References

1

B. Delaunay. Sur la sphère vide. Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskii i Estestvennyka Nauk, 7:793--800, 1934.

2

C. J. A. Delfinado and H. Edelsbrunner. An incremental algorithm for Betti numbers ofd simplicial complexes. In Proceedings of the 9th Annual Symposium on Computational Geometry, pages 232--239, 1993.

3

D. P. Dobkin and M. J. Laszlo. Primitives for the manipulation of three-dimensional subdivisions. Algorithmica, 4(1):3--32, 1989.

4

H. Edelsbrunner. A new approach to rectangle intersections, Part I. International Journal of Computer Mathematics, 13:209--219, 1983.

5

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

6

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.

7

H. Edelsbrunner and E. P. Mücke. Simulation of Simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Transactions on Graphics, 9(1):66--104, 1990.
http://www.geom.uiuc.edu/~mucke/GeomDir/sos90.ps.gz

8

H. Edelsbrunner and E. P. Mücke. Three-dimensional alpha shapes. ACM Transactions on Graphics, 13(1):43--72, 1994.
http://www.geom.uiuc.edu/~mucke/GeomDir/shapes94.ps.gz

9

H. Edelsbrunner and N. R. Shah. Incremental topological flipping works for regular triangulations. In Proceedings of the 8th Annual Symposium on Computational Geometry, pages 43--52, 1992.

10

P. J. Giblin. Graphs, Surfaces, and Homology. Second edition. Chapman and Hall, London, 1981.

11

H. Hadwiger. Vorlesungen über Inhalt, Oberfläche und Isoperimetrie. Springer-Verlag, Berlin, 1957.

12

E. P. Mücke. Shapes and Implementations in Three-Dimensional Geometry. PhD thesis, Department of Computer Science, University of Illinois at Urbana-Champaign, Ubana, Illinois, 1993. Technical report UIUCDCS-R-93-1836.
ftp://cs.uiuc.edu/pub/TechReports/UIUCDCS-R-93-1836.ps.Z

13

M. F. Richards. Areas, volumes, packing, and protein structure. Ann. Rev. Biophys. Bioeng., 6:151--176, 1977.

14

R. Schneider. Convex Bodies: the Brunn-Minkowski Theory. Cambridge University Press, 1993.