| Name | affine JSON |
| Version |
2.4.0
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| Summary | Matrices describing affine transformation of the plane |
| upload_time | 2023-01-19 23:44:30 |
| maintainer | |
| docs_url | None |
| author | |
| requires_python | >=3.7 |
| license | |
| keywords |
affine
transformation
matrix
|
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No requirements were recorded.
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Affine
======
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>`__.
Usage
-----
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)
Usage with GIS data packages
----------------------------
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)
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"description": "Affine\n======\n\nMatrices describing 2D affine transformation of the plane.\n\n.. image:: https://github.com/rasterio/affine/actions/workflows/ci.yml/badge.svg?branch=main\n :target: https://github.com/rasterio/affine/actions/workflows/ci.yml\n\n.. image:: https://codecov.io/gh/rasterio/affine/branch/main/graph/badge.svg\n :target: https://codecov.io/gh/rasterio/affine\n\nThe Affine package is derived from Casey Duncan's Planar package. Please see\nthe copyright statement in `affine/__init__.py <affine/__init__.py>`__.\n\nUsage\n-----\n\nThe 3x3 augmented affine transformation matrix for transformations in two\ndimensions is illustrated below.\n\n::\n\n | x' | | a b c | | x |\n | y' | = | d e f | | y |\n | 1 | | 0 0 1 | | 1 |\n\nMatrices can be created by passing the values ``a, b, c, d, e, f`` to the\n``affine.Affine`` constructor or by using its ``identity()``,\n``translation()``, ``scale()``, ``shear()``, and ``rotation()`` class methods.\n\n.. code-block:: pycon\n\n >>> from affine import Affine\n >>> Affine.identity()\n Affine(1.0, 0.0, 0.0,\n 0.0, 1.0, 0.0)\n >>> Affine.translation(1.0, 5.0)\n Affine(1.0, 0.0, 1.0,\n 0.0, 1.0, 5.0)\n >>> Affine.scale(2.0)\n Affine(2.0, 0.0, 0.0,\n 0.0, 2.0, 0.0)\n >>> Affine.shear(45.0, 45.0) # decimal degrees\n Affine(1.0, 0.9999999999999999, 0.0,\n 0.9999999999999999, 1.0, 0.0)\n >>> Affine.rotation(45.0) # decimal degrees\n Affine(0.7071067811865476, -0.7071067811865475, 0.0,\n 0.7071067811865475, 0.7071067811865476, 0.0)\n\nThese matrices can be applied to ``(x, y)`` tuples to obtain transformed\ncoordinates ``(x', y')``.\n\n.. code-block:: pycon\n\n >>> Affine.translation(1.0, 5.0) * (1.0, 1.0)\n (2.0, 6.0)\n >>> Affine.rotation(45.0) * (1.0, 1.0)\n (1.1102230246251565e-16, 1.414213562373095)\n\nThey may also be multiplied together to combine transformations.\n\n.. code-block:: pycon\n\n >>> Affine.translation(1.0, 5.0) * Affine.rotation(45.0)\n Affine(0.7071067811865476, -0.7071067811865475, 1.0,\n 0.7071067811865475, 0.7071067811865476, 5.0)\n\nUsage with GIS data packages\n----------------------------\n\nGeoreferenced raster datasets use affine transformations to map from image\ncoordinates to world coordinates. The ``affine.Affine.from_gdal()`` class\nmethod helps convert `GDAL GeoTransform\n<https://gdal.org/user/raster_data_model.html#affine-geotransform>`__,\nsequences of 6 numbers in which the first and fourth are the x and y offsets\nand the second and sixth are the x and y pixel sizes.\n\nUsing a GDAL dataset transformation matrix, the world coordinates ``(x, y)``\ncorresponding to the top left corner of the pixel 100 rows down from the\norigin can be easily computed.\n\n.. code-block:: pycon\n\n >>> geotransform = (-237481.5, 425.0, 0.0, 237536.4, 0.0, -425.0)\n >>> fwd = Affine.from_gdal(*geotransform)\n >>> col, row = 0, 100\n >>> fwd * (col, row)\n (-237481.5, 195036.4)\n\nThe reverse transformation is obtained using the ``~`` operator.\n\n.. code-block:: pycon\n\n >>> rev = ~fwd\n >>> rev * fwd * (col, row)\n (0.0, 99.99999999999999)\n\n\n",
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