In this thesis we study and design a surface modelling based on the representation of surfaceswith an atlas. - The first part of it is dedicated to the study of our modelling.Such a modelling allows to work locally on the surface without being afraid of any lose of globalconsistency. Furthermore the representation with an atlas is a notion coming from differentialgeometry. Our modelling inherits then good properties from this mathematical theory, andespecially to solve the continuity problem between the patches with which piecewiseparametric representation of surfaces meets frequently : our geometrical modelis a regular (or a quasi-regular) surface.We present this modelling among those which are used in Computer Graphics and in its differentialgeometric background. - In the second part of this thesis, we propose an algorithm for designing such a modellingfrom a triangular mesh.This mesh is supposed to be a connected and compact 2-manifold.The algorithm processes in three steps. Each steps reveals a geometrical problemfor which we propose an innovative solution. In particular we demonstrate that the nerve of a well-shaped covering is a combinatorial triangulation. We study also the$C^1$-diffeomorphic parameterization of a planar crown, and finally the convex combinationas a smooth blending of surfaces.
