Procedural surfaces may include offset surfaces, generalized
cylinder surfaces, blending surfaces etc. The typical solution method is
minimization
[69]. In this case, no convex box assistance is available
in general, and we need a dense sampling for an initial
approximation which may be expensive, and no rigorous guarantees for
the solution's reliability are generally available.
For certain classes of procedural surfaces such as offsets and
evolutes of rational surfaces involving radicals of polynomials, it is
possible to use the auxiliary variable method, described in Sect.
4.5, to remove radicals from the formulation, followed by
solution via the IPP algorithm of Chap. 4.
Alternatively, some procedural surfaces admit a rational
parametrization (e.g. offsets [240,324], pipe and canal
surfaces [241,256]) in which case the problem reduces to
the formulation of Sect. 5.5.2.