The concept of alpha shapes is an approach to
formalize the intuitive notion of "shape" for spatial point sets.
The Alpha shape is a concrete geometric concept which is mathematically
well defined: it is a generalization of the convex hull and a subgraph
of the Delaunay triangulation. Given a finite point set, a family of shapes
can be derived from the Delaunay triangulation of the point set; a real
parameter, "alpha," controls the desired level of detail. The
set of all real alpha values leads to a whole family of shapes capturing
the intuitive notion of "crude" versus "fine" shapes
of a point set.
Here is an example for different values of alpha.
Notice the second picture which displays the boundary of the point set's