18.  Random models with 3D surfaces

For surface objects, we use surface models, where the elementary random object is a surface. A surface in ${ℝ}^3$ is a set of points considered as a topological space, any "interior" point of which has an open neighborhood homeomorphic (bi-continuous bijection) to the unit ball of the Euclidean plane ${ℝ}^2$ . In this article, a surface (necessarily continuous by definition) will be topologically closed (i.e. it contains its possible edges), simple, not necessarily closed, rectifiable of finite area, and in some cases sufficiently smooth (i.e. of class