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I have an ellipse which has -45 degree axis.

How can I transform the ellipse into a circle? Can I use shear transformation along the x/y axis?

enter image description here

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  • $\begingroup$ Do you just require the outcome to be a circle (any size circle), or does the diagram indicate that you require specifically that size circle from that size ellipse? $\endgroup$ – trichoplax Apr 18 at 20:40
  • $\begingroup$ The circle size can be arbitrary size. I just want the transformed into complete circle. thank you very much. $\endgroup$ – Ick-Sung Choi Apr 19 at 1:33
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You can use a shear, or equivalently a rotation by 45, scale along one of the axes, rotate back (which is equivalent to the shear which you are looking for).

EDIT: On second thought, you don't need to even rotate back unless your circle is marked, since a circle is rotation invariant (if the rotation is around its center).

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  • $\begingroup$ Thank you very much for your kind answer. $\endgroup$ – Ick-Sung Choi Apr 22 at 0:07

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