17.  2D and 3D random curve models

For filiform objects, it's best to use curve models, where the elementary random object is a curve (necessarily continuous by definition), simple (i.e., without double points), topologically closed (i.e., it contains its two possible end points), sufficiently regular (e.g., of class $C^2$ by pieces, or even Lipchitzian by pieces (p. 9 of ), and rectifiable of finite length.

A field of curves...