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13.342 Articles in journals published by the UPC
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Plane Self Stresses and projected Polyhedra I: The Basic Pattem

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Crapo, Henry
Whiteley, Walter
Document typeArticle
Defense date1993
PublisherUniversité du Québec à Montréal
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
Abstract
Voilà plus d’un siècle, le géomètre (et physicien) Clerk Maxwell décrivait une relation surprenante entre les autocontraintes statiques des charpentes de graphes planaires, et les projections orthogonales de polyèdres sphériques tridimensionnels, en utilisant un outil géométrique appelé la figure réciproque. On entreprend, dans cet article, une analyse approfondie des trois relations entre les autocontraintes, les diagrammes réciproques et les polyèdres spatiaux, à la fois pour les polyèdres sphériques et les polyèdres orientés generaux, et les graphes de leurs aretes. Nous débuterons par la théorie fondamentale des charpentes, des réciproques et des projections spatiales. Ces réciproques sont des outils efficaces pour reconnaître les images de polyèdre (dans des domaines comme l’analyse de scènes) et dans la reconnaissance de motifs d’autocontraintes dans les charpentes planes (au tours de l’étude de leur rigidité statique et dans des etudes connexes comme la juxtaposition de sphères).
 
More than a century ago the geometer (and physicist) Clerk Maxwell described a surprising connection between static self stresses in frameworks with planar graphs, and orthogonal projections of spherical polyhedra from 3-space, using a geometric tool called the reciprocal figure. This paper initiates a thorough analysis of the 3-way connections among self stresses, reciprocal diagrams and spatial polyhedra, for both spherical polyhedra and general oriented polyhedra, and the graphs of their edges. We begin with the basic theory of frameworks, reciprocals and spatial projections. These reciprocals are useful tools both for recognizing pictures of polyhedra (in fields such as scene analysis) and for recognizing the patterns of self stresses in plane frameworks (in the study of their static rigidity and in related studies such as sphere packing).
CitationCrapo, Henry; Whiteley, Walter. "Plane Self Stresses and projected Polyhedra I: The Basic Pattem". Structural Topology, 1993, núm. 20 
URIhttp://hdl.handle.net/2099/1091
ISSN0226-9171
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  • Structural topology - 1993 núm 20 [8]
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