  For a given point set $S$ in a plane, we develop a distributed algorithm to
compute the $\alpha-$shape of $S$. $\alpha-$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 $r$.
  Such distributed algorithms are very useful in domains such as sensor
networks, where each point represents a sensing node, the location of which is
not 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.
