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# Alpha Shapes: Definition and Software

**
Nataraj Akkiraju -
Herbert Edelsbrunner -
Michael Facello - **

Ping Fu -
Ernst P. Mücke -
Carlos Varela -

### Abstract:

*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/ `

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<epm@ansys.com> `11-Sep-95`