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I have a 2D transform that is not conformal. What are some methods that can be used to change the transform so that it is conformal, preferably with the least amount of change required?

One naive way is to create many different transforms that differ from the original transform by a small amount and test each one to see if it is conformal. However this method won't be effective for testing large changes because there will be too many variations to test.

Here is an example of a transform that I'm looking to make conformal.

$x^{'} = x^2$

$y^{'} = y$

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    Conformal transformation do not work like that. The condition that a transformation is conformal is highly restrictive so you cannot expect that adding some _small_ change will render your mapping conformal. – 2017-01-29
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    It's possible to take a conformal transform and make a small change to make it non-conformal, so I'm assuming the reverse is possible for certain non-conformal transforms. – 2017-01-29

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