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The Crust and the β-Skeleton: Combinatorial Curve Reconstruction

✍ Scribed by Nina Amenta; Marshall Bern; David Eppstein

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
226 KB
Volume
60
Category
Article
ISSN
1077-3169

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✦ Synopsis

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 extraneous edges. The required sampling density varies with the local feature size on the curve, so that areas 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 β-skeleton, using a specific value of β.

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