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Edge-unfolding almost-flat convex polyhedral terrains

By M. Eng. Massachusetts Institute of Technology Yanping Chen

Abstract

In this thesis we consider the centuries-old question of edge-unfolding convex polyhedra, focusing specifically on edge-unfoldability of convex polyhedral terrain which are "almost at" in that they have very small height. We demonstrate how to determine whether cut-trees of such almost-at terrains unfold and prove that, in this context, any partial cut-tree which unfolds without overlap and "opens" at a root edge can be locally extended by a neighboring edge of this root edge. We show that, for certain (but not all) planar graphs G, there are cut-trees which unfold for all almost-at terrains whose planar projection is G. We also demonstrate a non-cut-tree-based method of unfolding which relies on "slice" operations to build an unfolding of a complicated terrain from a known unfolding of a simpler terrain. Finally, we describe several heuristics for generating cut-forests and provide some computational results of such heuristics on unfolding almost-at convex polyhedral terrains.by Yanping Chen.Thesis (M. Eng.)--Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 97-98)

Topics: Electrical Engineering and Computer Science.
Publisher: Massachusetts Institute of Technology
Year: 2013
OAI identifier: oai:dspace.mit.edu:1721.1/84729
Provided by: DSpace@MIT

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