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| 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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| H. Edelsbrunner and E. P. Mucke. Simulation of
Simplicity: a technique to cope with degenerate cases in geometric algorithms.
ACM Trans. Graphics 9 (1990), 66-104. Download Article (PostScript) |
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| B. Joe. Construction of three-dimensional Delaunay triangulations using local transformations. Comput. Aided Geom. Design 8 (1991), 123-142. | |
| H. Edelsbrunner and E. P. Mucke. Three-dimensional
alpha shapes. ACM Trans. Graphics 13 (1994), 43-72. Download Article (PostScript) |
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| H. Edelsbrunner and N. R. Shah. Incremental topological flipping works for regular triangulations. Algorithmica 15 (1996), 223-241. | |
| C. J. A. Delfinado and H. Edelsbrunner. An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere. Comput. Aided Geom. Design 12 (1995), 771-784. | |
| H. Edelsbrunner and P. Fu. Measuring space filling diagrams and voids. Rept. UIUC-BI-MB-94-01, Beckman Inst., Molecular Biophysics Group, Univ. Illinois at Urbana-Champaign, 1994. | |
| H. Edelsbrunner. The union of balls and its dual shape. Discrete Comput. Geom. 13 (1995), 415-440. | |
| E. P. Mucke. Shapes and Implementations in Three-Dimensional
Geometry. PhD Thesis, Rept. UIUCDCS-R-93-1836, Dept. Comput. Sci.,
Univ. Illinois at Urbana-Champaign, 1993. Download Article(PostScript) |
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| H. Edelsbrunner, M. Facello, P. Fu, and J. Liang. Measuring proteins and voids in proteins. In "Proc. 28th Ann. Hawaii Internat. Conf. System Sci. 1995'', 256-264. | |
| M. A. Facello. Implementation of a randomized algorithm for Delaunay and regular triangulations in three dimensions. Comput. Aided Geom. Design 12 (1995), 349-370. | |
| N. Akkiraju, H. Edelsbrunner, M. Facello, P. Fu, E. P. Mucke, and C. Varela. Alpha shapes: definition and software. In "Proc. Internat. Comput. Geom. Software Workshop 1995'', Minneapolis. | |
| H. Edelsbrunner, M. A. Facello, and J. Liang. On the definition and the construction of pockets in macromolecules. In "Proc. Pacific Sympos. Biocomputing 1996'', World Scientific. | |
| B. Delaunay. Sur la sphère vide. Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskii i Estestvennyka Nauk, 7:793--800, 1934. | |
| H. Edelsbrunner, D. G. Kirkpatrick, and R. Seidel. On the shape of a set of points in the plane. IEEE Transactions on Information Theory, IT-29(4):551--559, 1983. | |
| M. F. Richards. Areas, volumes, packing, and protein structure. Ann. Rev. Biophys. Bioeng., 6:151--176, 1977. | |
| D. P. Dobkin and M. J. Laszlo. Primitives for the manipulation of three-dimensional subdivisions. Algorithmica, 4(1):3--32, 1989. | |
| H. Edelsbrunner. A new approach to rectangle intersections, Part I. International Journal of Computer Mathematics, 13:209--219, 1983. | |