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Added typescript definitions to handle the transformation matrix.
I also changed the logic a little bit. Instead of just inverting the position, I rounded the transformation matrix to a straight inversion. This inverted the entire image (although still aligned). I stuck with rounding the transformation matrix because then it will more closely match what would happen of the transformation matrix was actually applied.
I still don't have an example of an image with more interesting transformation values to fully test out the code, but I think it is a strict improvement from what was there before.