dc.contributor.author Sun, Julie en dc.date.accessioned 2006-08-22 14:23:16 (GMT) dc.date.available 2006-08-22 14:23:16 (GMT) dc.date.issued 1999 en dc.date.submitted 1999 en dc.identifier.uri http://hdl.handle.net/10012/1111 dc.description.abstract In this thesis, we study foldings of orthogonal polygons into orthogonal polyhedra. The particular problem examined here is whether a paper cutout of an orthogonal polygon with fold lines indicated folds up into a simple orthogonal polyhedron. The folds are orthogonal and the direction of the fold (upward or downward) is also given. We present a polynomial time algorithm to solve this problem. Next we consider the same problem with the exception that the direction of the folds are not given. We prove that this problem is NP-complete. Once it has been determined that a polygon does fold into a polyhedron, we consider some restrictions on the actual folding process, modelling the case when the polyhedron is constructed from a stiff material such as sheet metal. We show an example of a polygon that cannot be folded into a polyhedron if folds can only be executed one at a time. Removing this restriction, we show another polygon that cannot be folded into a polyhedron using rigid material. en dc.format application/pdf en dc.format.extent 254674 bytes dc.format.mimetype application/pdf dc.language.iso en en dc.publisher University of Waterloo en dc.rights Copyright: 1999, Sun, Julie. All rights reserved. en dc.subject Computer Science en dc.subject folding en dc.subject orthogonal en dc.subject polyhedra en dc.subject rectilinear en dc.subject paper en dc.subject cutout en dc.title Folding Orthogonal Polyhedra en dc.type Master Thesis en dc.pending false en uws-etd.degree.department School of Computer Science en uws-etd.degree Master of Mathematics en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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