Reconstructing polygons from X-rays
type: Item
instance of: scholarly article
title: Reconstructing polygons from X-rays
zbMATH Open document ID: 0873.52016
DOI: 10.1007/BF00151583
author: Steven Skiena
author: Henk Meijer
published in: Geometriae Dedicata
publication date: 1997-11-04T00:00:00Z
review text: The paper contains results on the geometric tomography of polygons in the plane. The authors present strategies for the interactive reconstruction of simple polygons from carefully chosen \(X\)-ray probes, thus generalizing previous results about convex polygons. In particular, they show that \(n+h+2\) parallel \(X\)-ray probes suffice to determine an \(n\)-gon \(P\) with \(h\) vertices on its convex hull (no three vertices being collinear). Furthermore, if an upper bound \(n'\) on the number of vertices of \(P\) is given, then \(2n'+2\) parallel probes or \(3n'\) origin probes are sufficient. Recently, R. Gardner proved that star-shaped polygons cannot be reconstructed from a constant number of parallel \(X\)-ray probes from predetermined directions. Here a logarithmic lower bound for the much stronger case of interactive reconstruction is proved, although the considered polygons are not necessarily star-shaped. In the final part of the paper, some interesting open questions are collected (referring to simple polygons with holes, to non-simple polygons and to higher dimensions, etc.).
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52C05
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 51N20
Mathematics Subject Classification ID: 92C55
zbMATH DE Number: 912990
zbMATH Keywords: parallel \(X\)-ray
zbMATH Keywords: origin \(X\)-ray
zbMATH Keywords: simple polygon
zbMATH Keywords: predetermined direction
zbMATH Keywords: interactive reconstruction
zbMATH Keywords: successive determination
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00151583
OpenAlex ID: W155543678
description: scientific article; zbMATH DE number 912990