We divide the computation of polygonal approximations of implicit objects into two phases: sampling and structuring. Unlike
classical treatments, we study each phase separately. Classical sampling methods are reviewed, and a new sampling method is
proposed; this method uses physically-based particle systems, and is more robust than classical enumeration and continuation
methods. We describe a broad taxonomy of structuring problems. According to this taxonomy, the presence of an independent
structuring phase casts the modeling problem as a problem in non-parametric scattered data interpolation, which we propose to
solve using computational morphology. The use of global structuring is described in detail for curves: we prove that minimal
spanning trees are good morphological tools for arcs. A couple of methods are also suggested for surfaces.