1. A method for encoding/decoding three-dimensional meshes of dots or vertices connected in the form of facets delimited by edges; the mesh M is defined by connectivity data T and geometry data G; the method comprises: a step of lossless encoding of the connectivity data T into encoded connectivity data Tc, a step of iteratively generating a progressive mesh hierarchy, i.e. a set of meshes with progressive levels of detail, PM(M*), characterized in that it also comprises a step of generating a piecewise smooth approximation M* of the original mesh M, from the mesh connectivity T; this piecewise smooth approximation M* is described as follows: a. the encoded connectivity information Tc (the list of triangles of the mesh M), b. a small number N of control dots C=(c k ) kε{1,. .. , N} , previously defined and c. a set of indexes S of edges, called protruding edges, of the mesh M, identified beforehand; the progressive mesh hierarchy PM(M*) is used to calculate a prediction of approximation errors in M* compared with the original mesh M.