Chintakunta, HarishKrim, Hamid2015-07-022015-07-0220131885-4508http://hdl.handle.net/11441/26544We demonstrate real time tracking of systematic failures in sensor networks, using distributed computation of the α−shape derived from the network. More generally, our work may be applied to tracking the boundary of any time varying object, whose data is captured in the form of a point cloud. We also demonstrate the use of a new geometric object called the Delaunay-Cech shape, which is geometrically more appropriate than an ˇ α−shape for some cases. For a given point set S in a plane, we develop a distributed algorithm to compute the α−shape of S. α−shapes are well known geometric objects which generalize the idea of a convex hull, and provide a good definition for the shape of S. We assume that the distances between pairs of points which are closer than a certain distance r > 0 are provided, and we show constructively that this information is sufficient to compute the alpha shapes for a range of parameters, where the range depends on r.application/pdfengAtribución-NoComercial-SinDerivadas 4.0 Españahttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess