Example 1: Sectioning of offset surfaces
An offset of a parametric surface is not parametric in general. One needs to implicitize or to approximate.
Our approach is to compute the implicit equation in a generic way since all the data comes in floating point. Then specialization of the coefficients (plus verification) is required.
The concrete implicit equation
The generic implicitation is accomplished by a variety of Computer Algebra tools such as resultants, Groebner Bases, multisymmetric functions, etc.