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...
- 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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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 |
dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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 |
dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_14cb |
dc.rights.local.spa.fl_str_mv |
Acceso cerrado |
rights_invalid_str_mv |
Acceso cerrado http://purl.org/coar/access_right/c_14cb |
dc.format.eng.fl_str_mv |
application/pdf |
institution |
Universidad EAFIT |
bitstream.url.fl_str_mv |
https://repository.eafit.edu.co/bitstreams/e4d2e9d0-8610-4693-8b18-b288d1d26645/download https://repository.eafit.edu.co/bitstreams/a4d3436f-0b37-487e-9945-bd78f0abf4ea/download |
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repository.name.fl_str_mv |
Repositorio Institucional Universidad EAFIT |
repository.mail.fl_str_mv |
repositorio@eafit.edu.co |
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