Repositorio Institucional Universidad EAFIT ::Examinando por Materia "Topology"

Examinando por Materia "Topology"

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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/CAE
In 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.
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/CAE
In 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)
Adaptative cubical grid for isosurface extraction
(2009) Congote, John; Moreno, Aitor; Barandiaran, Iñigo; Barandiaran, Javier; Ruíz, Óscar E.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
This work proposes a variation on the Marching Cubes algorithm, where the goal is to represent implicit functions with higher resolution and better graphical quality using the same grid size -- The proposed algorithm displaces the vertices of the cubes iteratively until the stop condition is achieved -- After each iteration, the difference between the implicit and the explicit representations are reduced, and when the algorithm finishes, the implicit surface representation using the modified cubical grid is more detailed, as the results shall confirm -- The proposed algorithm corrects some topological problems that may appear in the discretisation process using the original grid
Bi-curve and multi-patch smoothing with application to the shipyard industry
(2007) Leiceaga, Xoán A.; Ruíz, Oscar; Vanegas, Carlos; Soto, Eva; Prieto, José; Rodríguez, Manuel; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Algorithms are proposed and implemented in a commercial system which allow for the C1-continuity matching between adjacent B-spline curves and B-spline patches -- These algorithms only manipulate the positions of the control points, therefore respecting the constraint imposed by the sizes of the available commercial steel plates -- The application of the algorithms respect the initial hull partition made by the designers and therefore the number and overall shape and position of the constitutive patches remains unchanged -- Algorithms were designed and tested for smoothing the union of (a) two B-spline curves sharing a common vertex, (b) two B-spline surfaces sharing a common border, and (c) four B-spline surfaces sharing a common vertex -- For this last case, an iterative heuristic degreeof-freedom elimination algorithm was implemented -- Very satisfactory results were obtained with the application of the presented algorithms in shipyards in Spain
Bifurcations and Sequences of Elements in Non-Smooth Systems Cycles
(Scientific Research Publishing, 2013-09) Arango, Iván; Pineda, Fabio; Ruíz, Óscar; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
This article describes the implementation of a novel method for detection and continuation of bifurcations in non- smooth complex dynamic systems -- The method is an alternative to existing ones for the follow-up of associated phe- nomena, precisely in the circumstances in which the traditional ones have limitations (simultaneous impact, Filippov and first derivative discontinuities and multiple discontinuous boundaries) -- The topology of cycles in non-smooth sys- tems is determined by a group of ordered segments and points of different regions and their boundaries -- In this article, we compare the limit cycles of non-smooth systems against the sequences of elements, in order to find patterns -- To achieve this goal, a method was used, which characterizes and records the elements comprising the cycles in the order that they appear during the integration process -- The characterization discriminates: a) types of points and segments; b) direction of sliding segments; and c) regions or discontinuity boundaries to which each element belongs -- When a change takes place in the value of a parameter of a system, our comparison method is an alternative to determine topo- logical changes and hence bifurcations and associated phenomena -- This comparison has been tested in systems with discontinuities of three types: 1) impact; 2) Filippov and 3) first derivative discontinuities -- By coding well-known cy- cles as sequences of elements, an initial comparison database was built -- Our comparison method offers a convenient approach for large systems with more than two regions and more than two sliding segments
Boolean 2D Shape Similarity For Surface Reconstruction
(2001) Ruíz, Óscar E.; Cadavid, Carlos A.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Surface 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 vision
Boundary Representation of Anatomical Features
(2002) Ruíz, Óscar E.; Karangelis, Grigorios; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
In Simulationen für Bestrahlungstherapieplanung und andere medizinischen und bioingenieur wissenschaftlichen Anwendungen hat man traditionellerweise die anatomischen Eigenschaften mittels volumenbasierten Techniken angezeigt -- Trotzdem, während der Bedarf an Behandlung, Organsimulation und Erzeugung von Prothese präziser wird, reicht es nicht die Menge und die Position von solchen Features zu wissen, sondern auch Detailstufen, die vergleichbar sind zu denjenigen, die man für ingenieurwissenschaftliche Techniken verwendet (finite element analysis, rapid prototyping, Herstellung, usw.) -- Dieser Artikel präsentiert Bemühungen und Ergebnisse in der Anwendung von computerunterstützten geometrischen Algorithmen auf biomedizinischen Applikationen, wobei diese Algorithmen sich ursprünglich auf die Begrenzung von Formen gerichtet haben, die auf Planarmustern von anatomischen Zielregionen basierten
Computational geometry in the preprocessing of point clouds for surface modeling
(1998) Ruíz, O.E.; Posada, J.L.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
In Computer Aided Geometric Design ( CAGD ) the automated fitting of surfaces to massive series of data points presents several difficulties: (i) even the formal definition of the problem is ambiguous because the mathematical characteristics (continuity, for example) of the surface fit are dependent on non-geometric considerations, (ii) the data has an stochastic sampling component that cannot be taken as literal, and, (iii) digitization characteristics, such as sampling interval and directions are not constant, etc -- In response, this investigation presents a set of computational tools to reduce, organize and re-sample the data set to fit the surface -- The routines have been implemented to be portable across modeling or CAD servers -- A case study is presented from the footwear industry, successfully allowing the preparation of a foreign, neutral laser digitization of a last for fitting a B-spline surface to it -- Such a result was in the past attainable only by using proprietary software, produced by the same maker of the digitizing hardware
Coupling Terrain and Building Database Information for Ray-Tracing Applications
(2003) Fontán, F.P.; Ruíz S., O.E.; Peña, S.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
In this paper a methodology for the combination and integration into a single data base of terrain and building data is presented -- This study is justified if ray-tracing techniques are to be used in propagation and channel modeling studies -- Usually terrain is available in grid or elevation form while building information is normally facet-oriented -- Ray-tracing (RT) techniques deal with flat facets and straight edges, if possible in triangular format -- To allow the use of RT on urban areas over irregular terrain a common format made up of facets and edges is therefore needed -- In this article, the procedure to accomplish this data homogeneity is presented -- It is assumed that terrain data is available in two formats: a) grid elevation and b) contour or iso-altitude lines -- Building data is assumed available in plant, polygonal planar contour form, a primitive and yet widely used format which is yet to be transformed into 3D entities -- The geometric modeling of joint terrain and building data is further difficuledt because union of surface objects (even after achieving a unified format) is undefined from the point of view of 3D boolean operations
DigitLAB, an Environment and Language for Manipulation of 3D Digitizations
(Presses internationales Polytechnique, 2000) Ruíz, Óscar E.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
In Computer Aided Geometric Design the fitting of surfaces to massive series of data points has many applications, ranging from medicine to aerophotogrametry -- However, even the mathematical meaning of fitting a surface to a set of points is dependent on functional considerations, and not only on the geometric properties of the point set -- Also, characteristics of some parts of the data set must be interpreted as stochastic in nature, while others must be taken as literal and therefore they become constraints of the surface -- For these reasons, among others, automated surface fitting alone does not produce results usable at industrial level -- At the same time, it does not take advantage of sampling patterns, particular shapes of the cross sections, functionally different regions within the object, etc -- The latest literature reviews show the need for utilities to process point data sets that must be asynchronous, (applicable at any time and upon any region of the point set) -- Addressing this need, this article reports new tools developed within DigitLAB, a language that allows topological traversal, retrieval and statistical modifications to the data, and surface fitting -- They can handle arbitrary topology, as case studies in medicine, mathematics, landscaping, etc discussed here demonstrate
Effects of aberrations in vortex-beams generated with amplitude diffraction gratings
(SPIE, 2016-01-01) Cuartas-Vélez, C.; Echeverri-Chacón, S.; Restrepo, R.; Universidad EAFIT. Departamento de Ciencias Básicas; Óptica Aplicada
We present a mathematical model for the generation of vortex-beams by using a square profile amplitude fork diffraction grating with arbitrary topological charge. The mathematical framework of aberrations in the forked-shape diffraction grating is analysed, and the resulting diffracted pattern is simulated. Three cases of desired distortions (aberrations) in the diffraction grating are considered, obtaining phase modulation from the amplitude grating. Experimental optical vortices are generated by using a transmission spatial light modulator, which is used as a dynamic diffraction grating, allowing us to aberrate it. We show the effect of aberrations in the experimental diffracted vortex-beams and compare it with the numerical simulation. © 2016 SPIE.
Electronic and Topological Analysis for New Phases of Chromium Nitride
(WILEY-V C H VERLAG GMBH, 2018-01-01) Marin-Suarez, Marco; Alzate-Vargas, Leidy L.; David, Jorge; Arroyave-Franco, Mauricio; Velez, Mario E.; Universidad EAFIT. Departamento de Ciencias Básicas; Electromagnetismo Aplicado (Gema)
Chromium nitride (CrN) in its NaCl-type phase has been widely studied through density functional theory (DFT) in order to analyze its electronic properties. By the means of DFT with the Becke's three parameter Lee-Yang-Parr (B3LYP) hybrid functional, the same stoichiometry is studied in two unreported hypothetical phases in addition to the nonsynthesized and previously reported zinc-blende-type phase. The cohesive energy of every structure is calculated, and the analysis of this quantity indicated that all crystals are stable and that there is an unreported phase more stable than the synthesized one. The calculated electronic dispersion relation and density of electronic states allowed for the determination that these three phases have a conducting behavior. The symmetry of some bands is determined as a result of the crystal field splitting for chromium d states. The topology of the electron density was studied in order to determine its properties at bond critical points (BCPs). The form of the Laplacian of the density and its gradient trajectories allowed to locate ring critical points in these structures. From these calculations, it is concluded that all three phases are ionic crystals. The synthesized NaCl-type phase is studied in order to compare and confirm the results. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Ellipse-based Principal Component Analysis for Self-intersecting Curve Reconstruction from Noisy Point Sets
(Springer Berlin Heidelberg, 2011) Ruíz, O.; Vanegas, C.; Cadavid, C.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Surface reconstruction from cross cuts usually requires curve reconstruction from planar noisy point samples -- The output curves must form a possibly disconnected 1manifold for the surface reconstruction to proceed -- This article describes an implemented algorithm for the reconstruction of planar curves (1manifolds) out of noisy point samples of a sel-fintersecting or nearly sel-fintersecting planar curve C -- C:[a,b]⊂R→R is self-intersecting if C(u)=C(v), u≠v, u,v∈(a,b) (C(u) is the self-intersection point) -- We consider only transversal self-intersections, i.e. those for which the tangents of the intersecting branches at the intersection point do not coincide (C′(u)≠C′(v)) -- In the presence of noise, curves which self-intersect cannot be distinguished from curves which nearly sel fintersect -- Existing algorithms for curve reconstruction out of either noisy point samples or pixel data, do not produce a (possibly disconnected) Piecewise Linear 1manifold approaching the whole point sample -- The algorithm implemented in this work uses Principal Component Analysis (PCA) with elliptic support regions near the selfintersections -- The algorithm was successful in recovering contours out of noisy slice samples of a surface, for the Hand, Pelvis and Skull data sets -- As a test for the correctness of the obtained curves in the slice levels, they were input into an algorithm of surface reconstruction, leading to a reconstructed surface which reproduces the topological and geometrical properties of the original object -- The algorithm robustly reacts not only to statistical noncorrelation at the self-intersections(nonmanifold neighborhoods) but also to occasional high noise at the nonselfintersecting (1manifold) neighborhoods
Estructuras y topología de los clústeres Cu7Zn3
(Universidad EAFIT, 2014) González Tavera, Robinson; David Caro, Jorge León
Extending marching cubes with adaptative methods to obtain more accurate iso-surfaces
(Springer Verlag, 2010-01-01) Congote, J.; Moreno, A.; Barandiaran, I.; Barandiaran, J.; Ruiz, O.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
This work proposes an extension of the Marching Cubes algorithm, where the goal is to represent implicit functions with higher accuracy using the same grid size. The proposed algorithm displaces the vertices of the cubes iteratively until the stop condition is achieved. After each iteration, the difference between the implicit and the explicit representations is reduced, and when the algorithm finishes, the implicit surface representation using the modified cubical grid is more accurate, as the results shall confirm. The proposed algorithm corrects some topological problems that may appear in the discretization process using the original grid. © 2010 Springer-Verlag Berlin Heidelberg.
Face Reconstruction with structured light
(SciTePress, 2011-03) Congote, John; Barandiaran, Iñigo; Barandiaran, Javier; Nieto, Marcos; Ruíz, Óscar; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
This article presents a methodology for reconstruction of 3D faces which is based on stereoscopic images of the scene using active and passive surface reconstruction -- A sequence of gray patterns is generated, which are projected onto the scene and their projection recorded by a pair of stereo cameras -- The images are rectified to make coincident their epipolar planes and so to generate a stereo map of the scene -- An algorithm for stereo matching is applied, whose result is a bijective mapping between subsets of the pixels of the images -- A particular connected subset of the images (e.g. the face) is selected by a segmentation algorithm -- The stereo mapping is applied to such a subset and enables the triangulation of the two image readings therefore rendering the (x;y; z) points of the face, which in turn allow the reconstruction of the triangular mesh of the face -- Since the surface might have holes, bilateral filters are applied to have the holes filled -- The algorithms are tested in real conditions and we evaluate their performance with virtual datasets -- Our results show a good reconstruction of the faces and an improvement of the results of passive systems
FEA Structural Optimization Based on Metagraphs
(Springer Verlag, 2019-01-01) Montoya-Zapata D.; Acosta D.A.; Ruiz-Salguero O.; Sanchez-Londono D.; Montoya-Zapata D.; Acosta D.A.; Ruiz-Salguero O.; Sanchez-Londono D.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Procesos Ambientales (GIPAB)
Evolutionary Structural Optimization (ESO) seeks to mimic the form in which nature designs shapes. This paper focuses on shape carving triggered by environmental stimuli. In this realm, existing algorithms delete under - stressed parts of a basic shape, until a reasonably efficient (under some criterion) shape emerges. In the present article, we state a generalization of such approaches in two forms: (1) We use a formalism that enables stimuli from different sources, in addition to stress ones (e.g. kinematic constraints, friction, abrasion). (2) We use metagraphs built on the Finite Element constraint graphs to eliminate the dependency of the evolution on the particular neighborhood chosen to be deleted in a given iteration. The proposed methodology emulates 2D landmark cases of ESO. Future work addresses the implementation of such stimuli type, the integration of our algorithm with evolutionary based techniques and the extension of the method to 3D shapes. © 2019, Springer International Publishing AG, part of Springer Nature.
FEA Structural Optimization Based on Metagraphs
(Springer Verlag, 2019-01-01) Montoya-Zapata D.; Acosta D.A.; Ruiz-Salguero O.; Sanchez-Londono D.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Desarrollo y Diseño de Procesos
Evolutionary Structural Optimization (ESO) seeks to mimic the form in which nature designs shapes. This paper focuses on shape carving triggered by environmental stimuli. In this realm, existing algorithms delete under - stressed parts of a basic shape, until a reasonably efficient (under some criterion) shape emerges. In the present article, we state a generalization of such approaches in two forms: (1) We use a formalism that enables stimuli from different sources, in addition to stress ones (e.g. kinematic constraints, friction, abrasion). (2) We use metagraphs built on the Finite Element constraint graphs to eliminate the dependency of the evolution on the particular neighborhood chosen to be deleted in a given iteration. The proposed methodology emulates 2D landmark cases of ESO. Future work addresses the implementation of such stimuli type, the integration of our algorithm with evolutionary based techniques and the extension of the method to 3D shapes. © 2019, Springer International Publishing AG, part of Springer Nature.
FEA Structural Optimization Based on Metagraphs
(Springer Verlag, 2019-01-01) Montoya-Zapata D.; Acosta D.A.; Ruiz-Salguero O.; Sanchez-Londono D.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Evolutionary Structural Optimization (ESO) seeks to mimic the form in which nature designs shapes. This paper focuses on shape carving triggered by environmental stimuli. In this realm, existing algorithms delete under - stressed parts of a basic shape, until a reasonably efficient (under some criterion) shape emerges. In the present article, we state a generalization of such approaches in two forms: (1) We use a formalism that enables stimuli from different sources, in addition to stress ones (e.g. kinematic constraints, friction, abrasion). (2) We use metagraphs built on the Finite Element constraint graphs to eliminate the dependency of the evolution on the particular neighborhood chosen to be deleted in a given iteration. The proposed methodology emulates 2D landmark cases of ESO. Future work addresses the implementation of such stimuli type, the integration of our algorithm with evolutionary based techniques and the extension of the method to 3D shapes. © 2019, Springer International Publishing AG, part of Springer Nature.
Fixed grid finite element analysis for 3D structural problems
(World Scientific Publishing Co., 2005) García, Manuel J.; Henao, Miguel A.; Ruíz, Óscar E.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Fixed Grid (FG) methodology was first introduced by García and Steven as an engine for numerical estimation of two-dimensional elasticity problems -- The advantages of using FG are simplicity and speed at a permissible level of accuracy -- Two dimensional FG has been proved effective in approximating the strain and stress field with low requirements of time and computational resources -- Moreover, FG has been used as the analytical kernel for different structural optimisation methods as Evolutionary Structural Optimisation, Genetic Algorithms (GA), and Evolutionary Strategies -- FG consists of dividing the bounding box of the topology of an object into a set of equally sized cubic elements -- Elements are assessed to be inside (I), outside (O) or neither inside nor outside (NIO) of the object -- Different material properties assigned to the inside and outside medium transform the problem into a multi-material elasticity problem -- As a result of the subdivision NIO elements have non-continuous properties -- They can be approximated in different ways which range from simple setting of NIO elements as O to complex noncontinuous domain integration -- If homogeneously averaged material properties are used to approximate the NIO element, the element stiffness matrix can be computed as a factor of a standard stiffness matrix thus reducing the computational cost of creating the global stiffness matrix. An additional advantage of FG is found when accomplishing re-analysis, since there is no need to recompute the whole stiffness matrix when the geometry changes -- This article presents CAD to FG conversion and the stiffness matrix computation based on non-continuous elements -- In addition inclusion/exclusion of O elements in the global stiffness matrix is studied -- Preliminary results shown that non-continuous NIO elements improve the accuracy of the results with considerable savings in time -- Numerical examples are presented to illustrate the possibilities of the method

Examinando por Materia "Topology"

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