar, the same factor is used for both directions.
center (Optional[Tuple[float, float]]) – Optional center of the scaling. Defaults to the center of the image.

class pillow_affine.transforms.Translate(translation, inverse=False)¶

Bases: pillow_affine.transforms.ElementaryTransform

Affine translation transformation

Parameters

translation (Tuple[float, float]) – Horizontal and vertical translation.
inverse (bool) – If True, the translation will be performed in the opposite direction. Defaults to False.

class pillow_affine.transforms.ComposedTransform(*transforms)¶

Bases: pillow_affine.transforms.AffineTransform

Composed affine transformation by chaining multiple AffineTransform s together. An simple example might look like:

from PIL import Image
from pillow_affine import transforms

image = Image.open(...)
transform = transforms.ComposedTransform(
    transforms.Rotate(30.0), transforms.Translate((50.0, 100.0))
)

transform_params = transform.extract_transform_params(image.size)
transformed_image = image.transform(*transform_params)

Parameters: transforms (AffineTransform) – Individual AffineTransform s.

pillow_affine.utils module¶

pillow_affine.utils.Coordinate¶: alias of typing.Tuple

pillow_affine.utils.Matrix¶: alias of typing.Tuple

pillow_affine.utils.matmul(matrix1, matrix2)¶

Matrix product

\[\begin{split}\begin{pmatrix} a_1 & b_1 & c_1 \\ d_1 & e_1 & f_1 \\ 0 & 0 & 1 \\ \end{pmatrix} \cdot \begin{pmatrix} a_2 & b_2 & c_2 \\ d_2 & e_2 & f_2 \\ 0 & 0 & 1 \\ \end{pmatrix} = \begin{pmatrix} a & b & c \\ d & e & f \\ 0 & 0 & 1 \\ \end{pmatrix}\end{split}\]

Parameters

matrix1 (Tuple[float, float, float, float, float, float]) – Parameters \(a_1\), \(b_1\), \(c_1\), \(d_1\), \(e_1\), \(f_1\).
matrix2 (Tuple[float, float, float, float, float, float]) – Parameters \(a_2\), \(b_2\), \(c_2\), \(d_2\), \(e_2\), \(f_2\).

Return type

Tuple[float, float, float, float, float, float]

Returns

Parameters \(a\), \(b\), \(c\), \(d\), \(e\), \(f\).

pillow_affine.utils.left_matmuls(*matrices)¶

Matrix product of \(N\) matrices from the left

\[\begin{split}\begin{pmatrix} a_N & b_N & c_N \\ d_N & e_N & f_N \\ 0 & 0 & 1 \\ \end{pmatrix} \cdot \quad\dots\quad \cdot \begin{pmatrix} a_n & b_n & c_n \\ d_n & e_n & f_n \\ 0 & 0 & 1 \\ \end{pmatrix} \quad\dots\quad \cdot \begin{pmatrix} a_1 & b_1 & c_1 \\ d_1 & e_1 & f_1 \\ 0 & 0 & 1 \\ \end{pmatrix} = \begin{pmatrix} a & b & c \\ d & e & f \\ 0 & 0 & 1 \\ \end{pmatrix}\end{split}\]

Parameters: *matrices – Parameters \(a_n\), \(b_n\), \(c_n\), \(d_n\), \(e_n\), \(f_n\) of each matrix.
Return type: Tuple[float, float, float, float, float, float]
Returns: Parameters \(a\), \(b\), \(c\), \(d\), \(e\), \(f\).

pillow_affine.utils.matinv(matrix)¶

Matrix inverse

\[\begin{split}\begin{pmatrix} a & b & c \\ d & e & f \\ 0 & 0 & 1 \\ \end{pmatrix}^{-1} = \begin{pmatrix} a^\prime & b^\prime & c^\prime \\ d^\prime & e^\prime & f^\prime \\ 0 & 0 & 1 \\ \end{pmatrix}\end{split}\]

Parameters: matrix (Tuple[float, float, float, float, float, float]) – Parameters \(a\), \(b\), \(c\), \(d\), \(e\), \(f\).
Return type: Tuple[float, float, float, float, float, float]
Returns: Parameters \(a^\prime\), \(b^\prime\), \(c^\prime\), \(d^\prime\), \(e^\prime\), \(f^\prime\).

pillow_affine.utils.deg2rad(angle_in_deg)¶

Converts an angle from degrees to radians

Parameters: angle_in_deg (float) – Angle in degrees.
Return type: float
Returns: Angle in radians.

pillow_affine.utils.transform_coordinate(coordinate, matrix)¶

Transforms a coordinate based on an affine matrix

\[\begin{split}\begin{pmatrix} a & b & c \\ d & e & f \\ 0 & 0 & 1 \\ \end{pmatrix} \cdot \begin{pmatrix} x \\ y \\ 1 \\ \end{pmatrix} = \begin{pmatrix} x^\prime \\ y^\prime \\ 1 \\ \end{pmatrix}\end{split}\]

Parameters

coordinate (Tuple[float, float]) – Coordinate (\(x\), \(y\)).
matrix (Tuple[float, float, float, float, float, float]) – Affine parameters \(a\), \(b\), \(c\), \(d\), \(e\), \(f\).

Return type

Tuple[float, float]

Returns

Transformed coordinate (\(x^\prime\), \(y^\prime\)).

pillow_affine package¶

Submodules¶

pillow_affine.matrix module¶

pillow_affine.transforms module¶

pillow_affine.utils module¶

Module contents¶