Volume approximation of convex bodies by inscribed polytopes

DOI10.1007/BF01458430zbMath0628.52006MaRDI QIDQ1093161

Peter M. Gruber

Publication date: 1988

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164415

zbMATH Keywords

convex bodiesvolume approximationinscribed convex polytopes

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Inequalities and extremum problems involving convexity in convex geometry (52A40) Multidimensional problems (41A63) Convex sets in (3) dimensions (including convex surfaces) (52A15)

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Asymptotic approximation of convex curves ⋮ Best and random approximation of a convex body by a polytope ⋮ A geometric lower bound theorem ⋮ The spherical convex floating body ⋮ A concentration inequality for random polytopes, Dirichlet-Voronoi tiling numbers and the geometric balls and bins problem ⋮ A method for approximating the solution set of a system of convex inequalities by polytopes ⋮ Volume approximation of smooth convex bodies by three-polytopes of restricted number of edges ⋮ Exact asymptotics of the uniform error of interpolation by multilinear splines ⋮ New analysis of the sphere covering problems and optimal polytope approximation of convex bodies ⋮ Approximation of convex sets by polytopes ⋮ Ulam floating bodies ⋮ The error of polytopal approximation with respect to the symmetric difference metric and the \(L_p\) metric ⋮ A discrete methodology for controlling the sign of curvature and torsion for NURBS ⋮ Approximation of general smooth convex bodies ⋮ Asymptotic approximation of smooth convex bodies by general polytopes

Cites Work

• Approximation of convex bodies by polytopes
• Polygonal approximation of plane convex bodies
• On Blaschke's rolling theorems
• Metric entropy of some classes of sets with differentiable boundaries
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