The Surface Area Deviation of the Euclidean Ball and a Polytope

Abstract

While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex bodies by arbitrarily positioned polytopes with a fixed number of vertices in the symmetric surface area deviation.

References in corpus (1)

• Convergence of algorithms for reconstructing convex bodies and directional measures

Cited by in corpus (6)

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• Intrinsic and Dual Volume Deviations of Convex Bodies and Polytopes
• Approximation of the Euclidean ball by polytopes with a restricted number of facets
• A Concentration Inequality for Random Polytopes, Dirichlet-Voronoi Tiling Numbers and the Geometric Balls and Bins Problem
• An intrinsic volume metric for the class of convex bodies in ${\mathbb{R}}^n$
• Constrained convex bodies with extremal affine surface areas