How to transform a ellipse to circle

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mina sh
mina sh 2020-7-16
回答： Image Analyst 2020-7-17
I have some data which looks like it can be fitted with an ellips. However, I want to transform it so it would be in a cricle.How can I do it?

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回答（2 个）

Matt J
Matt J 2020-7-16
If the equation for the ellipse is
x.'*Q*x =1
then you simply take the cholesky decomposition of the 2x2 matrix Q,
L=chol(Q)
and make the change of variables y=L*x. The equation for y is
y.'y=1
which is the equation for a circle of radius 1.
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Bruno Luong
Bruno Luong 2020-7-17
编辑：Bruno Luong 2020-7-17
Now that looks right.
One think you must pay attention is the determinant of V.
I don't know where it comes from but the determinant must be +/-1. Some algorithm return V with det=+1, other doesn't specify the sign of V.
If det(V)==-1 you could get the transformation that flips your plots (however still maps the ellipse to a circle), like looks at the mirror. If that kind of transformation is problem for you, just reverse the sign of one colume of V, then do the rest identical.
mina sh
mina sh 2020-7-17
编辑：mina sh 2020-7-17
Thanks Bruno. You helped a lot. I checked the deteminant of V and it is +1.

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Image Analyst
Image Analyst 2020-7-17
Are you just worried that your x and y are distorted, like digitally it's roughly round but because of the shape of the figure window and axes inside it, the shape looks stretched? If so experiment around with
axis equal
You might also want to play with xlim() and ylim()

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