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Transformation of one shape into another

  1. Jun 5, 2009 #1
    I have been out of class for really long, I don't remember anything,
    I have lately become interested in transformation of one shape into another. :confused: Is this also about topology ?

    If so, I would like to know how you can define such a beautiful transformation ? It is just so strange to me, true!, how a star can turn into a circle with some sort of computation.

    -Forgive and Forget
    Thank you
  2. jcsd
  3. Jun 5, 2009 #2
    Re: Transformation

    Well, yeah. That's topology. Informally known as rubber sheet topology. A donut and a ceramic coffee cup are topologically objects of equivalence. A sphere and a cube with rounded edges and corners are equivalent objects, etc...
  4. Jun 5, 2009 #3
    Re: Transformation

    Thankyou That's interesting, But if I want to turn a sphere into make a cube, how can I be able to do it ? :redface:
  5. Jun 5, 2009 #4
    Re: Transformation

    I don't know the mathematical machinery. It's not my fault--I only care for the physics! But that's a topological no-no. Sharp corners are out, just as the hole in a donut distinguishes it from a sphere, the sharp points are distinguishing features that distinguish one shape from another. If it has places where differentiation gives you infinite values it's not a manifold--I think.

    We'll both have to wait for the mathematical geniuses to show up, to say why.
  6. Jun 8, 2009 #5
    Re: Transformation

    You can find a conformal map from any open polygon to the open unit disk using the Schwarz Christoffel mapping,

    The key thing being that they are open (boundary not included), so that the corners are not a problem.
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