Nataraj Akkiraju -
Herbert Edelsbrunner -
Michael Facello -
Ping Fu -
Ernst P. Mücke -
Carlos Varela -
The concept of an 
-shape of a finite set of points in
, with weights, is defined and illustrated.
An -shape is a polytope which is not necessarily convex nor
connected and can be derived from the (weighted) Delaunay
triangulation of the point set, with a parameter controlling
the desired level of detail.
The set of all values leads to a
descrete family of shapes capturing the intuitive notion of ``crude''
versus ``fine'' shapes of a point set.
Software that computes such shapes in 
and 
is available via anonymous ftp from:
ftp://ftp.ncsa.uiuc.edu/Visualization/Alpha-shape/