On the Shape of a Set of Points in the Plane

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Authors H. Edelsbrunner, D. Kirkpatrick, R. Seidel
Journal/Conference Name IEEE Transactions on Information Theory
Paper Category
Paper 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 optimal O(n \log n) algorithm that constructs \alpha -shapes is developed.
Date of publication 2004
Code Programming Language C++

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