Anisotropic adapted unstructured triangular surface grids are generated using a new and efficient procedure based upon the Delaunay principle. The mesh anisotropy is controlled by a change of metrics over the surface. In order to improve the surface grid definition, a generalization of the Farin's algorithm has been developed to obtain \lq $G^1$\rq   surfaces by joining triangular Bézier surface patches. Different local mesh operators are proposed to control the surface grid generation process and a remeshing anisotropic grid generation algorithm is described. This algorithm has been developed keeping in mind its 3D generalization.