Showing a limited preview of this publication:
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.
Keywords.: Convex bodies; polytopes; visibility; diameter maximization; antipodality; criticality; double normals; codiameter
Received: 2008-10-20
Revised: 2009-04-01
Published Online: 2010-04-13
Published in Print: 2011-January
© de Gruyter 2011