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Conformal mapping. From an ellipse to a rectangle

  1. Jun 23, 2006 #1
    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.
     
  2. jcsd
  3. Jun 23, 2006 #2

    AKG

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    Conformally? I don't think so. Conformal mappings preserve angles.
     
  4. Jun 23, 2006 #3
    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
     
  5. Jun 24, 2006 #4

    AKG

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    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?
     
  6. Jun 24, 2006 #5
    AKG, what you are saying is obvious and I knew it. But, except these four points, is there a transformation?
     
  7. Jun 24, 2006 #6

    Hurkyl

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    Are you really looking to turn an ellipse into a rectangle, or are you more interested in their interiors?
     
  8. Jun 25, 2006 #7
    I am trying to transform the ellipse into a rectangle
     
  9. Aug 29, 2008 #8
    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
     
  10. Oct 22, 2010 #9
    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.
     
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