Examinando por Autor "Cadavid, Carlos"
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Ítem A curvature-sensitive parameterization-independent triangulation algorithm(2008-09) Ruíz, Óscar; Congote, John; Cadavid, Carlos; Lalinde, Juan G.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAETriangulations of a connected subset F of parametric surfaces S(u,v) (with continuity C2 or higher) are required because a C0 approximation of such F(called a FACE) is widely required for finite element analysis, rendering, manufacturing, design, reverse engineering, etc -- The triangulation T is such an approximation, when its piecewise linear subsets are triangles (which, on the other hand, is not a compulsory condition for being C0) -- A serious obstacle for algorithms which triangulate in the parametric space u−v is that such a space may be extremely warped, and the distances in parametric space be dramatically different of the distances in R3 -- Recent publications have reported parameter -independent triangulations, which triangulate in R3 space -- However, such triangulations are not sensitive to the curvature of the S(u,v) -- The present article presents an algorithm to obtain parameter-independent, curvature-sensitive triangulations -- The invariant of the algorithm is that a vertex v of the triangulation if identified, and a quasiequilateral triangulation around v is performed on the plane P tangent to S(u,v) at v -- The size of the triangles incident to v is a function of K(v), the curvature of S(u,v) at v -- The algorithm was extensively and successfully tested, rendering short running times, with very demanding boundary representationsÍtem 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 A first lesson in Algebraic Geometry(Universidad EAFIT, 2005-12-01) Cadavid, Carlos; Universidad EAFITÍtem Gabriel-constrained Parametric Surface Triangulation(2008-10) Ruíz, Óscar E.; Cadavid, Carlos; Lalinde, Juan G.; Serrano, Ricardo; Peris-Fajarnés, Guillermo; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEThe Boundary Representation of a 3D manifold contains FACES (connected subsets of a parametric surface S : R2−R3) -- In many science and engineering applications it is cumbersome and algebraically difficult to deal with the polynomial set and constraints (LOOPs) representing the FACE -- Because of this reason, a Piecewise Linear (PL) approximation of the FACE is needed, which is usually represented in terms of triangles (i.e. 2-simplices) -- Solving the problem of FACE triangulation requires producing quality triangles which are: (i) independent of the arguments of S, (ii) sensitive to the local curvatures, and (iii) compliant with the boundaries of the FACE and (iv) topologically compatible with the triangles of the neighboring FACEs -- In the existing literature there are no guarantees for the point (iii) -- This article contributes to the topic of triangulations conforming to the boundaries of the FACE by applying the concept of parameter independent Gabriel complex, which improves the correctness of the triangulation regarding aspects (iii) and (iv) -- In addition, the article applies the geometric concept of tangent ball to a surface at a point to address points (i) and (ii) -- Additional research is needed in algorithms that (i) take advantage of the concepts presented in the heuristic algorithm proposed and (ii) can be proved correctÍtem Geodesic-based manifold learning for parameterization of triangular meshes(Springer Verlag, 2014) Acosta, Diego A.; Ruíz, Óscar E.; Arroyave, Santiago; Ebratt, Roberto; Cadavid, Carlos; Londono, Juan J.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEReverse Engineering (RE) requires representing with free forms (NURBS, Spline, Bézier) a real surface which has been pointsampled -- To serve this purpose, we have implemented an algorithm that minimizes the accumulated distance between the free form and the (noisy) point sample -- We use a dualdistance calculation point to / from surfaces, which discourages the forming of outliers and artifacts -- This algorithm seeks a minimum in a function that represents the fitting error, by using as tuning variable the control polyhedron for the free form -- The topology (rows, columns) and geometry of the control polyhedron are determined by alternative geodesicbased dimensionality reduction methods: (a) graphapproximated geodesics (Isomap), or (b) PL orthogonal geodesic grids -- We assume the existence of a triangular mesh of the point sample (a reasonable expectation in current RE) -- A bijective composition mapping allows to estimate a size of the control polyhedrons favorable to uniformspeed parameterizations -- Our results show that orthogonal geodesic grids is a direct and intuitive parameterization method, which requires more exploration for irregular triangle meshes -- Isomap gives a usable initial parameterization whenever the graph approximation of geodesics on be faithful -- These initial guesses, in turn, produce efficient free form optimization processes with minimal errors -- Future work is required in further exploiting the usual triangular mesh underlying the point sample for (a) enhancing the segmentation of the point set into faces, and (b) using a more accurate approximation of the geodesic distances within , which would benefit its dimensionality reductionÍtem Manifold Learning with Orthogonal Geodesic Grids(2014) Ruíz, Óscar E.; Cadavid, Carlos; Ebratt, Roberto; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEIn Reverse Engineering, it is capital to find a parametric trimmed surface which approximates a triangular mesh (2-manifold with border) M in R3 -- This article proposes and implements a quasi isometry f: M -> R2 which allows a parameterization of M -- We consider quasi - developable 2- manifolds M in R3 -- f(p) = (u,w) with (u,w) being the coordinates of p in M under a grid of geodesic curves Ci(u) and Cj(w) on M -- We seek that the geodesic curves Ci(u) and Cj(w) be orthogonal to each other on M -- This means, that the Ci(u) should not cross each other, and each Ci(u) should intersect each Cj(w) in perpendicular mannerÍtem Una primera lección de Geometría algebraica(Universidad EAFIT, 2005) Cadavid, Carlos; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEEn este artículo se explica cómo aparece la Geometría Algebraica, partiendo del estudio de los conjuntos de soluciones de sistemas algebraicosÍtem Principal component analisis-PCA-and Delone Triangulations for PL approximation C1-continuous 1-manifolds in Rn(ACTA Press, 2004-08) Ruíz, Óscar; Cadavid, Carlos; García, Manuel J.; Martinod, Ronald; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEÍtem Principal component and Voronoi skeleton alternatives for curve reconstruction from noisy point sets(Taylor & Francis, 2007-10) Ruíz, Óscar; Vanegas, Carlos; Cadavid, Carlos; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAESurface reconstruction from noisy point samples must take into consideration the stochastic nature of the sample -- In other words, geometric algorithms reconstructing the surface or curve should not insist in following in a literal way each sampled point -- Instead, they must interpret the sample as a “point cloud” and try to build the surface as passing through the best possible (in the statistical sense) geometric locus that represents the sample -- This work presents two new methods to find a Piecewise Linear approximation from a Nyquist-compliant stochastic sampling of a quasi-planar C1 curve C(u) : R → R3, whose velocity vector never vanishes -- One of the methods articulates in an entirely new way Principal Component Analysis (statistical) and Voronoi-Delaunay (deterministic) approaches -- It uses these two methods to calculate the best possible tape-shaped polygon covering the planarised point set, and then approximates the manifold by the medial axis of such a polygon -- The other method applies Principal Component Analysis to find a direct Piecewise Linear approximation of C(u) -- A complexity comparison of these two methods is presented along with a qualitative comparison with previously developed ones -- It turns out that the method solely based on Principal Component Analysis is simpler and more robust for non self-intersecting curves -- For self-intersecting curves the Voronoi-Delaunay based Medial Axis approach is more robust, at the price of higher computational complexity -- An application is presented in Integration of meshes originated in range images of an art piece -- Such an application reaches the point of complete reconstruction of a unified meshÍtem A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres(Universidad EAFIT, 2013-03-22) Cadavid, Carlos; Vélez Caicedo, Juan Diego; Universidad EAFIT; Universidad Nacional de ColombiaÍtem Spectral-based vertex re-labeling for mesh segmentation(2015) Mejía, Daniel; Ruíz, Óscar E.; Cadavid, Carlos; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEMesh segmentation can be achieved by considering (a) geometric, (b) topologic or (c) a combination of geometric and topologic features on the surface Altough considering geometric characteristics would be relatively easy, our main intention is to keep the discussion on the topological aspect given that topology-based methods are foggy in their basic understanding impairing consistent application -- This article re-labels the vertices of the mesh based on the Fiedler vector (Laplacian 2nd eigenvector) for encoding the connectivity among part feature sub-meshes -- Second differences of such vector with respect to the re-labeling labeling are computed after a filter has been applied to determine the mesh partition -- The segmentation achieved by the proposed algorithm locates properly several topological features, provided the homogeneity of the triangular meshÍtem The π-geography problem and the Hurwitz problem(Universidad EAFIT, 2009-06-01) Cadavid, Carlos; Vélez-C.,Juan D.; Universidad EAFIT; Universidad Nacional de Colombia, Medellín