Reconstruction of convex bodies of revolution from the areas of their shadows
type: Item
instance of: scholarly article
title: Reconstruction of convex bodies of revolution from the areas of their shadows
zbMATH Open document ID: 1066.52004
author: Artem Zvavitch
author: D. Ryabogin
published in: Archiv der Mathematik
publication date: 2005-02-25T00:00:00Z
review text: The paper shows how to reconstruct a three-dimensional convex body \(K\) of revolution when we know the areas of all its projections. It can be done with the help of two formulas. The first formula presents the curvature function \(f(K)\) of \(K\) as a function of the areas of the projections of \(K\). The second formula is an explicit expression for the support function of \(K\) in terms of \(f(K)\). It is proved under the assumptions that \(\partial K\) is of class \(C^ 5\) and that the Gauss curvature of \(K\) at each point is positive.
reviewed by: Marek Lassak
Mathematics Subject Classification ID: 52A15
Mathematics Subject Classification ID: 52A21
Mathematics Subject Classification ID: 52A38
zbMATH DE Number: 2138526
zbMATH Keywords: convex body
zbMATH Keywords: convex body of revolution
zbMATH Keywords: projection
zbMATH Keywords: shadow
zbMATH Keywords: area
zbMATH Keywords: support function
zbMATH Keywords: curvature
MaRDI profile type: Publication
full work available at URL: s00013-004-1071-6
OpenAlex ID: W1981884899
DOI: 10.1007/S00013-004-1071-6
description: scientific article; zbMATH DE number 2138526