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        "author": "Sean Gillies",
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        "description": "Affine\n======\n\nMatrices describing affine transformation of the plane.\n\n.. image:: https://travis-ci.org/sgillies/affine.svg?branch=master\n    :target: https://travis-ci.org/sgillies/affine\n\n.. image:: https://coveralls.io/repos/sgillies/affine/badge.svg\n    :target: https://coveralls.io/r/sgillies/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<http://www.gdal.org/classGDALDataset.html#af9593cc241e7d140f5f3c4798a43a668>`__,\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\n",
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