An iterative algorithm for reconstructing inscribed triangles
type: Item
instance of: scholarly article
title: An iterative algorithm for reconstructing inscribed triangles
zbMATH Open document ID: 0712.65119
DOI: 10.1007/BF02575723
published in: Calcolo
publication date: 1989-01-01T00:00:00Z
review text: Let K be a convex smooth body in \({\mathbb{R}}^ 2\), and let three directions be given. According to a theorem of \textit{H. Kramer} and \textit{A. B. Németh} [Rev. Anal. Numér. Théorie Approximation 1, 63-71 (1972; Zbl 0352.53002)] there are precisely two triangles inscribed to K with sides parallel to the given directions. The paper gives an algorithm for determining these triangles from the projection of K in the given directions. The algorithm is applied to the problem of recovering K from four projections.
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 53C65
zbMATH DE Number: 4172341
zbMATH Keywords: integral geometry
zbMATH Keywords: Radon transform
zbMATH Keywords: reconstruction of inscribed triangles
zbMATH Keywords: algorithm
author: Giacomo Michelacci
reviewed by: Frank Natterer
MaRDI profile type: Publication
cites work: On successive approximations for nonexpansive mappings in Banach spaces
cites work: Characterisation of measurable plane sets which are reconstructable from their two projections
cites work: Tomographic reconstruction of a convex body
cites work: Q3754464
cites work: Tomography of convex bodies and inscribed polygons
description: scientific article; zbMATH DE number 4172341