The surface discretization in the real space is constrained directly to the surface body. The parametric space of the surface is not explicitly used for the mesh generation but it is used to perform some local operations. The meshing is done using the AFT. This technique exhibits several advantages, namely the high quality runtime point placement and geometrical locality, that are important for its application to 3D surfaces. Both features are related to the curvature of 3D surfaces which requires a specific treatment within the context of the direct approach. The first feature guarantees that the generated mesh represents well the underlying surface (or its part) at each step of the method and that the geometrical operations are performed close to the surface. The second one ensures that geometrical operations are also performed only in the small neighbourhood of the inserted node. This makes the AFT on the surface robust and efficient.
The mesh generation is carried out in a hierarchical manner. Firstly, the boundary curves of the surface are discretized using the mass curve of the required element density. The AFT is then applied to triangulate the actual surface.