frep:why

# Why not just implicit?

What is the difference between traditional “implicits” and FRep ?
Why is “implicit surface” not a very good term?
It sounds well … Should we keep it?

There are several reasons why the terms “implicit surfaces” or even “implicit modeling” do not fit shape modeling and CG with real functions well enough. We do not propose to change the existing terminology! It means wasting time. Simply keep the following in your mind when using it:

• “Implicit surfaces” came from “implicit functions”. But using an implicit function one cannot describe even a sphere. Why? A short excursus in school math can help to explain this.
z = f(x,y) is called an explicit function of two variables. Here z is a function of x and y.
f(x,y,z)=0 is called an implicit function of two variables. Here z is also a function of x and y, but defined implicitly. It means that for every given pair (x,y) there is one and only one value of z. It is not enough to define a sphere!
The definition of a zero set of an explicit function of three variables s=f(x,y,z) looks exactly the same: f(x,y,z)=0 but has quite different meaning. These zero sets (or isossurfaces) are usually called “implicit surfaces” by reasons explained above.
• With “implicit surfaces” many things look quite “implicit” even in the descriptions of the algorithms. The use of explicit functions of three variables and their isosurfaces makes things much more clear.
• “Implicit surfaces” usually are not supposed to cover the variety of modeling techniques such as set operations with R-functions, sweeping and others. 