Article contents
Asymptotic approximation of smooth convex bodies by general polytopes
Part of:
General convexity
Published online by Cambridge University Press: 26 February 2010
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
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- Copyright © University College London 1999
References
1.Aurenhammer, F.. Power diagrams: properties, algorithms and applications. SIAM J. Comput. 16 (1987), 78–96.CrossRefGoogle 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
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