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How can I rotate a parabola.

  1. Sep 5, 2012 #1
    How can I "rotate" a parabola.

    I want to take an image and make it kind of wavy to distort it (like in a capcha form the letters are distorted sometimes with a wave) . So i figure that I could translate the pixels along a parabola. So the function where y=X[itex]^{2}[/itex] would make the image curve downwards. If i want to curve it in other directions I would need to somehow rotate that parabola. I am not an expert at math so I have no idea how to do this. Im sure it is a simple thing but It would really help me alot. Thanks for any advice.
     
  2. jcsd
  3. Sep 5, 2012 #2
    Re: How can I "rotate" a parabola.

    Write the parabola in parametric form:

    [tex]y = t^2, \quad x = t[/tex]

    Pick an angle [itex]\theta[/itex] to rotate by. The general equations governing the new coordinates are

    [tex]x'(t) = x(t) \cos \theta - y(t) \sin \theta \\
    y'(t) = y(t) \cos \theta + x(t) \sin \theta[/tex]

    (It's not strictly necessary to write in parametric, but it's usually easy to plot that way rather than go back and resolve for [itex]y(x)[/itex]).
     
  4. Sep 6, 2012 #3
    Re: How can I "rotate" a parabola.

    Thank you very much for your answer. It also gives me some more insight on how to rotate other things too. It will be very helpful.
     
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