Compendium of Publications on: Differential Operators on Manifolds for CAD CAM CAE and Computer Graphics

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dc.contributor.authorMejia-Parra, Daniel
dc.date.accessioned2020-12-29T07:33:07Z
dc.date.available2020-12-29T07:33:07Z
dc.date.issued2020-05-20
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.en_US
dc.description.sponsorship- Research and Academic Institutions: Vicomtech Foundation and EAFIT University - Industrial Companies: Lantek Laser Solutions, GKN - Driveline, BTI - Biotechnology Institute - Government Institutions: Basque Government (ELKARTEK, HAZITEK, Basque Industry 4.0 programs)en_US
dc.identifier.citationMejia-Parra, Daniel. Differential Operators on Manifolds for CAD CAM CAE and Computer Graphics. Ph.D. Thesis. EAFIT University Library, 2020. url: http://hdl.handle.net/10784/17067en_US
dc.identifier.urihttps://diglib.eg.org:443/handle/10.2312/2632993
dc.language.isoenen_US
dc.publisherEAFIT Universityen_US
dc.subjectComputer Graphicsen_US
dc.subjectComputational Geometryen_US
dc.subjectComputer-Aided Designen_US
dc.subjectComputer-Aided Manufacturingen_US
dc.subjectInteractive Visualizationen_US
dc.subject3D Simulationen_US
dc.subject3D Mesh Registrationen_US
dc.subjectMesh Segmentationen_US
dc.subjectMesh Parameterizationen_US
dc.titleCompendium of Publications on: Differential Operators on Manifolds for CAD CAM CAE and Computer Graphicsen_US
dc.typeThesisen_US
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