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This fixes an issue where most non-trivial transformations were not being correctly applied to arcs. The endpoints would move but the arc radii and rotation angle would remain unchanged, resulting in an incorrect final path. Test cases illustrate some of the ways this failed previously.
I left a lot of algebra in the comments, which hopefully sheds light on how the transformation works. I can trim it down if you think the math is too obvious (or add more English if the math isn't obvious enough).