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Article | REF: AF220 V1

Convex Geometry II. Distances and Measures, Approximation, Comparison and Symmetrisation

Author: Jean-Charles PINOLI

Publication date: November 10, 2020

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8. Approximation of convex bodies in...

Above: Approximation of convex bodies in ℝ2n

The approximation of a convex body X by "simpler" convex bodies (called approximants) (often polytopes) can take two main forms: direct, by an inscribed (inner approximation) or circumscribed (outer approximation) approximant (p. 103 of ) or a homothetic pair framing X) (bi-approximation), and asymptotic, by a sequence of approximants converging to X.

This approximation requires the use of a volumetric...

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