Three-dimensional alpha shapes

Authors:
Herbert Edelsbrunner;Ernst P. Mücke
Affiliations:
Univ. of Illinois, Urbana-Champaign;Univ. of Illinois, Urbana-Champaign
Venue:
ACM Transactions on Graphics (TOG)
Year:
1994

Citing 16
Cited 241

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Abstract

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 &agr;-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 &agr; &egr; 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 0(n2), worst case. A robust implementation of the algorithm is discussed, and several applications in the area of scientific computing are mentioned.