Triangular and quadrilateral finite element mesh generation on poorly parameterized free-form surfaces

The non-uniform rational B-spline (NURBS) surfaces are widely employed for the exchange of geometric models between different computer aided design and computer aided engineering systems. However, if the input surfaces are poorly parameterized, surface meshing algorithms may fail or the constructed meshes could be ill conditioned. This paper presents a new method that can generate well-conditioned meshes, even on poorly parameterized freeform surfaces, by regenerating NURBS surfaces. At the outset, adequate points are sampled on the poorly parameterized original surfaces. New surfaces are then created by interpolating these points. Finally, mesh generation is performed on the new surfaces. By employing this method, models with poorly parameterized surfaces can be successfully meshed.