Volume 44, Number 1, January-March 2010
|Page(s)||45 - 59|
|Published online||08 February 2010|
Explicit polyhedral approximation of the Euclidean ball
Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau, France ; Frederic.Bonnans@inria.fr
2 Commissariat à l'Energie Atomique, Direction de la Protection et de la Sûreté Nucléaire, Service Sûreté Nucléaire, Centre de Fontenay aux Roses, B.P. No 6, 92265 Fontenay aux Roses Cedex, France; email@example.com
We discuss the problem of computing points of I Rn whose convex hull contains the Euclidean ball, and is contained in a small multiple of it. Given a polytope containing the Euclidean ball, we introduce its successor obtained by intersection with all tangent spaces to the Euclidean ball, whose normals point towards the vertices of the polytope. Starting from the L∞ ball, we discuss the computation of the two first successors, and give a complete analysis in the case when n=6.
Mathematics Subject Classification: 90C05
Key words: Polyhedral approximation / convex hull / invariance by a group of transformations / canonical cuts / reduction
© EDP Sciences, ROADEF, SMAI, 2010
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