FRACLETTES

The area in which this project fits is geometric modeling for Computer Aided Geometric Design (CAGD) and digital simulation. We propose to tackle the problem of digital representation, analysis and characterization of rough surfaces for digital simulation. Roughness is a complex concept, that is multi-scale, and based on the study of the local behavior of a surface in a given neighborhood. The evaluation of roughness on surfaces is essential for many experimental problems. It explains the numerous studies carried out in the application fields related to physics and mechanics, where the control and management of the surface topographies is a major need for manufacturers. A large number of standardized conventional parameters are currently available to attempt to appreciate this concept in the different application areas that make use of it. But it is often difficult, for a given application domain or a special need, to know precisely which parameter(s) connect(s) the topography of a surface to the physical phenomena that it undergoes. This is explained because, to a given parameter value can correspond roughness associated with varied geometries and physical properties. This is mainly due to the fact that conventional roughness measurements are, for the most part, based on a global statistical quantification. The geometric characterization that we propose aims to overcome this major drawback. It seems essential to us to more easily establish relations with the physical properties of surfaces. However, we will not focus on the impact of roughness on physical properties, which is very specific to each area. The objective of this project is twofold: 1) Theoretical: model the roughness and define tools for manipulation, composition, analysis and geometric characterization. To do this, we propose to rely on a generic approach using wavelet analysis and roughness synthesis from deterministic fractal models. We believe that the BC-IFS fractal model (developed in our team) will allow us to define this geometric characterization from the differential properties that can be defined on these surfaces. 2) Practical: generate a corpus (digital database) of rough geometric models in different forms, so that each user can find the models they are used to handling. It will first serve to master the notion of roughness. In a second step, we plan to make it available to researchers, engineers or industrialists (from different disciplines and fields of applications). In particular, they will be able to use it to perform numerical simulations or assess the impact of different types of roughness on the physical properties of an object. Despite the richness of the roughness generated by deterministic fractal models, this will certainly not be enough to represent all the varieties that can be encountered in reality. However, these rough models could serve as a reference base for generating new families of roughness, from combination operators (addition, multiplication, dilation, reduction, offset, ...).