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-2- X hâve in view in the présent paper. For pedagogy's sake, we présent both descriptors of flatness and roughness in 2 and 3 dimensions successively. Fig. 1 indieates the main notation used in the paper. X dénotés a "broken pie ce of métal in (R2 or in the "base of whieh has the unit length (in (R2) or the unit area (in (R^) • The part a"bove X is denoted by Xe,, and the boundary between X and Xe is ÔX. The fracture results from an effort made in the vertical direction (z axis). The length (resp. surface area) of ÔX is denoted as L (resp. as S). 'The parameters L and A look like global ones because we have chosen unit sampling zones. Indeed they are local. If the sampling zone Z is not a unit zone, one has to divide L (resp. S) by the length (resp. the area) of Z. sampling zone (wifh a uni^ )en$Vh) Sampling zone (wifh a unir surface) 2 - FLATNESS We call flatness the measure (L or S) of the boundary dX. Intuitively, we could expect that the more tortuous ÔX is, the rougher the material will be. Indeed the three fig. 2a, b and c clearly show that in IR^, three very différent boundaries may exhibit the same length 1. Even if we décidé to divide L by the chord m n joining the two extremities (or a straight line which