On the shape of a set of points in the plane

@inproceedings{Edelsbrunner1983OnTS,
  title={On the shape of a set of points in the plane},
  author={Herbert Edelsbrunner and David G. Kirkpatrick and Raimund Seidel},
  booktitle={IEEE Transactions on Information Theory},
  year={1983}
}
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 optimal O(n \log n) algorithm that constructs \alpha -shapes is developed. 

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