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Résumé : This chapter looks at different ways of modeling curves and surfaces based on the nature of their definition, analytical or discrete or completely discrete and also shows how to extract the characteristic lines and points of a surface. This modeling consists of constructing a discrete geometric support, that is an assembly of edges for a curve or a triangulation for a surface. This support will be used instead of the analytical definition, thus simplified and replaced in a unified manner. The chapter also examines the identification of particular points and lines that characterize a curve or a surface based on a discretization or triangulation describing this curve or surface. Geometric modeling can be summarized as going in both directions – from a representation in one form to a representation in another, more appropriate form, with respect to meshing or remeshing problems or characterization.