Superfície mínima discreta

Detalhes bibliográficos
Autor(a) principal: Moreira, Nadia Cardoso
Data de Publicação: 2014
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da Universidade Federal do Espírito Santo (riUfes)
Texto Completo: http://repositorio.ufes.br/handle/10/6791
Resumo: The Minimal Surfaces problem emerged from the study of the Calculus of Variations with the meaning of being a regular surface of smallest area among those that set a specific boundary. This problem was proposed by Lagrange in 1760 and is called the Plateau Problem due to experimental studies of the physicist Joseph Antoine Ferdinand Plateau. This work proposes a numerical solution to a discrete version of the Plateau Problem from the proposed method by Pinkall and Polthier. Of the discrete viewpoint case, surfaces are simplicial complexes with certain restrictions and we use the concepts of Dirichlet Energy over applications that have triangulated surfaces as domain in order to developed a mathematically consistent algorithm to obtain a minimum surface given a boundary.
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spelling Carmo, Fabiano Petronetto doMoreira, Nadia CardosoCrissaff, Lhaylla dos SantosGonçalves Júnior, EtereldesAraujo, Alancardek Pereira2017-05-10T12:27:55Z2017-05-12T06:00:04Z2014-02-272014-02-27The Minimal Surfaces problem emerged from the study of the Calculus of Variations with the meaning of being a regular surface of smallest area among those that set a specific boundary. This problem was proposed by Lagrange in 1760 and is called the Plateau Problem due to experimental studies of the physicist Joseph Antoine Ferdinand Plateau. This work proposes a numerical solution to a discrete version of the Plateau Problem from the proposed method by Pinkall and Polthier. Of the discrete viewpoint case, surfaces are simplicial complexes with certain restrictions and we use the concepts of Dirichlet Energy over applications that have triangulated surfaces as domain in order to developed a mathematically consistent algorithm to obtain a minimum surface given a boundary.O problema de Superfícies Mínimas surgiu a partir do estudo do Cálculo de Variações com o significado de ser a superfície regular de menor área dentre aquelas que definem um bordo específico. Este problema foi proposto por Lagrange em 1760 e é chamado de Problema de Plateau devido aos estudos experimentais do físico Joseph Antoine Ferdinand Plateau. Esta dissertação propõe uma solução numérica para uma versão discreta do Problema de Plateau a partir do método proposto por Pinkall e Polthier. Do ponto de vista discreto, as superfícies são complexos simpliciais com certas restrições e usaremos os conceitos de Energia de Dirichlet sobre aplicações que possuem superfícies trianguladas como domínio a fim de obter um algoritmo matematicamente consistente para obter uma superfície mínima dado um determinado bordo.CAPESTexthttp://repositorio.ufes.br/handle/10/6791porUniversidade Federal do Espírito SantoMestrado em MatemáticaPrograma de Pós-Graduação em MatemáticaUFESBRCentro de Ciências ExatasPlateau problemDiscrete minimal surfaceCotangent weight schemeDirichlet energySuperfície mínima discretaPeso cotangenteEnergia de DirichletGeometria diferencialSuperfícies mínimasPlateau, Problema deMatemática51Superfície mínima discretainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da Universidade Federal do Espírito Santo (riUfes)instname:Universidade Federal do Espírito Santo (UFES)instacron:UFESCAPESORIGINALDissertacao Nadia Cardoso Moreira.pdfDissertacao Nadia Cardoso Moreira.pdfapplication/pdf10364157http://repositorio.ufes.br/bitstreams/b0d1720d-f477-4bfc-9db6-2df43febb5d9/download89c12de504caaa9949b31836792cad54MD51CC-LICENSElicense_urllicense_urltext/plain; charset=utf-849http://repositorio.ufes.br/bitstreams/51994e70-5935-463b-8bc7-9478721e77aa/download4afdbb8c545fd630ea7db775da747b2fMD52license_textlicense_texttext/html; charset=utf-822064http://repositorio.ufes.br/bitstreams/05e7a9f9-287f-4fb2-bfd3-e6804f4fcb67/downloadef48816a10f2d45f2e2fee2f478e2fafMD53license_rdflicense_rdfapplication/rdf+xml; charset=utf-823148http://repositorio.ufes.br/bitstreams/72a11b2f-343c-48e5-8e50-3208485afb2d/download9da0b6dfac957114c6a7714714b86306MD54LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.ufes.br/bitstreams/b8a5dea0-6877-41c6-a0e5-265836c347d3/download8a4605be74aa9ea9d79846c1fba20a33MD5510/67912024-06-30 16:36:55.289oai:repositorio.ufes.br:10/6791http://repositorio.ufes.brRepositório InstitucionalPUBhttp://repositorio.ufes.br/oai/requestopendoar:21082024-07-11T14:40:23.133718Repositório Institucional da Universidade Federal do Espírito Santo (riUfes) - Universidade Federal do Espírito Santo (UFES)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
dc.title.none.fl_str_mv Superfície mínima discreta
title Superfície mínima discreta
spellingShingle Superfície mínima discreta
Moreira, Nadia Cardoso
Plateau problem
Discrete minimal surface
Cotangent weight scheme
Dirichlet energy
Superfície mínima discreta
Peso cotangente
Energia de Dirichlet
Matemática
Geometria diferencial
Superfícies mínimas
Plateau, Problema de
51
title_short Superfície mínima discreta
title_full Superfície mínima discreta
title_fullStr Superfície mínima discreta
title_full_unstemmed Superfície mínima discreta
title_sort Superfície mínima discreta
author Moreira, Nadia Cardoso
author_facet Moreira, Nadia Cardoso
author_role author
dc.contributor.advisor1.fl_str_mv Carmo, Fabiano Petronetto do
dc.contributor.author.fl_str_mv Moreira, Nadia Cardoso
dc.contributor.referee1.fl_str_mv Crissaff, Lhaylla dos Santos
dc.contributor.referee2.fl_str_mv Gonçalves Júnior, Etereldes
dc.contributor.referee3.fl_str_mv Araujo, Alancardek Pereira
contributor_str_mv Carmo, Fabiano Petronetto do
Crissaff, Lhaylla dos Santos
Gonçalves Júnior, Etereldes
Araujo, Alancardek Pereira
dc.subject.eng.fl_str_mv Plateau problem
Discrete minimal surface
Cotangent weight scheme
Dirichlet energy
topic Plateau problem
Discrete minimal surface
Cotangent weight scheme
Dirichlet energy
Superfície mínima discreta
Peso cotangente
Energia de Dirichlet
Matemática
Geometria diferencial
Superfícies mínimas
Plateau, Problema de
51
dc.subject.por.fl_str_mv Superfície mínima discreta
Peso cotangente
Energia de Dirichlet
dc.subject.cnpq.fl_str_mv Matemática
dc.subject.br-rjbn.none.fl_str_mv Geometria diferencial
Superfícies mínimas
Plateau, Problema de
dc.subject.udc.none.fl_str_mv 51
description The Minimal Surfaces problem emerged from the study of the Calculus of Variations with the meaning of being a regular surface of smallest area among those that set a specific boundary. This problem was proposed by Lagrange in 1760 and is called the Plateau Problem due to experimental studies of the physicist Joseph Antoine Ferdinand Plateau. This work proposes a numerical solution to a discrete version of the Plateau Problem from the proposed method by Pinkall and Polthier. Of the discrete viewpoint case, surfaces are simplicial complexes with certain restrictions and we use the concepts of Dirichlet Energy over applications that have triangulated surfaces as domain in order to developed a mathematically consistent algorithm to obtain a minimum surface given a boundary.
publishDate 2014
dc.date.submitted.none.fl_str_mv 2014-02-27
dc.date.issued.fl_str_mv 2014-02-27
dc.date.accessioned.fl_str_mv 2017-05-10T12:27:55Z
dc.date.available.fl_str_mv 2017-05-12T06:00:04Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
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dc.identifier.uri.fl_str_mv http://repositorio.ufes.br/handle/10/6791
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dc.format.none.fl_str_mv Text
dc.publisher.none.fl_str_mv Universidade Federal do Espírito Santo
Mestrado em Matemática
dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Matemática
dc.publisher.initials.fl_str_mv UFES
dc.publisher.country.fl_str_mv BR
dc.publisher.department.fl_str_mv Centro de Ciências Exatas
publisher.none.fl_str_mv Universidade Federal do Espírito Santo
Mestrado em Matemática
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