Polytopal approximation of elongated convex bodies

2016/12/14 by Bonnet, Gilles
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1612.04706

Abstract

This paper presents bounds for the best approximation, with respect to the Hausdorff metric, of a convex body K by a circumscribed polytope P with a given number of facets. These bounds are of particular interest if K is elongated. To measure the elongation of the convex set, its isoperimetric ratio V_j(K)^1/j V_i(K)^-1/i is used.

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