Geometrical description of surface topography by means of an equivalent conformal profile model

Using the concepts of the theory of homogenisation, an equivalent conformal geometrical representation of sampled profiles (or surfaces) is proposed. This approach is based on a parametered representation taking as a parameter the spatial angularity of micro-segments (or micro-facets) constituting the surface topography. The result is a curve of developed length (developed surface) identical to the developed length (developed surface) of the profile (of the surface) but in which the notion of connectivity has disappeared. The general shape of the equivalent conformal profile can be compared to that of an ellipse (or ellipsoid) whose descriptive parameters (parameters a, b, local radii of curvature, perimeter, area of section, …) are used for a hierarchical scaling in a comparative study in which the functional topographic features of the surfaces are involved (adhesion, contact mechanics, coatings, …).