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dc.contributor.advisorPottmann, Helmut
dc.contributor.authorSun, Xiang
dc.date.accessioned2013-03-16T07:21:05Z
dc.date.available2014-12-31T00:00:00Z
dc.date.issued2012-06
dc.identifier.citationSun, X. (2012). Discrete Curvatures and Discrete Minimal Surfaces. KAUST Research Repository. https://doi.org/10.25781/KAUST-TX818
dc.identifier.doi10.25781/KAUST-TX818
dc.identifier.urihttp://hdl.handle.net/10754/273092
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.
dc.language.isoen
dc.subjectCurvature
dc.subjectDiscret minimal surface
dc.subjectDiscrete differential geometry
dc.subjectKoenigs mesh
dc.subjectOptimization
dc.titleDiscrete Curvatures and Discrete Minimal Surfaces
dc.typeThesis
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.rights.embargodate2014-12-31
thesis.degree.grantorKing Abdullah University of Science and Technology
dc.contributor.committeememberKasimov, Aslan R.
dc.contributor.committeememberMitra, Niloy J.
thesis.degree.disciplineApplied Mathematics and Computational Science
thesis.degree.nameMaster of Science
dc.rights.accessrightsAt the time of archiving, the student author of this thesis opted to temporarily restrict access to it. The full text of this thesis became available to the public after the expiration of the embargo on 2014-12-31.
refterms.dateFOA2014-12-31T00:00:00Z


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