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For a given point set $S$ in a plane, we develop a distributed algorithm tocompute the $\alpha-$shape of $S$. $\alpha-$shapes are well known geometricobjects which generalize the idea of a convex hull, and provide a gooddefinition for the shape of $S$. We assume that the distances between pairs ofpoints which are closer than a certain distance $r>0$ are provided, and we showconstructively that this information is sufficient to compute the alpha shapesfor a range of parameters, where the range depends on $r$.  Such distributed algorithms are very useful in domains such as sensornetworks, where each point represents a sensing node, the location of which isnot necessarily known.  We also introduce a new geometric object called the Delaunay-\v{C}ech shape,which is geometrically more appropriate than an $\alpha-$shape for some cases,and show that it is topologically equivalent to $\alpha-$shapes.

Distributed boundary tracking using alpha and Delaunay-Cech shapes