On the shape of a set of points in the plane

Authors:
H. Edelsbrunner;D. Kirkpatrick;R. Seidel
Affiliations:
-;-;-
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

A generalization of the convex hull of a finite set of points in the plane is introduced and analyzed. This generalization leads to a family of straight-line graphs, "alpha-shapes," which seem to capture the intuitive notions of "fine shape" and "crude shape" of point sets. It is shown that a-shapes are subgraphs of the closest point or furthest point Delaunay triangulation. Relying on this result an optimalO(n log n)algorithm that constructsalpha-shapes is developed.