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.
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.
(Versions for Mac OS and Windows.)