Matrices describing affine transformation of the plane
Matrices describing 2D affine transformation of the plane.
.. image:: https://github.com/rasterio/affine/actions/workflows/ci.yml/badge.svg?branch=main :target: https://github.com/rasterio/affine/actions/workflows/ci.yml
.. image:: https://codecov.io/gh/rasterio/affine/branch/main/graph/badge.svg :target: https://codecov.io/gh/rasterio/affine
The Affine package is derived from Casey Duncan's Planar package. Please see
the copyright statement in affine/__init__.py <affine/__init__.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 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 ~
operator.
.. code-block:: pycon
rev = ~fwd rev * fwd * (col, row) (0.0, 99.99999999999999)