On the shape of a set of points in the plane Edelsbrunner, Herbert ; https://orcid.org/0000-0002-9823-6833 Kirkpatrick, David Seidel, Raimund 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. IEEE 1983 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/4128 Edelsbrunner H, Kirkpatrick D, Seidel R. On the shape of a set of points in the plane. <i>IEEE Transactions on Information Theory</i>. 1983;29(4):551-559. doi:<a href="https://doi.org/10.1109/TIT.1983.1056714 ">10.1109/TIT.1983.1056714 </a> eng info:eu-repo/semantics/altIdentifier/doi/10.1109/TIT.1983.1056714 info:eu-repo/semantics/altIdentifier/issn/0018-9162 info:eu-repo/semantics/altIdentifier/e-issn/1558-0814 info:eu-repo/semantics/closedAccess