The alpha shape programs are based on the theory of alpha shapes, Delaunay 
triangulations, and simulated perturbation.  The following papers had a
significant influence on the program development.

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REFERENCES

[1]     Herbert Edelsbrunner and Ernst Mucke.  Simulation of Simplicity:
        a technique to cope with degenerate cases in geometric algorithms.
        ACM Transactions on Graphics, 9(1):66-104, 1990.
        [ftp://cs.uiuc.edu/pub/geometry/edels/sos-90.ps.Z]

[2]     Barry Joe. Construction of three-dimensional Delaunay triangulations
        using local transformations.  Computer Aided Geometric Design,
        8(2):123-142, 1991.

[3]     Herbert Edelsbrunner and Ernst Mucke.  Three-dimensional alpha shapes.
        ACM Transactions on Graphics, 13(1):43-72, 1994.
        [ftp://cs.uiuc.edu/pub/edels/geometry/shapes-94.Z]

[4]     Herbert Edelsbrunner and Nimish Shah.  Incremental topological
        flipping works for regular triangulations.  In the Proceedings of
        the 8th Annual Symposium on Computational Geometry, 1992, 43-52.

[5]     Cecil Delfinado and Herbert Edelsbrunner.  An incremental algorithm
        for Betti numbers of simplicial complexes.  In the Proceedings of the
        9th Annual Symposium on Computational Geometry, 1993, 232-239.

[6]     Herbert Edelsbrunner and Ping Fu.  Measuring space filling diagrams
        and voids.  Report UIUC-BI-MB-94-01, Beckman Institute, Molecular
        Biophysics Group, University of Illinois at Urbana Champaign, 1994.

[7]     Herbert Edelsbrunner.  The union of balls and its dual shape.
        In the Proceedings of the 9th Annual Symposium on Computational
        Geometry, 1993, 218-231.

[8]     Ernst Mucke.  Shapes and Implementations in Three-Dimensional Geometry.
        PhD Thesis.  Department of Computer Science, University of Illinois at
        Urbana-Champaign.  Technical Report UIUCDCS-R-93-1836.
        [ftp://cs.uiuc.edu/pub/TechReports/UIUCDCS-R-93-1836.ps.Z]

[9]     Herbert Edelsbrunner, Michael Facello, Ping Fu and Jie Liang.
        Measuring proteins and voids in proteins.  In the Proceedings of the
        28th Hawaii Conference on System Sciences, 1995, to appear.

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QUOTE
               ................................................................
               "... but that's mathematics, and that doesn't convince anybody."
               -- George Francis
               ................................................................