Random observation that I don't recall seeing before: the edges from the sequence of convex hulls of a shelling of a point set forms a pointed pseudotriangulation: that is, it's a planar graph in which each interior face has three convex vertices and each vertex has one reflex angle.

But not every pointed pseudotriangulation can come from a shelling in this way: one can only have pseudotriangles with a single chain of reflex vertices, and there's some sort of acyclicity condition on the direction these chains can point. So the pseudotriangulations below do not come from shellings:

Since shellings are closely related to antimatroids, and antimatroids are related to certain kinds of greedy algorithms, perhaps this connection can lead to some algorithms for finding optimal pseudotriangulations...