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Defining implicit function given a parametric function

  1. Feb 10, 2009 #1
    1. The problem statement, all variables and given/known data


    Given a continuous parametric function f : R2 -> R3 specifying a 2D
    surface in 3D space, define a continuous implicit function g : R3 -> R
    corresponding to the same surface.

    2. Relevant equations

    You’ll likely want to use the infimum function.
    You can ignore the inside/outside convention: g can be everywhere
    nonnegative.

    3. The attempt at a solution

    My thought on this is that... Since g is an implicit function and is non negative everywhere else.. Then if a point lies on the surface described by g, g(x,y,z) = 0 at that point. Since g is zero on the surface and continuous and increasing everywhere else, it must include an infimum of some sort and a modified function of f, where f(s,t) = (x,y,z).. And I'm stuck from then on..

    Someone help please? Any help is appreciated..
     
  2. jcsd
  3. Feb 10, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I think they are trying to get you to think of defining g as the distance from a point to the surface. Can you define this distance in terms of an infimum?
     
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