Inequalities for the curvature of curves and surfaces

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2005, Pages 272-277

  Cohen Steiner, David ^a   Edelsbrunner, Herbert ^a  

^a Duke University   (United States)

Author keywords

Approximation; Bottleneck distance; Curvature; Fr chet distance; Integral geometry; Persistence diagrams; Stability

Indexed keywords

ALGEBRA; COMPUTATIONAL GEOMETRY; TOPOLOGY;

APPROXIMATION; BOTTLENECK DISTANCE; CURVATURE; FRÉCHET DISTANCE; INTEGRAL GEOMETRY; PERSISTENCE DIAGRAMS;

SURFACES;

EID: 33244493319     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1064092.1064134     Document Type: Conference Paper

References (17)

1. H. ALT AND M. GODAU. Computing the Fréchet distance between two polygonal curves. Int. J. Comput. Geom. Appl. 5 (1995), 75-91.
2. T. BANCHOFF. Critical points and curvature for embedded polyhedra. J. Diff. Geom. 1 (1967), 245-256.
3. L. BROECKER AND M. KUPPE. Integral geometry of tame sets. Preprint, Math. Dept., Westfälische Wilhelms-Universität, Münster, Germany, 2000.
4. G. CARLSSON AND A. ZOMORODIAN. Computing persistent homology. In "Proc. 20th Ann. Sympos. Comput. Geom., 2004", 347-356.
5. D. COHEN-STEINER. Topics in Surface Discretization. Ph. D. thesis, Ecole Polytechnique, Palaiseau, France, 2003.
6. D. COHEN-STEINER, H. EDELSBRUNNER AND J. HARER. Stability of persistence diagrams. In "Proc. 21st Ann. Sympos. Comput. Geom., 2005", to appear.
7. D. COHEN-STEINER AND J.-M. MORVAN. Restricted Delaunay triangulations and normal cycles. In "Proc. 19th Ann. Sympos. Comput. Geom., 2003", 312-321.
8. M. P. DO CARMO. Differential Geometry of Curves and Surfaces. Prentice Hall, Upper Saddle River, New Jersey, 1976.
9. H. EDELSBRUNNER, D. LETSCHER AND A. ZOMORODIAN. Topological persistence and simplification. Discrete Comput. Geom. 28 (2002), 511-533.
10. I. FÁRY. Sur certaines inégalités géométriques. Acta Sci. Math. Szeged 12 (1950), 117-124.
11. J. H. G. Fu. Convergence of curvatures in secant approximations. J. Diff. Geom. 37 (1993), 177-190.
12. J. MILNOR. Euler characteristic and finitely additive Steiner measures. In Collected Papers, volume 1: Geometry, Publish or Perish, Houston, Texas, 1994.
13. J. R. MUNKRES. Elements of Algebraic Topology. Addison-Wesley, Redwood City, California, 1984.
14. L. SANTALÓ. Integral Geometry and Geometric Probability. Addison-Wesley, 1976, reprinted by Cambridge Univ. Press, England, 2004.
15. J. STEINER. Gesammelte Werke. Prussian Academy of Sciences, 1881, reprinted by Chelsea, New-York, 1971.
16. S. TABACHNIKOV. The tale of a geometric inequality. MASS colloquium lecture, 1999.
17. R. VAN DAMME AND L. ALBOUL. Tight triangulations. In Mathematical Methods for Curves and Surfaces, eds. M. Daehlen, L. Lyche and L. L. Schumaker, Vanderbilt Univ. Press, Nashville, Tennessee, 517-526, 1995.