Does this only work when you have 4 patches for every vertex? What happens with < or > 4?
@adam Great question. Everything works out beautifully when all vertices have degree 4. Otherwise, there are two basic approaches. One is to cook up different types of spline patches (beyond simple bicubic Bezier patches) that allow you to nicely connect up the patches near this vertex. See for instance a bunch of nice work by Jorg Peters or Scott Schaefer. The other is to use subdivision, as described later in these slides. Here it is easy to get 1st derivatives to match everywhere, and 2nd derivatives to match almost everywhere. However, unlike spline patches, subdivision surfaces are harder (though not impossible) to evaluate directly at a specific point; you have to repeatedly refine until you have the value you want. So, like all other things in life, it's a trade off. :-)