Matrices describing 2D affine transformation of the plane.

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The Affine package is derived from Casey Duncan's Planar package. Please see the copyright statement in src/affine.py <src/affine.py>__.

The 3x3 augmented affine transformation matrix for transformations in two dimensions is illustrated below.

::

| x' | | a b c | | x | | y' | = | d e f | | y | | 1 | | 0 0 1 | | 1 |

Matrices can be created by passing the values a, b, c, d, e, f to the affine.Affine constructor or by using its identity(), translation(), scale(), shear(), and rotation() class methods.

.. code-block:: pycon

from affine import Affine Affine.identity() Affine(1.0, 0.0, 0.0, 0.0, 1.0, 0.0) Affine.translation(1.0, 5.0) Affine(1.0, 0.0, 1.0, 0.0, 1.0, 5.0) Affine.scale(2.0) Affine(2.0, 0.0, 0.0, 0.0, 2.0, 0.0) Affine.shear(45.0, 45.0) # decimal degrees Affine(1.0, 0.9999999999999999, 0.0, 0.9999999999999999, 1.0, 0.0) Affine.rotation(45.0) # decimal degrees Affine(0.7071067811865476, -0.7071067811865475, 0.0, 0.7071067811865475, 0.7071067811865476, 0.0)

These matrices can be applied to (x, y) tuples using the * operator (or the @ matrix multiplier operator for future releases) to obtain transformed coordinates (x', y').

.. code-block:: pycon

Affine.translation(1.0, 5.0) * (1.0, 1.0) (2.0, 6.0) Affine.rotation(45.0) * (1.0, 1.0) (1.1102230246251565e-16, 1.414213562373095)

They may also be multiplied together to combine transformations.

.. code-block:: pycon

Affine.translation(1.0, 5.0) * Affine.rotation(45.0) Affine(0.7071067811865476, -0.7071067811865475, 1.0, 0.7071067811865475, 0.7071067811865476, 5.0)

Georeferenced raster datasets use affine transformations to map from image coordinates to world coordinates. The affine.Affine.from_gdal() class method helps convert GDAL GeoTransform <https://gdal.org/user/raster_data_model.html#affine-geotransform>__, sequences of 6 numbers in which the first and fourth are the x and y offsets and the second and sixth are the x and y pixel sizes.

Using a GDAL dataset transformation matrix, the world coordinates (x, y) corresponding to the top left corner of the pixel 100 rows down from the origin can be easily computed.

.. code-block:: pycon

geotransform = (-237481.5, 425.0, 0.0, 237536.4, 0.0, -425.0) fwd = Affine.from_gdal(*geotransform) col, row = 0, 100 fwd * (col, row) (-237481.5, 195036.4)

The reverse transformation is obtained using the ~ inverse operator.

.. code-block:: pycon

rev = ~fwd rev * fwd * (col, row) (0.0, 99.99999999999999)