Decomposing Rotations into Shear Mappings

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Decomposing rotation matrices into three shear matrices, one can rotate an image an arbitrary number of degrees by simply performing shear operations. This allows rotations to be performed in basic image-editing software without free rotate, such as Paint.

Contributed by: Nate Orlow (October 2013)
Open content licensed under CC BY-NC-SA



The specific choices for and are explained in [1]. Using these, I manually computed the height and width of the resulting cropped image and used these values for the cropping functions. Similar calculations can be performed for counterclockwise rotations, but I restricted the values for here to the range 0 to 90 in order to program one case.

Try out your own image in the "myimage" variable. The coin image provided is from Wikimedia Commons.


[1] DataGenetics. "Rotating Images" (blog). (Oct 8, 2013)

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