On Tue, 08 Jul 2003 02:21:15 +0100, Vasileios Zografos

>I am trying to understand what the level set function is but I cannot

>find a good source of information the explains it. Could someone tell me

>what it is or point me to the right direction?

>And what does it mean: the surface is given implicitly in terms of the

>level set function?

Look at a topographic map, such as this one of Finland.

<http://www.helsinki.fi/ml/maant/korkeus.gif>

At every point over this 2D region is a numeric value giving height

above sea level. Should global warming cause sea level to rise, the

outline of the coast will change accordingly. Thus each level gives a

set of curves, called a level set.

In 3D we can also associate a numeric value with each point in space.

The level sets then will be surfaces. For example, if the values are

assigned by the function

f(x,y,z) = x^2 + y^2 + z^2

then the level set for f=4 will be a sphere of radius 2. Thus we say

that f(x,y,z) = 4 is an "implicit function" for a sphere.

Try experimenting with this software to get a feel for 2D level sets.

<http://www.peda.com/grafeq/>

(Versions for Mac OS and Windows.)