Geodesic-based manifold learning for parameterization of triangular meshes

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dc.citation.epage14spa
dc.citation.journalAbbreviatedTitleIJIDeMspa
dc.citation.journalTitleInternational Journal on Interactive Design and Manufacturing (IJIDeM)eng
dc.citation.journalTitleInternational Journal on Interactive Design and Manufacturingspa
dc.citation.spage1spa
dc.contributor.authorAcosta, Diego A.
dc.contributor.authorRuíz, Óscar E.
dc.contributor.authorArroyave, Santiago
dc.contributor.authorEbratt, Roberto
dc.contributor.authorCadavid, Carlos
dc.contributor.authorLondono, Juan J.
dc.contributor.departmentUniversidad EAFIT. Departamento de Ingeniería Mecánicaspa
dc.contributor.researchgroupLaboratorio CAD/CAM/CAEspa
dc.date.accessioned2016-11-18T21:56:35Z
dc.date.available2016-11-18T21:56:35Z
dc.date.issued2014
dc.description.abstractReverse Engineering (RE) requires representing with free forms (NURBS, Spline, Bézier) a real surface which has been pointsampled -- To serve this purpose, we have implemented an algorithm that minimizes the accumulated distance between the free form and the (noisy) point sample -- We use a dualdistance calculation point to / from surfaces, which discourages the forming of outliers and artifacts -- This algorithm seeks a minimum in a function that represents the fitting error, by using as tuning variable the control polyhedron for the free form -- The topology (rows, columns) and geometry of the control polyhedron are determined by alternative geodesicbased dimensionality reduction methods: (a) graphapproximated geodesics (Isomap), or (b) PL orthogonal geodesic grids -- We assume the existence of a triangular mesh of the point sample (a reasonable expectation in current RE) -- A bijective composition mapping allows to estimate a size of the control polyhedrons favorable to uniformspeed parameterizations -- Our results show that orthogonal geodesic grids is a direct and intuitive parameterization method, which requires more exploration for irregular triangle meshes -- Isomap gives a usable initial parameterization whenever the graph approximation of geodesics on be faithful -- These initial guesses, in turn, produce efficient free form optimization processes with minimal errors -- Future work is required in further exploiting the usual triangular mesh underlying the point sample for (a) enhancing the segmentation of the point set into faces, and (b) using a more accurate approximation of the geodesic distances within , which would benefit its dimensionality reductioneng
dc.formatapplication/pdfeng
dc.identifier.doi10.1007/s12008-014-0249-9
dc.identifier.issn1955-2505
dc.identifier.urihttp://hdl.handle.net/10784/9668
dc.language.isoengeng
dc.publisherSpringer Verlagspa
dc.relation.ispartofInternational Journal on Interactive Design and Manufacturing (IJIDeM), pp 1-14spa
dc.relation.urihttp://link.springer.com/article/10.1007/s12008-014-0249-9
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.rights.localAcceso abiertospa
dc.subject.keywordTriangulationspa
dc.subject.keywordPolyhedraspa
dc.subject.keywordAlgorithmsspa
dc.subject.keywordMinimal surfacesspa
dc.subject.keywordTopologyspa
dc.subject.keywordGraph theoryspa
dc.subject.keywordGeodesyspa
dc.subject.keywordNumerical grid generation (Numerical analysis)spa
dc.subject.keywordTriangulationeng
dc.subject.keywordPolyhedraeng
dc.subject.keywordAlgorithmseng
dc.subject.keywordMinimal surfaceseng
dc.subject.keywordTopologyeng
dc.subject.keywordGraph theoryeng
dc.subject.keywordGeodesyeng
dc.subject.keywordNumerical grid generation (Numerical analysis)eng
dc.subject.keywordIngeniería inversa.keywor
dc.subject.keywordSuperficies NURBS.keywor
dc.subject.keywordGeometría computacional.keywor
dc.subject.keywordReconstrucción superficial.keywor
dc.subject.keywordTriangulación de Delaunay.keywor
dc.subject.lembTRIANGULACIÓNspa
dc.subject.lembPOLIEDROspa
dc.subject.lembALGORITMOSspa
dc.subject.lembSUPERFICIES MÍNIMASspa
dc.subject.lembTOPOLOGÍAspa
dc.subject.lembTEORÍA DE GRAFOSspa
dc.subject.lembGEODESIAspa
dc.subject.lembGENERACIÓN NUMÉRICA DE MALLAS (ANÁLISIS NUMÉRICO)spa
dc.titleGeodesic-based manifold learning for parameterization of triangular mesheseng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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