[phkahler]

>> the surface of the patch is equal to the limit surface that would be obtained by the subdivision scheme.

That's not true if any of the vertices is extraordinary. In other words a vertex shared by more or less than 4 quads. The good news is that subdividing those quads each into 4 smaller ones will result in 3/4 of the surface area meeting the right criteria. Or the area hard to deal with becomes 1/4 the size.

The ultimate coolness of subdivision surfaces is that every vertex on a subdivided mesh is a leaner combination of the original vertices. The weights do not change during animation. The weights only change if the topology does. Another nice thing is that meshes at different LOD contain the vertices of the lower LOD mesh.

They really do everything with one exception - they can't exactly represent quadric surfaces which are so important in CAD tools.