# Defining implicit function given a parametric function

1. Feb 10, 2009

### mathnewbie123

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. Feb 10, 2009

### Dick

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?