How can I rotate a parabola.

  • #1

Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
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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]).
 
  • #3


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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