Parametric surface meshing using a combined advancing-front generalized Delaunay approach

An indirect method for meshing parametric surfaces conforming to a user-specifiable size map is presented. First, from this size specification, a Riemannian metric is defined so that the desired mesh is one with unit length edges with respect to the related Riemannian space (the so-called ‘unit mesh’). Then, based on the intrinsic properties of the surface, the Riemannian structure is induced into the parametric space. Finally, a unit mesh is generated completely inside the parametric space such that it conforms to the metric of the induced Riemannian structure. This mesh is constructed using a combined advancing-front—Delaunay approach applied within a Riemannian context. The proposed method can be applied to mesh composite parametric surfaces. Several examples illustrate the efficiency of our approach.