Examinando por Autor "Granados, Miguel"
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Ítem 2D Shape similarity as a complement for Voronoi-Delone methods in shape reconstruction(Elsevier, 2005) Ruíz S., Óscar E.; Cadavid, Carlos A.; Granados, Miguel; Peña, Sebastián; Vásquez, Eliana; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEIn surface reconstruction from planar slices it is necessary to build surfaces between corresponding 2D regions in consecutive levels -- The problem has been traditionally attacked with (i) direct reconstruction based on local geometric proximity between the regions, and (ii) classification of topological events between the slices, which control the evolution of the cross cuts -- These approaches have been separately applied with mixed success -- In the case (i), the results may be surfaces with over-stretched or unnatural branches, resulting from a local contour proximity which does not correspond to global similarity between regions -- In (ii), the consequences from topological events upon the actual surface realization have not been drawn -- In this paper an integration of (i) and (ii) is presented, which uses a criteria of similarity between composed 2D regions in consecutive slices to: (a) decide if a surface should actually relate those regions, (b) identify the topological transitions between levels and (c) construct the local surface for the related regions -- The method implemented hinders over-stretched and unnatural branches, therefore rendering a surface which adjusts to geometrically-sound topological events -- This is a good alternative when the surface reconstructed needs to be topologically faithful (for example in flow simulation) in addition to represent the a rough geometrical space (for example in radiation planning)Ítem Evaluation of 2D shape likeness for surface reconstruction(2001) Ruíz, Óscar Eduardo; Cadavid, Carlos Alberto; Granados, Miguel; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAESurface 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 means, the set of critical points of the associated level function is isomorphic to compact subsets of R1 or R2 -- 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 scopeÍtem Evaluation of 2D shape likeness for surface reconstruction(2002) Ruíz, Óscar Eduardo; Cadavid, Carlos Alberto; Granados, Miguel; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAESurface 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 scopeÍtem FEA-driven Geometric Modelling for Meshless Methods(Springer Paris, 2005-11) Ruíz, Óscar; Granados, Miguel; Cadavid, Carlos; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEOptimized Boolean Operations against orthogonal Fixed Grids (FG) for 2-manifold construction in quasi-meshless methods for Finite Element Analysis are presented -- A Piecewise Linear (PL) or Boundary Representation (B-Rep) B is assumed to be the boundary of a solid S ⊂ R3 -- On the other hand, R3 is partitioned into a 3-dimensional array of cubic, uniform cells Ci,j,k . Cells Ci,j,k with Ci,j,k ∩ S ≠Φ and Ci,j,k ∩ S ≠ Ci,j,k are particularly important for FG applications -- These are the cells Ci,j,k intersecting B, which happen to be Neither Inside nor Outside (NIO) of B -- The boundary ∂(Ci,j,k ∩ S ) of Ci,j,k ∩ S must be calculated from ∂Ci,j,k and B for a large number of cells Ci,j,k , which makes the normal boolean operations unpractical -- The article illustrates with examples the immersion of B-Rep models in Fixed Grids, visits the downstream results of the stress-strain calculations using FG and explains how this approach is used in Product Design OptimizationÍtem Geometrical degeneracy removal by virtual disturbances - An application to surface reconstruction from point slice samples(INSTICC-INST SYST TECHNOLOGIES INFORMATION CONTROL & COMMUNICATION, 2008-01-01) Ruiz, Oscar; Vasquez, Eliana; Pena, Sebastian; Granados, Miguel; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEIn surface reconstruction from slice samples (typical in medical imaging, coordinate measurement machines, stereolithography, etc.) the available methods attack the geometrical and topological properties of the surface. Topological methods classify the transitions occurred in the 2-manifold between two consecutive slices i and i+ 1. Geometrical methods synthesize the surface based on local proximity of the contours in consecutive slices. Superimposed 2D Voronoi Diagrams VDi and VDi+1 for slices i and i + 1, respectively, present topological problems if, for example, a site of VD i lies on an site or an edge of VDi+1. The usual treatment of this problem in literature is to apply a geometrical disturbance to either VDi or VDi+1, thus eliminating the degeneracy. In contrast, this article presents the implementation of a method which identifies the degenerate situation, constructs un-instantiated topological constructs, choses a geometrical instantiation based on a virtual disturbance introduced to the actual configuration. The algorithm was successfully applied to remove non-manifold topologies produced by well known algorithms in surface reconstruction.Ítem Geometrical degeneracy removal by virtual disturbances: An application to surface reconstruction from point slice samples(2008-01) Ruíz, Óscar; Vasquez, Eliana; Peña, Sebastián; Granados, Miguel; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEIn surface reconstruction from slice samples (typical in medical imaging, coordinate measurement machines, stereolithography, etc.) the available methods attack the geometrical and topological aspects or a combinationof these -- Topological methods classify the events occurred in the 2-manifold between two consecutive slices -- Geometrical methods synthesize the surface based on local proximity of contours in consecutive slices -- Many of these methods work with modifications of Voronoi - Delaunay (VD) techniques, applied on slices i and i+1 -- Superimposed 2D Voronoi Diagrams VDi and VDi+1 (used in surface reconstruction) present topological problems if, for example, a site of VDi lies on an site or an edge of VDi+1 -- The usual treatment of this problem in literature is to apply a geometrical disturbance to either VDi or VDi+1, thus eliminating the degeneracy -- Recent works seek to quantify the amount of the disturbance applied in relation to the probability distribution of the event “change in the topology of VD” -- In this article, in contrast, virtual disturbances are proposed and implemented, which allow for the application of subsequent steps of the algorithm at hand (in this case, tetrahedra construction for surface reconstruction) regardless of to the geometrical exception -- Tetrahedra (or any other downstream constructs) can then be instantiated as per non-degenerate conditions -- Although this method is applied for surface reconstruction, it gives insight as to how to circumvent degeneracies in procedures based on VD methodsÍtem Usage of 2D Region Similarity For Surface Reconstruction From Planar Samples(2003) Ruíz S., Óscar E.; Cadavid, Carlos A.; Granados, Miguel; Peña, Sebastián; Vásquez, Eliana; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEIn surface reconstruction from planar slices it is necessary to build surfaces between corresponding 2D regions in consecutive levels -- The problem has been traditionally attacked with (i) direct reconstruction based on local geometric proximity between the regions, and (ii) classification of topological events between the slices, which control the evolution of the cross cuts -- These approaches have been separately applied with mixed success -- In the case (i), the results may be surfaces with over-stretched or unnatural branches, resulting from a local contour proximity which does not correspond to global similarity between regions -- In (ii), the consequences from topological events upon the actual surface realization have not been drawn -- In this paper an integration of (i) and (ii) is presented, which uses a criteria of similarity between composed 2D regions in consecutive slices to: (a) decide if a surface should actually relate those regions, (b) identify the topological transitions between levels and (c) construct the local surface for the related regions -- The method implemented hinders over-stretched and unnatural branches, therefore rendering a surface which adjusts to geometrically-sound topological events -- This is a good alternative when the surface reconstructed needs to be topologically faithful (for example in flow simulation) in addition to represent the a rough geometrical space (for example in radiation planning)