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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,
    http://www.math.udel.edu/~driscoll/research/conformal.html

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