TY - JOUR AB - Frequently, data in scientific computing is in its abstract form a finite 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 article introduces the formal notion of the family of alpha-shapes of a finite point set in R3. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter alpha is-an-element-of R 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(n2), worst case. A robust implementation of the algorithm is discussed, and several applications in the area of scientific computing are mentioned. AU - Edelsbrunner, Herbert AU - Mücke, Ernst ID - 4037 IS - 1 JF - ACM Transactions on Graphics TI - Three-dimensional alpha shapes VL - 13 ER -