Discrete Curvatures and Discrete Minimal Surfaces

Handle URI:
http://hdl.handle.net/10754/273092
Title:
Discrete Curvatures and Discrete Minimal Surfaces
Authors:
Sun, Xiang ( 0000-0003-0242-0319 )
Abstract:
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.
Advisors:
Pottmann, Helmut ( 0000-0002-3195-9316 )
Committee Member:
Kasimov, Aslan; Mitra, Niloy J.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
Jun-2012
Type:
Thesis
Appears in Collections:
Applied Mathematics and Computational Science Program; Theses; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.advisorPottmann, Helmuten
dc.contributor.authorSun, Xiangen
dc.date.accessioned2013-03-16T07:21:05Z-
dc.date.available2013-03-16T07:21:05Z-
dc.date.issued2012-06en
dc.identifier.urihttp://hdl.handle.net/10754/273092en
dc.description.abstractThis thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.en
dc.language.isoenen
dc.subjectCurvatureen
dc.subjectDiscret minimal surfaceen
dc.subjectDiscrete differential geometryen
dc.subjectKoenigs meshen
dc.subjectOptimizationen
dc.titleDiscrete Curvatures and Discrete Minimal Surfacesen
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberKasimov, Aslanen
dc.contributor.committeememberMitra, Niloy J.en
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameMaster of Scienceen
dc.person.id113351en
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