`12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697` ``````Affine ====== Matrices describing affine transformation of the plane. .. image:: https://travis-ci.org/sgillies/affine.svg?branch=master :target: https://travis-ci.org/sgillies/affine .. image:: https://coveralls.io/repos/sgillies/affine/badge.svg :target: https://coveralls.io/r/sgillies/affine The Affine package is derived from Casey Duncan's Planar package. Please see the copyright statement in `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 `__, 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) ``````