Three - dimensional Alpha Shapes 1

Frequently, data in scientiic computing is in its abstract form a nite point set in space, and it is sometimes useful or required to compute what one might call the \shape" of the set. For that purpose, this paper introduces the formal notion of the family of-shapes of a nite point set in IR 3. Each shape is a well-deened polytope, derived from the Delaunay triangulation of the point set, with a parameter 2 IR controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size n in time O(n 2), worst case. A robust implementation of the algorithm is discussed and several applications in the area of scientiic computing are mentioned. Any opinions, ndings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reeect the view of the National Science Foundation.