Conformal mapping. From an ellipse to a rectangle

[traianus]

Is it possible to transform an ellipse

x^2/a^2 + y^2/b^2 = 1 ("a" minor or major semiaxis)

Into a rectangle?
If so, how can I do it? I am not very familiar so please explain all the details. I know the transformation from a circle to an airfoil, but not this one.

 

[AKG]

Conformally? I don't think so. Conformal mappings preserve angles.

 

[traianus]

I know that there is a transformation from a rectangle to an ellipse (book advanced enginnering mathematics by Kreyszig) but it is not conformal somewhere

 

[AKG]

Like I just said, conformal mappings preserve angles. There are at least four places where a rect-angle ('rect' means 'right', 'angle' means 'angle') cannot be mapped conformally to an ellipse. Are there any right angles on the boundary of an ellipse?

 

[traianus]

AKG, what you are saying is obvious and I knew it. But, except these four points, is there a transformation?

 

[Hurkyl]

Are you really looking to turn an ellipse into a rectangle, or are you more interested in their interiors?

 

[traianus]

I am trying to transform the ellipse into a rectangle

 

[afrdzak]

I know that there is a transformation from a rectangle to an ellipse (book advanced enginnering mathematics by Kreyszig) but it is not conformal somewhere

Hi, I found your quote while doing a search for transforming a rectangle to an ellipse. I found the book you mentioned and could not find the information I am looking for.

Can anyone assist me in finding out how to transform a rectangle into an ellipse?

Thanks

 

[lvirany]

What you can do is map the ellipse to the real axis and map the real axis to a regular 4-sided polygon using Schwartz-Christoffel.