Examinando por Autor "Cadavid, C.A."
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Ítem 2D shape similarity as a complement for Voronoi-Delone methods in shape reconstruction(PERGAMON-ELSEVIER SCIENCE LTD, 2005-02-01) Ruiz, O.E.; Cadavid, C.A.; Granados, M.; Peña, S.; Vásquez, E.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEIn surface reconstruction from planar cross sections it is necessary to build surfaces between 2D contours in consecutive cross sections. This problem has been traditionally attacked by (i) direct reconstruction based on local geometric proximity between the contours, and (ii) classification of topological events between the cross sections. These approaches have been separately applied with limited success. In case (i), the resulting surfaces may have overstretched or unnatural branches. These arise from local contour proximity which does not reflect global similarity between the contours. In case (ii), the topological events are identified but are not translated into the actual construction of a surface. This article presents an integration of the approaches (i) and (ii). Similarity between the composite 2D regions bounded by the contours in consecutive cross sections is used to: (a) decide whether a surface should actually relate two composite 2D regions, (b) identify the type and location of topological transitions between cross sections and (c) drive the surface construction for the regions found to be related in step (a). The implemented method avoids overstretched or unnatural branches, rendering a surface which is both geometrically intuitive and topologically faithful to the cross sections of the original object. The presented method is a good alternative in cases in which correct reproduction of the topology of the surface (e.g. simulation of flow in conduits) is more important than its geometry (e.g. assessment of tumor mass in radiation planning). © 2004 Elsevier Ltd. All rights reserved.Ítem Normal factorization in SL(2, Z) and the confluence of singular fibers in elliptic fibrations(Springer Verlag, 2009-01-01) Cadavid, C.A.; Vélez, J.D.; Cadavid, C.A.; Vélez, J.D.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y AplicacionesIn this article we obtain a result about the uniqueness of factorization in terms of conjugates of the matrix of, of some matrices representing the conjugacy classes of those elements of SL(2,Z) arising as the monodromy around a singular fiber in an elliptic fibration (i.e. those matrices that appear in Kodaira's list). Namely we prove that if M is a matrix in Kodaira's list, and M = G1 ···Gr where each Gi is a conjugate of U in SL(2,Z), then after applying a finite sequence of Hurwitz moves the product G1 ···Gr can be transformed into another product of the form H1 ···HnG'n+1 ···G'r where H1 ···Hn is some fixed shortest factorization of M in terms of conjugates of U, and G'n+1 ···G'r = Id2×2. We use this result to obtain necessary and sufficient conditions under which a relatively minimal elliptic fibration without multiple fibers f: S ? D = {z ? C: |z| < 1}, admits a weak deformation into another such fibration having only one singular fiber. © 2009 Heldermann Verlag.Ítem Spectral-based mesh segmentation(Springer-Verlag France, 2017-08-01) Mejia, D.; Ruiz-Salguero, O.; Cadavid, C.A.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEIn design and manufacturing, mesh segmentation is required for FACE construction in boundary representation (B-Rep), which in turn is central for feature-based design, machining, parametric CAD and reverse engineering, among others. Although mesh segmentation is dictated by geometry and topology, this article focuses on the topological aspect (graph spectrum), as we consider that this tool has not been fully exploited. We pre-process the mesh to obtain a edge-length homogeneous triangle set and its Graph Laplacian is calculated. We then produce a monotonically increasing permutation of the Fiedler vector (2nd eigenvector of Graph Laplacian) for encoding the connectivity among part feature sub-meshes. Within the mutated vector, discontinuities larger than a threshold (interactively set by a human) determine the partition of the original mesh. We present tests of our method on large complex meshes, which show results which mostly adjust to B-Rep FACE partition. The achieved segmentations properly locate most manufacturing features, although it requires human interaction to avoid over segmentation. Future work includes an iterative application of this algorithm to progressively sever features of the mesh left from previous sub-mesh removals.Ítem Spectral-based mesh segmentation(Springer-Verlag France, 2017-08-01) Mejia, D.; Ruiz-Salguero, O.; Cadavid, C.A.; Mejia, D.; Ruiz-Salguero, O.; Cadavid, C.A.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y AplicacionesIn design and manufacturing, mesh segmentation is required for FACE construction in boundary representation (B-Rep), which in turn is central for feature-based design, machining, parametric CAD and reverse engineering, among others. Although mesh segmentation is dictated by geometry and topology, this article focuses on the topological aspect (graph spectrum), as we consider that this tool has not been fully exploited. We pre-process the mesh to obtain a edge-length homogeneous triangle set and its Graph Laplacian is calculated. We then produce a monotonically increasing permutation of the Fiedler vector (2nd eigenvector of Graph Laplacian) for encoding the connectivity among part feature sub-meshes. Within the mutated vector, discontinuities larger than a threshold (interactively set by a human) determine the partition of the original mesh. We present tests of our method on large complex meshes, which show results which mostly adjust to B-Rep FACE partition. The achieved segmentations properly locate most manufacturing features, although it requires human interaction to avoid over segmentation. Future work includes an iterative application of this algorithm to progressively sever features of the mesh left from previous sub-mesh removals.Ítem Triangular mesh parameterization with trimmed surfaces(Springer-Verlag France, 2015-04-28) Ruiz, O.E.; Mejia, D.; Cadavid, C.A.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEGiven a 2-manifold triangular mesh M subset of R-3, with border, a parameterization of M is a FACE or trimmed surface F = {S, L-0, ... , L-m. F is a connected subset or region of a parametric surface S, bounded by a set of LOOPs L-0, ... , L-m such that each L-i subset of S is a closed 1-manifold having no intersection with the other L-j LOOPs. The parametric surface S is a statistical fit of the mesh M. L-0 is the outermost LOOP bounding F and L-i is the LOOP of the i-th hole in F (if any). The problem of parameterizing triangular meshes is relevant for reverse engineering, tool path planning, feature detection, redesign, etc. State-of-art mesh procedures parameterize a rectangular mesh M. To improve such procedures, we report here the implementation of an algorithm which parameterizes meshes M presenting holes and concavities. We synthesize a parametric surface S subset of R-3 which approximates a superset of the mesh M. Then, we compute a set of LOOPs trimming S, and therefore completing the FACE F = {S, L-0, ... , L-m. Our algorithm gives satisfactory results for M having low Gaussian curvature (i.e., M being quasi-developable or developable). This assumption is a reasonable one, since M is the product of manifold segmentation pre-processing. Our algorithm computes: (1) a manifold learning mapping phi : M -> U subset of R-2, (2) an inverse mapping S : W subset of R-2 -> R-3, with W being a rectangular grid containing and surpassing U. To compute phi we test IsoMap, Laplacian Eigenmaps and Hessian local linear embedding (best results with HLLE). For the back mapping (NURBS) S the crucial step is to find a control polyhedron P, which is an extrapolation of M. We calculate P by extrapolating radial basis functions that interpolate points inside phi(M). We successfully test our implementation with several datasets presenting concavities, holes, and are extremely non-developable. Ongoing work is being devoted to manifold segmentation which facilitates mesh parameterization.