Matrices describing 2D affine transformation of the plane.
The Affine package is derived from Casey Duncan's Planar package. Please see the copyright statement in 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.
>>> 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').
>>> 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.
>>> 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,
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.
>>> 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.
>>> rev = ~fwd
>>> rev * fwd * (col, row)
(0.0, 99.99999999999999)
