We can prove that if a smooth curve is sampled densely enough, then the crust of the samples approximates the curve, with no extraneous features. The minimum required sampling density varies along the curve according to the Local Feature Size (which is also simply defined), so that areas of less detail can be sampled less densely.
The crust is easy to compute using Voronoi diagrams in O(n log n) time (even in practice). We will demonstrate the computation of crusts on arbitrary point sets.