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General method of parameterization

  1. Dec 3, 2014 #1
    is there a general formula/algorithm to parameterize an equation?

    for example if i have a function
    f(x,y)=0
    then can i always change it to the form x(t),y(t)?

    or if i had g(x,y,z)=0

    then can i change it to something like x(u,v),y(u,v),z(u,v)

    i know of examples, like if i have x^2+y^2=1 then i know its cos(t),sin(t) but theres alot of other functions out there.

    I guess what im asking, is if there is always a parameterization in terms of elementary functions, and if not, what kinds of numeric algorithms are available?
     
  2. jcsd
  3. Dec 3, 2014 #2

    Orodruin

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    This depends on the properties of the function. The general answer is no.
     
  4. Dec 3, 2014 #3
    so is there an algorithm i could use in computer programming that takes f(x,y)=0 for example and returns an ordered set of points?
     
  5. Dec 3, 2014 #4

    Orodruin

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    This is again going to depend on your function. Perhaps the only functions you will encounter are nice enough. A computer code will never give you the full set of points simply because of memory limitations. You might want a finite set of points that give you a reasonable approximation? The contour plotting function of softwares like matlab or mathematica should be able to do that for you.
     
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