Dupin cyclides

Introduction: We will study the problem of finding a Dupin cyclide given three contact conditions. A contact condition is a point m in R3 and an orientation at that point, i.e., a vector with initial point m, this vector can be seen as the normal vector of an oriented plane through m. A Dupin cyclid...

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Autores:
Villa Isaza, Alejandro Alberto
Tipo de recurso:
Fecha de publicación:
2014
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/51894
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/51894
http://bdigital.unal.edu.co/46120/
Palabra clave:
51 Matemáticas / Mathematics
Dupin cyclides
Surfaces
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Paluszny Kluczynsky, Marco (Thesis advisor)def8f538-41e2-45d9-87b4-b38d4972e523-1Villa Isaza, Alejandro Albertof9f81b0c-abf7-4c43-8ebe-3ad53467c7bb3002019-06-29T13:01:49Z2019-06-29T13:01:49Z2014https://repositorio.unal.edu.co/handle/unal/51894http://bdigital.unal.edu.co/46120/Introduction: We will study the problem of finding a Dupin cyclide given three contact conditions. A contact condition is a point m in R3 and an orientation at that point, i.e., a vector with initial point m, this vector can be seen as the normal vector of an oriented plane through m. A Dupin cyclide that, historically, is defined as the envelope of a family of spheres which are simultaneously tangent to three given spheres, can be defined in the context of the projective five-dimensional space as 2-plane section of a quadric in this projective space. The points of this quadric correspond to oriented spheres in 3D.Maestríaapplication/pdfspaUniversidad Nacional de Colombia Sede Medellín Facultad de Ciencias Escuela de MatemáticasEscuela de MatemáticasVilla Isaza, Alejandro Alberto (2014) Dupin cyclides. Maestría thesis, Universidad Nacional de Colombia - Sede Medellín.51 Matemáticas / MathematicsDupin cyclidesSurfacesDupin cyclidesTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMORIGINAL1039449231.2014.pdfTesis de Doctorado en Ciencias - Matemáticasapplication/pdf3884821https://repositorio.unal.edu.co/bitstream/unal/51894/1/1039449231.2014.pdf0b326fb1981571df6d23a4ed99d95273MD51THUMBNAIL1039449231.2014.pdf.jpg1039449231.2014.pdf.jpgGenerated Thumbnailimage/jpeg3948https://repositorio.unal.edu.co/bitstream/unal/51894/2/1039449231.2014.pdf.jpg44637e881d67726c8c36a05322f701e9MD52unal/51894oai:repositorio.unal.edu.co:unal/518942023-04-19 08:04:09.378Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Dupin cyclides
title Dupin cyclides
spellingShingle Dupin cyclides
51 Matemáticas / Mathematics
Dupin cyclides
Surfaces
title_short Dupin cyclides
title_full Dupin cyclides
title_fullStr Dupin cyclides
title_full_unstemmed Dupin cyclides
title_sort Dupin cyclides
dc.creator.fl_str_mv Villa Isaza, Alejandro Alberto
dc.contributor.advisor.spa.fl_str_mv Paluszny Kluczynsky, Marco (Thesis advisor)
dc.contributor.author.spa.fl_str_mv Villa Isaza, Alejandro Alberto
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
topic 51 Matemáticas / Mathematics
Dupin cyclides
Surfaces
dc.subject.proposal.spa.fl_str_mv Dupin cyclides
Surfaces
description Introduction: We will study the problem of finding a Dupin cyclide given three contact conditions. A contact condition is a point m in R3 and an orientation at that point, i.e., a vector with initial point m, this vector can be seen as the normal vector of an oriented plane through m. A Dupin cyclide that, historically, is defined as the envelope of a family of spheres which are simultaneously tangent to three given spheres, can be defined in the context of the projective five-dimensional space as 2-plane section of a quadric in this projective space. The points of this quadric correspond to oriented spheres in 3D.
publishDate 2014
dc.date.issued.spa.fl_str_mv 2014
dc.date.accessioned.spa.fl_str_mv 2019-06-29T13:01:49Z
dc.date.available.spa.fl_str_mv 2019-06-29T13:01:49Z
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TM
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/51894
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/46120/
url https://repositorio.unal.edu.co/handle/unal/51894
http://bdigital.unal.edu.co/46120/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Medellín Facultad de Ciencias Escuela de Matemáticas
Escuela de Matemáticas
dc.relation.references.spa.fl_str_mv Villa Isaza, Alejandro Alberto (2014) Dupin cyclides. Maestría thesis, Universidad Nacional de Colombia - Sede Medellín.
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/51894/1/1039449231.2014.pdf
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repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
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