Persistent Link:
http://hdl.handle.net/10150/202980
Title:
Weighted Delaunay Triangulations of Piecewise-Flat Surfaces
Author:
Gorlina, Yuliya
Issue Date:
2011
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Given a triangulated piecewise-flat surface and a function on the vertices we can define the Dirichlet energy, which is related to the Dirichlet energy of a smooth function. To find the Delaunay triangulation of the piecewise flat surface, we modify the triangulation by a sequence of edge flips, called the flip algorithm, which transform an edge which is not Delaunay into one that is Delaunay. It is known that the flip algorithm works in the plane as well as for a piecewise-flat surface, where we have to ensure that only finitely many triangulations are possible.When the vertices of a piecewise-flat surface have weights, we want to find the weighted Delaunay triangulation using a flip algorithm. In this dissertation, we prove that the maximum edge length during the algorithm is bounded, which guarantees that there are finitely many triangulations. Thus the flip algorithm terminates and the resulting triangulation is weighted Delaunay.Additionally, we give a new way to find what we call the relaxed weighted Delaunay on a flat surface.
Type:
text; Electronic Dissertation
Keywords:
Mathematics
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Glickenstein, David

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleWeighted Delaunay Triangulations of Piecewise-Flat Surfacesen_US
dc.creatorGorlina, Yuliyaen_US
dc.contributor.authorGorlina, Yuliyaen_US
dc.date.issued2011-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractGiven a triangulated piecewise-flat surface and a function on the vertices we can define the Dirichlet energy, which is related to the Dirichlet energy of a smooth function. To find the Delaunay triangulation of the piecewise flat surface, we modify the triangulation by a sequence of edge flips, called the flip algorithm, which transform an edge which is not Delaunay into one that is Delaunay. It is known that the flip algorithm works in the plane as well as for a piecewise-flat surface, where we have to ensure that only finitely many triangulations are possible.When the vertices of a piecewise-flat surface have weights, we want to find the weighted Delaunay triangulation using a flip algorithm. In this dissertation, we prove that the maximum edge length during the algorithm is bounded, which guarantees that there are finitely many triangulations. Thus the flip algorithm terminates and the resulting triangulation is weighted Delaunay.Additionally, we give a new way to find what we call the relaxed weighted Delaunay on a flat surface.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectMathematicsen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorGlickenstein, Daviden_US
dc.contributor.committeememberPickrell, Douglasen_US
dc.contributor.committeememberLin, Kevinen_US
dc.contributor.committeememberVenkatarami, Shankaren_US
dc.contributor.committeememberGlickenstein, Daviden_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.