Compendium of publications on: differential operators on manifolds for CAD CAM CAE and computer graphics

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dc.contributor.advisorRuiz Salguero, Oscar Eduardospa
dc.contributor.advisorPosada Velásquez, Jorge Leónspa
dc.contributor.authorMejía Parra, Daniel
dc.coverage.spatialMedellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degreeseng
dc.creator.degreeDoctor in Engineeringspa
dc.creator.emaildmejiap@eafit.edu.cospa
dc.creator.emailoruiz@eafit.edu.cospa
dc.creator.emailjposada@vicomtech.orgspa
dc.creator.grantorVicomtech Foundation, Basque Research and Technology Alliance (BRTA), Mikeletegi 57, Donostia / San Sebastián 20009, Spain.spa
dc.date.accessioned2020-07-21T19:44:02Z
dc.date.available2020-07-21T19:44:02Z
dc.date.issued2020
dc.description.abstractThis Doctoral Thesis develops novel articulations of Differential Operators on Manifolds for applications on Computer Aided Design, Manufacture and Computer Graphics, as follows: (1) Mesh Parameterization and Segmentation. Development and application of Laplace-Beltrami, Hessian, Geodesic and Curvature operators for topology and geometry – driven segmentations and parameterizations of 2-manifold triangular meshes. Applications in Reverse Engineering, Manufacturing and Medicine. (2) Computing of Laser-driven Temperature Maps in thin plates. Spectral domain - based analytic solutions of the transient, non-homogeneous heat equation for simulation of temperature maps in multi-laser heated thin plates, modeled as 2-manifolds plus thickness. (3) Real-time estimation of dimensional compliance of hot out-of-forge workpieces. A Special Orthogonal SO(3) transformation between 2-manifolds is found, which enables a distance operator between 2-manifolds in R^3 (or m-manifolds in R^n). This process instruments the real-time assessment of dimensional compliance of hot workpieces, in the factory floor shop. (4) Slicing or Level-Set computation for 2-manifold triangular meshes in Additive Manufacturing. Development of a classification of non-degenerate (i.e. non-singular Hessian) and degenerate (i.e. singular Hessian) critical points of non-Morse functions on 2-manifold objects, followed by computation of level sets for Additive Manufacturing. Most of the aforementioned contributions have been screened and accepted by the international scientific community (and published). Non-published material corresponds to confidential developments which are commercially exploited by the sponsors and therefore banned from dissemination.spa
dc.formatapplication/pdfeng
dc.identifier.ddc515.243 M516
dc.identifier.urihttp://hdl.handle.net/10784/17067
dc.language.isospaspa
dc.publisherUniversidad EAFITspa
dc.publisher.departmentEscuela de Ingenieríaspa
dc.publisher.placeMedellínspa
dc.publisher.programDoctorado en Ingenieríaspa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.localAcceso abiertospa
dc.subjectCAD CAM CAEspa
dc.subjectGeometría computacionalspa
dc.subjectOperadores diferencialesspa
dc.subjectInspección dimensionalspa
dc.subjectTransferencia de calorspa
dc.subjectMaquinado laserspa
dc.subject.keywordCAD CAM CAEspa
dc.subject.keywordComputational geometryspa
dc.subject.keywordDifferential operatorsspa
dc.subject.keywordComputer graphicsspa
dc.subject.keywordMesh parameterizationspa
dc.subject.keywordMesh segmentationspa
dc.subject.keywordHeat transferspa
dc.subject.keywordLaser machiningspa
dc.subject.keywordDimensional inspectionspa
dc.subject.lembDISEÑO EN INGENIERÍAspa
dc.subject.lembDISEÑO CON AYUDA DE COMPUTADORspa
dc.subject.lembECUACIÓN DEL CALORspa
dc.subject.lembCÁLCULO DE VARIACIONESspa
dc.titleCompendium of publications on: differential operators on manifolds for CAD CAM CAE and computer graphicsspa
dc.typedoctoralThesiseng
dc.typeinfo:eu-repo/semantics/doctoralThesiseng
dc.type.hasVersionacceptedVersioneng
dc.type.localTesis Doctoralspa

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Doctorado en Ingeniería (tesis)