Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T19:25:14.131Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic approximation of smooth convex bodies by general polytopes

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Monika Ludwig
Monika Ludwig
Affiliation:
Institut für Analysis, Technische Universität Wien, Wiedner Hauptstraβe 8 10/1142, A-1040 Wien, Austria e-mail: [email protected]
Get access

Extract

For the optimal approximation of convex bodies by inscribed or circumscribed polytopes there are precise asymptotic results with respect to different notions of distance. In this paper we derive some results on optimal approximation without restricting the polytopes to be inscribed or circumscribed.

MSC classification

Secondary: 52A27: Approximation by convex sets
Type
Research Article
Information
Mathematika , Volume 46 , Issue 1 , June 1999 , pp. 103 - 125
Copyright
Copyright © University College London 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Aurenhammer, F.. Power diagrams: properties, algorithms and applications. SIAM J. Comput. 16 (1987), 78–96.CrossRefGoogle Scholar
2.Bandle, C.. Isoperimetric inequalities and applications (Pitman, Boston, 1980).Google Scholar
3.JrBöröczky, K.. and Ludwig, M.. Approximation of convex bodies and a momentum lemma for power diagrams, Monatsh. Math. 127 (1999), 101–110.Google Scholar
4.Tóth, L. Fejes, Lagerungen in der Ebene, aufder Kugel und im Raum (2nd ed.) (Springer, Berlin, 1972).CrossRefGoogle Scholar
5.Glasauer, S. and Gruber, P. M.. Asymptotic estimates for best and stepwise approximation of convex bodies III, Forum Math. 9 (1997), 383–404.CrossRefGoogle Scholar
6.Gruber, P. M.. Volume approximation of convex bodies by inscribed polytopes, Math. Ann. 281 (1988), 229–245.CrossRefGoogle Scholar
7.Gruber, P. M.. Volume approximation of convex bodies by circumscribed polytopes, Applied Geometry and Discrete Mathematics, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 4. (Amer. Math. Soc, Providence, RI, 1991, 309–317).CrossRefGoogle Scholar
8.Gruber, P. M.. Aspects of approximation of convex bodies, Handbook of Convex Geometry (ed. Gruber, P. M. and Wills, J.) (North-Holland, Amsterdam, 1993, 319–345).CrossRefGoogle Scholar
9.Gruber, P. M.. Asymptotic estimates for best and stepwise approximation of convex bodies II, Forum Math. 5 (1993), 521 538.Google Scholar
10.Gruber, P. M. and Kenderov, P.. Approximation of convex bodies by polytopes, Rend. Circ. Mat. Palermo 31 (1982), 195–225.CrossRefGoogle Scholar
11.McClure, D. and Vitale, R.. Polygonal approximation of plane convex bodies, J. Math. Anal. Appl. 51 (1975), 326–358.CrossRefGoogle Scholar
12.Schneider, R.. Convex Bodies: the Brunn-Minkowski Theory (Cambridge, 1993).CrossRefGoogle Scholar