Ruiz Salguero, Oscar EduardoPosada Velásquez, Jorge León2020-07-212020http://hdl.handle.net/10784/17067This 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.application/pdfspaCAD CAM CAEGeometría computacionalOperadores diferencialesInspección dimensionalTransferencia de calorMaquinado laserdoctoralThesisinfo:eu-repo/semantics/openAccessDISEÑO EN INGENIERÍADISEÑO CON AYUDA DE COMPUTADORECUACIÓN DEL CALORCÁLCULO DE VARIACIONESCAD CAM CAEComputational geometryDifferential operatorsComputer graphicsMesh parameterizationMesh segmentationHeat transferLaser machiningDimensional inspectionAcceso abierto2020-07-21Mejía Parra, Daniel515.243 M516