Examinando por Materia "Diagramas de Voronoi"
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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 An algorithmic approach for simulating realistic irregular tilings(Universidad EAFIT, 2012) Betancourt Arango, Alejandro; Marín Sánchez, Freddy Hernán; Duque Cardona, Juan CarlosÍtem Boolean 2D Shape Similarity For Surface Reconstruction(2001) Ruíz, Óscar E.; Cadavid, Carlos A.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAESurface reconstruction problem (SRP) from planar samples has been traditionally approached by either (i) using local proximity between data points in adjacent layers, or by(ii) classifying the topological transitions that may explain the evolution of the cross sections -- Strategy (i) is robust in the sense that it has answers for every possible case, although in some scenarios renders counterintuitive surfaces, commented below -- Approach (ii) has mainly remained in the theoretical terrain -- The present work follows on aspect (ii), by using a Morse-based topological classification of the transitions, and complementing it with reasoning based on the geometry of the evolving cross sections to determine a high level description of the transitions from m to n contours (m:n transitions) -- This reasoning of shape similarity is performed by boolean operators -- Finally, the surface is synthesized using the m:n transitions -- This conjunction of topological and geometrical reasoning renders highly intuitive results, and allows for the incorporation of methods derived from the area of machine visionÍtem 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 Marching cubes in an unsigned distance field for surface reconstruction from unorganized point sets(2010) Congote, John; Moreno, Aitor; Barandiaran, Iñigo; Barandiaran, Javier; Posada, Jorge; Ruíz, Óscar; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAESurface reconstruction from unorganized point set is a common problem in computer graphics -- Generation of the signed distance field from the point set is a common methodology for the surface reconstruction -- The reconstruction of implicit surfaces is made with the algorithm of marching cubes, but the distance field of a point set can not be processed with marching cubes because the unsigned nature of the distance -- We propose an extension to the marching cubes algorithm allowing the reconstruction of 0-level iso-surfaces in an unsigned distance field -- We calculate more information inside each cell of the marching cubes lattice and then we extract the intersection points of the surface within the cell then we identify the marching cubes case for the triangulation -- Our algorithm generates good surfaces but the presence of ambiguities in the case selection generates some topological mistakesÍtem 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 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)