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Visibility and diameter maximization of convex bodies

Visibility and diameter maximization of convex bodies This paper considers the problem of diameter maximization of a convex body in the Euclidean space and its connection with Valentine's notion of visibility. The so-called diametral spectrum, or set of critical lengths, is studied in depth from a topological point of view. As a side result, we give a new characterization of planar convex bodies of constant width. Our methodology emphasizes the role played by the concepts of critical pair and critical curve. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Visibility and diameter maximization of convex bodies

Moreno, Joséé Pedro; Seeger, Alberto
Forum Mathematicum , Volume 23 (1) – Jan 1, 2011
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Publisher
de Gruyter
Copyright
©© de Gruyter 2011
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/FORM.2011.005
Publisher site
See Article on Publisher Site

Abstract

This paper considers the problem of diameter maximization of a convex body in the Euclidean space and its connection with Valentine's notion of visibility. The so-called diametral spectrum, or set of critical lengths, is studied in depth from a topological point of view. As a side result, we give a new characterization of planar convex bodies of constant width. Our methodology emphasizes the role played by the concepts of critical pair and critical curve.

Journal

Forum Mathematicum – de Gruyter

Published: Jan 1, 2011

Keywords: Convex bodies; polytopes; visibility; diameter maximization; antipodality; criticality; double normals; codiameter

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