Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How do i find the arc length of an implicit curve given by f[x,y]=0?

  1. Dec 13, 2009 #1
    ?
    i used the implicit function theorem to find dy/dx, then applied that to the arc length formula, but i have to integrate with respect to x and there is the implicit function y[x] inside the radical.
    also, if it matters, the curve is assumed to be closed.
     
  2. jcsd
  3. Dec 14, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    That depends strongly on what the specific function is. What is f(x,y) for this problem?
     
  4. Dec 14, 2009 #3
    So theres no general formula/algorithm? bummer. there is no information about the curve other than it cannot be parameterized(and trivially, cannot be put into the form y[x]
     
  5. Dec 15, 2009 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I am puzzled by this. Every curve can be given some parametric functions. And every curve can be written in terms of piecewise functions. Do you mean simply that you do not know what they are or that they would be very complicated?
     
  6. Dec 17, 2009 #5
    in general they would range in complexity. im writing a program that finds the arc length of a level curve of some function f[x,y]. do you mean every implicit curve has a parametric representation?
     
  7. Dec 19, 2009 #6
    I second HallsofIvy assertion that any curve (at least any curve that is implicitly or explicitly defined with analytic functions) can be parametrized.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How do i find the arc length of an implicit curve given by f[x,y]=0?
Loading...