Evaluation of 2D shape likeness for surface reconstruction

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dc.citation.epage24spa
dc.citation.issue15spa
dc.citation.journalTitleAnales de Ingeniería Gráficaeng
dc.citation.journalTitleAnales de Ingeniería Gráficaspa
dc.citation.spage16spa
dc.contributor.authorRuíz, Óscar Eduardo
dc.contributor.authorCadavid, Carlos Alberto
dc.contributor.authorGranados, Miguel
dc.contributor.departmentUniversidad EAFIT. Departamento de Ingeniería Mecánicaspa
dc.contributor.researchgroupLaboratorio CAD/CAM/CAEspa
dc.date.accessioned2016-11-30T21:07:43Z
dc.date.available2016-11-30T21:07:43Z
dc.date.issued2002
dc.description.abstractSurface 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 scopeeng
dc.formatapplication/pdfeng
dc.identifier.issn1137-7704
dc.identifier.urihttp://hdl.handle.net/10784/9795
dc.language.isoengeng
dc.relation.ispartofAnales de Ingeniería Gráfica, Issue 15, pp 16-24spa
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.rights.localAcceso cerradospa
dc.subject.keywordPrototype developmentspa
dc.subject.keywordMorse theoryspa
dc.subject.keywordIsomorphisms (Mathematics)spa
dc.subject.keywordManifolds (Mathematics)spa
dc.subject.keywordDesign imagingspa
dc.subject.keywordPrototype developmenteng
dc.subject.keywordMorse theoryeng
dc.subject.keywordIsomorphisms (Mathematics)eng
dc.subject.keywordManifolds (Mathematics)eng
dc.subject.keywordDesign imagingeng
dc.subject.keywordGeometría computacional.keywor
dc.subject.keywordReconstrucción superficial.keywor
dc.subject.keywordIngeniería inversa.keywor
dc.subject.lembDESARROLLO DE PROTOTIPOSspa
dc.subject.lembTEORÍA DE MORSEspa
dc.subject.lembISOMORFISMO (MATEMÁTICAS)spa
dc.subject.lembVARIEDADES (MATEMÁTICAS)spa
dc.subject.lembIMAGEN TRIDIMENSIONAL EN DISEÑOspa
dc.titleEvaluation of 2D shape likeness for surface reconstructioneng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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