Evaluation of 2D shape likeness for surface reconstruction

Surface or shape reconstruction from 3D digitizations performed in planar samplings are frequent in product design, reverse engineering, rapid prototyping, medical and artistic applications, etc -- The planar slicing of the object offers an opportunity to recover part of the neighborhood information...

Full description

Autores:
Ruíz, Óscar Eduardo
Cadavid, Carlos Alberto
Granados, Miguel
Tipo de recurso:
Fecha de publicación:
2002
Institución:
Universidad EAFIT
Repositorio:
Repositorio EAFIT
Idioma:
eng
OAI Identifier:
oai:repository.eafit.edu.co:10784/9795
Acceso en línea:
http://hdl.handle.net/10784/9795
Palabra clave:
DESARROLLO DE PROTOTIPOS
TEORÍA DE MORSE
ISOMORFISMO (MATEMÁTICAS)
VARIEDADES (MATEMÁTICAS)
IMAGEN TRIDIMENSIONAL EN DISEÑO
Prototype development
Morse theory
Isomorphisms (Mathematics)
Manifolds (Mathematics)
Design imaging
Prototype development
Morse theory
Isomorphisms (Mathematics)
Manifolds (Mathematics)
Design imaging
Geometría computacional
Reconstrucción superficial
Ingeniería inversa
Rights
License
Acceso cerrado
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repository_id_str
spelling 2016-11-30T21:07:43Z20022016-11-30T21:07:43Z1137-7704http://hdl.handle.net/10784/9795Surface or shape reconstruction from 3D digitizations performed in planar samplings are frequent in product design, reverse engineering, rapid prototyping, medical and artistic applications, etc -- The planar slicing of the object offers an opportunity to recover part of the neighborhood information essential to reconstruct the topological 2-manifold embedded in R3 that approximates the object surface -- Next stages of the algorithms find formidable obstacles that are classified in this investigation by the following taxonomy: (i) Although real objects have manifold boundaries, in objects with thin sections or walls, the manifold property remains in the data sample only at the price of very small sampling intervals and large data sets -- For relaxed sampling rates nonmanifold situations are likely -- (ii) The position of the planar slices may produce an associated level function which is non – Morse -- This for example allows the set of critical points of the associated level function to contain one or even two dimensional pieces -- The fact that the Hessian matrix at critical points is non-singular is the Morse condition (as a consequence, critical points are isolated), and allows for the algorithms presented here -- (iii) For Morse condition, the slicing interval may be such that several critical points occur between immediate slices (non- simple condition) -- This article presents the degenerate cases arising from points (i)-(iii) and discusses a shape reconstruction algorithm for digitizations holding the Morse – simple condition -- It presents the results of applying the prescribed algorithms to data sets, and discusses future actions that enlarge the mentioned scopeapplication/pdfengAnales de Ingeniería Gráfica, Issue 15, pp 16-24Acceso cerradohttp://purl.org/coar/access_right/c_14cbEvaluation of 2D shape likeness for surface reconstructioninfo:eu-repo/semantics/articlearticleinfo:eu-repo/semantics/publishedVersionpublishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1DESARROLLO DE PROTOTIPOSTEORÍA DE MORSEISOMORFISMO (MATEMÁTICAS)VARIEDADES (MATEMÁTICAS)IMAGEN TRIDIMENSIONAL EN DISEÑOPrototype developmentMorse theoryIsomorphisms (Mathematics)Manifolds (Mathematics)Design imagingPrototype developmentMorse theoryIsomorphisms (Mathematics)Manifolds (Mathematics)Design imagingGeometría computacionalReconstrucción superficialIngeniería inversaUniversidad EAFIT. Departamento de Ingeniería MecánicaRuíz, Óscar Eduardo5cd3ca43-7161-47b5-9466-aaafabf3baf1-1Cadavid, Carlos Albertocfa112a1-e3c0-45b4-a0d0-0fb696bb195d-1Granados, Miguel0148274b-c3ad-4eab-a8e8-23937fa282b5-1Laboratorio CAD/CAM/CAEAnales de Ingeniería GráficaAnales de Ingeniería Gráfica151624LICENSElicense.txtlicense.txttext/plain; charset=utf-82556https://repository.eafit.edu.co/bitstreams/e4d2e9d0-8610-4693-8b18-b288d1d26645/download76025f86b095439b7ac65b367055d40cMD51ORIGINALEvaluationOf2dShape.pdfEvaluationOf2dShape.pdfapplication/pdf306728https://repository.eafit.edu.co/bitstreams/a4d3436f-0b37-487e-9945-bd78f0abf4ea/downloada413478b84a29568e2512569e79d412bMD5210784/9795oai:repository.eafit.edu.co:10784/97952024-12-04 11:49:40.036restrictedhttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co
dc.title.eng.fl_str_mv Evaluation of 2D shape likeness for surface reconstruction
title Evaluation of 2D shape likeness for surface reconstruction
spellingShingle Evaluation of 2D shape likeness for surface reconstruction
DESARROLLO DE PROTOTIPOS
TEORÍA DE MORSE
ISOMORFISMO (MATEMÁTICAS)
VARIEDADES (MATEMÁTICAS)
IMAGEN TRIDIMENSIONAL EN DISEÑO
Prototype development
Morse theory
Isomorphisms (Mathematics)
Manifolds (Mathematics)
Design imaging
Prototype development
Morse theory
Isomorphisms (Mathematics)
Manifolds (Mathematics)
Design imaging
Geometría computacional
Reconstrucción superficial
Ingeniería inversa
title_short Evaluation of 2D shape likeness for surface reconstruction
title_full Evaluation of 2D shape likeness for surface reconstruction
title_fullStr Evaluation of 2D shape likeness for surface reconstruction
title_full_unstemmed Evaluation of 2D shape likeness for surface reconstruction
title_sort Evaluation of 2D shape likeness for surface reconstruction
dc.creator.fl_str_mv Ruíz, Óscar Eduardo
Cadavid, Carlos Alberto
Granados, Miguel
dc.contributor.department.spa.fl_str_mv Universidad EAFIT. Departamento de Ingeniería Mecánica
dc.contributor.author.none.fl_str_mv Ruíz, Óscar Eduardo
Cadavid, Carlos Alberto
Granados, Miguel
dc.contributor.researchgroup.spa.fl_str_mv Laboratorio CAD/CAM/CAE
dc.subject.lemb.spa.fl_str_mv DESARROLLO DE PROTOTIPOS
TEORÍA DE MORSE
ISOMORFISMO (MATEMÁTICAS)
VARIEDADES (MATEMÁTICAS)
IMAGEN TRIDIMENSIONAL EN DISEÑO
topic DESARROLLO DE PROTOTIPOS
TEORÍA DE MORSE
ISOMORFISMO (MATEMÁTICAS)
VARIEDADES (MATEMÁTICAS)
IMAGEN TRIDIMENSIONAL EN DISEÑO
Prototype development
Morse theory
Isomorphisms (Mathematics)
Manifolds (Mathematics)
Design imaging
Prototype development
Morse theory
Isomorphisms (Mathematics)
Manifolds (Mathematics)
Design imaging
Geometría computacional
Reconstrucción superficial
Ingeniería inversa
dc.subject.keyword.spa.fl_str_mv Prototype development
Morse theory
Isomorphisms (Mathematics)
Manifolds (Mathematics)
Design imaging
dc.subject.keyword.eng.fl_str_mv Prototype development
Morse theory
Isomorphisms (Mathematics)
Manifolds (Mathematics)
Design imaging
dc.subject.keyword..keywor.fl_str_mv Geometría computacional
Reconstrucción superficial
Ingeniería inversa
description Surface or shape reconstruction from 3D digitizations performed in planar samplings are frequent in product design, reverse engineering, rapid prototyping, medical and artistic applications, etc -- The planar slicing of the object offers an opportunity to recover part of the neighborhood information essential to reconstruct the topological 2-manifold embedded in R3 that approximates the object surface -- Next stages of the algorithms find formidable obstacles that are classified in this investigation by the following taxonomy: (i) Although real objects have manifold boundaries, in objects with thin sections or walls, the manifold property remains in the data sample only at the price of very small sampling intervals and large data sets -- For relaxed sampling rates nonmanifold situations are likely -- (ii) The position of the planar slices may produce an associated level function which is non – Morse -- This for example allows the set of critical points of the associated level function to contain one or even two dimensional pieces -- The fact that the Hessian matrix at critical points is non-singular is the Morse condition (as a consequence, critical points are isolated), and allows for the algorithms presented here -- (iii) For Morse condition, the slicing interval may be such that several critical points occur between immediate slices (non- simple condition) -- This article presents the degenerate cases arising from points (i)-(iii) and discusses a shape reconstruction algorithm for digitizations holding the Morse – simple condition -- It presents the results of applying the prescribed algorithms to data sets, and discusses future actions that enlarge the mentioned scope
publishDate 2002
dc.date.issued.none.fl_str_mv 2002
dc.date.available.none.fl_str_mv 2016-11-30T21:07:43Z
dc.date.accessioned.none.fl_str_mv 2016-11-30T21:07:43Z
dc.type.eng.fl_str_mv info:eu-repo/semantics/article
article
info:eu-repo/semantics/publishedVersion
publishedVersion
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dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.local.spa.fl_str_mv Artículo
status_str publishedVersion
dc.identifier.issn.none.fl_str_mv 1137-7704
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10784/9795
identifier_str_mv 1137-7704
url http://hdl.handle.net/10784/9795
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.ispartof.spa.fl_str_mv Anales de Ingeniería Gráfica, Issue 15, pp 16-24
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dc.rights.local.spa.fl_str_mv Acceso cerrado
rights_invalid_str_mv Acceso cerrado
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dc.format.eng.fl_str_mv application/pdf
institution Universidad EAFIT
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