Some nonrealizable line diagrams
type: Item
instance of: scholarly article
title: Some nonrealizable line diagrams
zbMATH Open document ID: 0827.52008
DOI: 10.1007/BF01258303
author: Rudi Penne
published in: Journal of Intelligent \& Robotic Systems
publication date: 1995-12-17T00:00:00Z
review text: Weaving patterns are planar configurations of lines, no three through a point, together with an ``under'' information given at each crossing. Such a weaving pattern may or may not be realizable, i.e., represent the projection of a three-dimensional configuration of disjoint lines. (To check this for a single instance amounts to a linear programming problem.) In the current article, the author provides a brief survey of work on weaving patterns line diagrams in the last few years, and a review of potentially relevant concepts from oriented matroid theory. His main result shows how, given a suitable planar drawing of a line configuration, one can explicitly construct ``under'' functions of nonrealizable weaving patterns. The corresponding nonrealizable ``under'' functions were much more abstractly given by \textit{W. Whiteley} in Prop. 5.8 of [Rigidity and polarity. II: Weaving lines and tensegrity frameworks, Geom. Dedicata 30, 255-279 (1989; Zbl 0675.51008)].
Mathematics Subject Classification ID: 52B40
Mathematics Subject Classification ID: 52C35
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 746203
zbMATH Keywords: weaving pattern
zbMATH Keywords: line diagrams
zbMATH Keywords: oriented matroid
zbMATH Keywords: line configuration
reviewed by: Günter M. Ziegler
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 746203