Surface mesh enhancement with geometric singularities identification

A method for generating geometric surface meshes from a discrete surface, called a reference mesh, is presented. First, the geometrical singularities are extracted from the reference mesh. Then, an almost smooth surface interpolating the reference mesh vertices is associated to the reference mesh. Finally, the reference mesh is adaptively refined via the smooth geometry in order to obtain an adequate approximation of the underlying geometry. Some numerical examples are given to show the efficiency of our approach. The method can transform a mesh composed of linear elements to a mesh constituted by quadratic elements.