Abstract
The skin of a set of weighted points in ℓd is defined as a differentiable and orientable (d}- 1)-manifold surrounding the points. The skin varies continuously with the points and weights and at all times maintains the homotopy equivalence between the dual shape of the points and the body enclosed by the skin. The variation allows for arbitrary changes in topological connectivity, each accompanied by a momentary violation of the manifold property. The skin has applications to molecular modeling and docking and to geometric metamorphosis.
Research reported in this paper is partially supported by the Office of Naval Research, grant N00014-95-1-0691, and by the National Science Foundation through the Alan T. Waterman award, grant CCR-9118874.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
N. Akkiraju, H. Edelsbrunner, M. Facello, P. Fu, E. P. Mücke and C. Varela. Alpha shapes: definition and software. In “Proc. Internat. Comput. Geom. Software Workshop”, ed. N. Amenta, Geometry Center Res. Rept. GCG-80, 1995.
J. M. Blaney and J. S. Dixon. A good ligand is hard to find: automated docking methods. Perspective in Drug Discovery and Design1 (1993), 301–319.
B. Delaunay. Sur la sphère vide. Izv. Akad. Nauk SSSR, Otdelenie Matematicheskii i Estestvennyka Nauk7 (1934), 793–800.
C. J. A. Delfinado and H. Edelsbrunner. An incremental algorithm for betti numbers of simplicial complexes. In “Proc. 9th Ann. Sympos. Comput. Geom. 1993”, 232–239.
H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag, Heidelberg, Germany, 1987.
H. Edelsbrunner. The union of balls and its dual shape. László Fejes Tóth Festschrift, eds. I. Bárány and J. Pach, Discrete Comput. Geom. 13 (1995), 415–440.
H. Edelsbrunner, M. Facello and J. Liang. On the definition and the construction of pockets in macromolecules. Manuscript, 1995.
H. Edelsbrunner, D. G. Kirkpatrick and R. Seidel. On the shape of a set of points in the plane. IEEE Trans. Inform. TheoryIT-29 (1983), 551–559.
H. Edelsbrunner and E. P. Mücke. Three-dimensional alpha shapes. ACM Trans. Graphics13 (1994), 43–72.
G. Farin. Curves and Surfaces for Computer Aided Geometric Design. Academic Press, Boston, 1988.
P. J. Giblin. Graphs, Surfaces and Homology. 2nd edition, Chapman and Hall, London, 1981.
M. Henle. A Combinatorial Introduction to Topology. Freeman, San Francisco, 1979.
J. R. Kent, W. E. Carlson and R. E. Parent. Shape transformation for polyhedral objects. Computer Graphics26 (1992), 47–54.
I. W. Kuntz. Structure-based strategies for drug design and discovery. Science257 (1992), 1078–1082.
B. Lee and F. M. Richards. The interpretation of protein structures: estimation of static accessibility. J. Mol Biol.55 (1971), 379–400.
J. Milnor. Morse Theory. Princeton Univ. Press, New Jersey, 1969.
F. P. Preparata and M. I. Shamos. Computational Geometry — an Introduction. Springer-Verlag, New York, 1985.
F. M. Richards. Areas, volumes, packing, and protein structure. Ann. Rev. Biophys. Bioeng.6 (1977), 151–176.
G. Voronoi. Nouvelles applications des paramètres continus à la théorie des formes quadratiques. J. Reine Angew. Math.133 (1907), 97–178.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Edelsbrunner, H. (1995). Smooth surfaces for multi-scale shape representation. In: Thiagarajan, P.S. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1995. Lecture Notes in Computer Science, vol 1026. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60692-0_63
Download citation
DOI: https://doi.org/10.1007/3-540-60692-0_63
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60692-5
Online ISBN: 978-3-540-49263-4
eBook Packages: Springer Book Archive