All of them work on an almost regular cell complex with triangular or quadrilateral faces. There are also so-called combined schemes which take special care at the boundaries of the surface. This is however not enough for some applications and further schemes are sought. The main open problems are to be found when we consider the manipulation of these objects. As the number of cells increases exponentially, it would not be possible to maintain a high number of objects at their full representation.
Adaptive methods represent objects using several layers.
The more layers one displays, the more details one can see. The cell that will be cancelled in a layer can be computed according to variational calculus. More efficient methods are still required. The solution for this situation should be compatible with the whole modelling system. Mainly in CAD systems, high order continuity surfaces are required.