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peanut

My thinking is 1. Translate 2. Rotate 3. Rotate -> scale -> translate 4. Rotate -> non-uniform scale -> translate

Correct?

wafer

It would be so much more difficult to imagine such transformation in a 3D world

jacheng

For 2, I don't think you can simply rotate. Since the origin is at 0,0 you will end up with the square only in quadrant I and II if you rotate about the origin by 45 degree. So you can rotate first by 0,0 and then translate by (0, -sqrt(2))