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dc.contributor.authorDemaine, Eriken
dc.date.accessioned2006-08-22 14:25:34 (GMT)
dc.date.available2006-08-22 14:25:34 (GMT)
dc.date.issued2001en
dc.date.submitted2001en
dc.identifier.urihttp://hdl.handle.net/10012/1068
dc.description.abstractThe results of this thesis concern folding of one-dimensional objects in two dimensions: planar linkages. More precisely, a planar linkage consists of a collection of rigid bars (line segments) connected at their endpoints. Foldings of such a linkage must preserve the connections at endpoints, preserve the bar lengths, and (in our context) prevent bars from crossing. The main result of this thesis is that a planar linkage forming a collection of polygonal arcs and cycles can be folded so that all outermost arcs (not enclosed by other cycles) become straight and all outermost cycles become convex. A complementary result of this thesis is that once a cycle becomes convex, it can be folded into any other convex cycle with the same counterclockwise sequence of bar lengths. Together, these results show that the configuration space of all possible foldings of a planar arc or cycle linkage is connected. These results fall into the broader context of folding and unfolding <I>k</I>-dimensional objects in <i>n</i>-dimensional space, <I>k</I> less than or equal to <I>n</I>. Another contribution of this thesis is a survey of research in this field. The survey revolves around three principal aspects that have received extensive study: linkages in arbitrary dimensions (folding one-dimensional objects in two or more dimensions, including protein folding), paper folding (normally, folding two-dimensional objects in three dimensions), and folding and unfolding polyhedra (two-dimensional objects embedded in three-dimensional space).en
dc.formatapplication/pdfen
dc.format.extent831699 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.rightsCopyright: 2001, Demaine, Erik. All rights reserved.en
dc.subjectComputer Scienceen
dc.subjectcomputational geometryen
dc.subjectdiscrete geometryen
dc.subjectalgorithmsen
dc.subjectlinkagesen
dc.titleFolding and Unfoldingen
dc.typeDoctoral Thesisen
dc.pendingfalseen
uws-etd.degree.departmentSchool of Computer Scienceen
uws-etd.degreeDoctor of Philosophyen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


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