Show simple item record

dc.contributor.authorDemaine, Eriken 14:25:34 (GMT) 14:25:34 (GMT)
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.format.extent831699 bytes
dc.publisherUniversity of Waterlooen
dc.rightsCopyright: 2001, Demaine, Erik. All rights reserved.en
dc.subjectComputer Scienceen
dc.subjectcomputational geometryen
dc.subjectdiscrete geometryen
dc.titleFolding and Unfoldingen
dc.typeDoctoral Thesisen
dc.pendingfalseen of Computer Scienceen
uws-etd.degreeDoctor of Philosophyen

Files in this item


This item appears in the following Collection(s)

Show simple item record


University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages