Abstract 
We construct a graph on a planar point set, which captures its shape in the following sense: if a smooth curve is sampled densely enough, the graph on the samples is a polygonalization of the curve, with no extraeous edges. The required sampling density varies with the LOCAL FEATURE SIZE on the curve, so that area of less detail can be sampled less densely. We give two different graphs that, in this sense, reconstruct smooth curves: a simple new construction which we call the crust, and the B skeleton, using a specific value of B.
