Overview

A curve can be defined using various categories of methods. Indeed, there are parametric, implicit or explicit curves. Using classical notations, a parametric curve is given by a function ? and a parameter t. Then, given t in some interval, the curve is defined by ?( t) where ?( t) ? , d = 2 or 3. Implicit curves in are given via a relation like f( x,y) = 0 where x and y denote the coordinates. Explicit curves in are defined by the pair ( x, y = f( x)). In , non-parametric curves are defined as the intersection of two surfaces.

In principle, function f or ? depends on modeling parameters ( p _i) i ?[1, np]. These parameters can be defined in the following ways:

• through a direct definition of the design variables: with this approach, the user of a CAD system directly defines the values of the parameters pi using a graphic interface. This way of processing is actually the simplest but it requires reasonably precise knowledge about the underlying models and their intrinsic variables,

• through the specification of the curve characteristics: the curve is defined by means of high level characteristics but the model, as completed by the CAD system, does not necessarily store this information. For instance, a circle can be defined while a NURBS type curve is generated inside the...