Method for encoding three-dimensional meshes of dots or vertices connected in the form of facets delimited by edges; the mesh M being defined by connectivity data T and geometry data G; the method comprising: - 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*), - a step of generating a piecewise smooth approximation M* of the original mesh M, from the mesh connectivity T; this piecewise smooth approximation M* being described by: a. the encoded connectivity information T c, b. a small number N of control dots C =( c k) k ∈{1,..., N}, previously defined, - the progressive mesh hierarchy PM(M*) being used to calculate a prediction of the approximation errors in M * compared with the original mesh M, characterized in that the piecewise smooth approximation M* is also described by: c. a set of indexes, their references in the mesh, S of edges, called protruding edges of the mesh M, identified beforehand, in that the approximate mesh M* is generated according to a Laplacian technique, which has been generalized to the case of meshes comprising protruding edges, in that a Laplacian matrix L is defined in which weights α and β are respectively associated with the special protruding or special outer edges and with the non-special edges, making it possible to assign different weights to the contribution of the vertices neighboring a dot depending their belonging to the two sets of special topological neighbors i s *, which are defined as sharing with same either an outer edge or a protruding edge, and normal topological neighbors i n *, defined as the topological neighbors not belonging to i s *, α being greater than β. the method comprising: - 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*), - a step of generating a piecewise smooth approximation M* of the original mesh M, from the mesh connectivity T; this piecewise smooth approximation M* being described by: a. the encoded connectivity information T c, b. a small number N of control dots C =( c k) k ∈{1,..., N}, previously defined, - the progressive mesh hierarchy PM(M*) being used to calculate a prediction of the approximation errors in M * compared with the original mesh M, characterized in that the piecewise smooth approximation M* is also described by: c. a set of indexes, their references in the mesh, S of edges, called protruding edges of the mesh M, identified beforehand, - 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*), - a step of generating a piecewise smooth approximation M* of the original mesh M, from the mesh connectivity T; this piecewise smooth approximation M* being described by: a. the encoded connectivity information T c, b. a small number N of control dots C =( c k) k ∈{1,..., N}, previously defined, - the progressive mesh hierarchy PM(M*) being used to calculate a prediction of the approximation errors in M * compared with the original mesh M, characterized in that the piecewise smooth approximation M* is also described by: c. a set of indexes, their references in the mesh, S of edges, called protruding edges of the mesh M, identified beforehand, a. the encoded connectivity information T c, b. a small number N of control dots C =( c k) k ∈{1,..., N}, previously defined, - the progressive mesh hierarchy PM(M*) being used to calculate a prediction of the approximation errors in M * compared with the original mesh M, characterized in that the piecewise smooth approximation M* is also described by: - the progressive mesh hierarchy PM(M*) being used to calculate a prediction of the approximation errors in M * compared with the original mesh M, characterized in that the piecewise smooth approximation M* is also described by: c. a set of indexes, their references in the mesh, S of edges, called protruding edges of the mesh M, identified beforehand, in that the approximate mesh M* is generated according to a Laplacian technique, which has been generalized to the case of meshes comprising protruding edges, in that a Laplacian matrix L is defined in which weights α and β are respectively associated with the special protruding or special outer edges and with the non-special edges, making it possible to assign different weights to the contribution of the vertices neighboring a dot depending their belonging to the two sets of special topological neighbors i s *, which are defined as sharing with same either an outer edge or a protruding edge, and normal topological neighbors i n *, defined as the topological neighbors not belonging to i s *, α being greater than β.