Examinando por Materia "Restricciones geométricas"
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Ítem Algebraic geometry and group theory in geometric constraint satisfaction for computer-aided design and assembly planning(Taylor & Francis, 1996) Ruíz, Óscar E.; Ferreira, Placid M.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEMechanical design and assembly planning inherently involve geometric constraint satisfaction or scene feasibility (GCS/SF) problems -- Such problems imply the satisfaction of proposed relations placed between undefined geometric entities in a given scenario -- If the degrees of freedom remaining in the scene are compatible with the proposed relations or constraints, a set of entities is produced that populate the scenario satisfying the relations -- Otherwise, a diagnostic of inconsistency of the problem is emitted -- This problem appears in various forms in assembly planning (assembly model generation), process planning, constraint driven design, computer vision, etc -- Previous attempts at solution using separate numerical, symbolic or procedural approaches suffer serious shortcomings in characterizing the solution space, in dealing simultaneously with geometric (dimensional) and topological (relational) inconsistencies, and in completely covering the possible physical variations of the problem -- This investigation starts by formulating the problem as one of characterizing the solution space of a set of polynomials -- By using theories developed in the area of algebraic geometry, properties of Grobner Bases are used to assess the consistency and ambiguity of the given problem and the dimension of its solution space -- This method allows for die integration of geometric and topological reasoning -- The high computational cost of Grobner Basis construction and the need for a compact and physically meaningful set of variables lead to the integration of known results on group theory -- These results allow the characterization of geometric constraints in terms of the subgroups of the Special Group of Euclidean displacements in E^3, SE(3) -- Several examples arc developed which were solved with computer algebra systems (MAPLE and Mathematica) -- They are presented to illustrate the use of the Euclidean group-based variables, and to demonstrate the theoretical completeness of the algebraic geometry analysis over the domain of constraints expressible as polynomialsÍtem Finite Element Modeling of Composite Materials using Kinematic Constraints(Universidad EAFIT, 2009-12) Barschke, Merlin; Uribe, David; Ruíz, Óscar E.; Jensen, Jens; López, Carlos; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEEl propósito de este artículo es presentar simulaciones del comportamiento de materiales compuestos basado en restricciones cinemáticas entre las mismas fibras y entre las fibras y la resina circundante -- En la revisión de literatura, los autores han encontrado que las restricciones cinemáticas no han sido plenamente explotadas para modelar materiales compuestos, probablemente debido a su alto costo computacional -- El propósito de este artículo es exponer la implementación y resultados de tal modelo, usando Análisis por Elementos Finitos de restricciones geométricas prescritas a los nodos de la resina y las fibras -- Las descripciones analíticas del comportamiento de materiales compuestos raramente aparecen -- Muchas aproximaciones para describir materiales compuestos en capas son basadas en la teoría de funciones C1 Z y C0Z, tal como la Teoría Clásica de Capas (CLT) -- Estas teorías de funciones contienen significativas simplificaciones del material, especialmente para compuestos tejidos -- Una aproximación hibrida para modelar materiales compuestos con Elementos Finitos (FEA) fue desarrollada por Sidhu y Averill [1] y adaptada por Li y Sherwood [2] para materiales compuestos tejidos con polipropileno de vidrio -- Este artículo presenta un método para obtener valores para las propiedades de los materiales compuestos -- Tales valores son usados para simular las fibras reforzadas tejidas aplicando elementos de capas en el software ANSYS -- El presente modelo requiere menos simplificaciones que las teorías C1Z y C0Z -- En el artículo presente, a diferencia del modelo Li–Sherwood, el tejido es modelado geométricamente -- Una Representación por la Frontera (B-Rep del modelo “Hand”) con genus 1 (con geometría compleja) fue usada para aplicar restricciones geométricas a las capas de resina, fibra, etcétera, mostrando que es apropiada para simular estructuras complejas -- En el futuro, las propiedades no–lineales de los materiales deben ser consideradas, y el trabajo experimental requerido debe ser realizadoÍtem Geometric constraint subsets and subgraphs in the analysis of assemblies and mechanisms(Universidad EAFIT, 2006-03) Ruíz, Óscar E.; Ferreira, Placid M.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEGeometric Reasoning ability is central to many applications in CAD/CAM/CAPP environments -- An increasing demand exists for Geometric Reasoning systems which evaluate the feasibility of virtual scenes specified by geometric relations -- Thus, the Geometric Constraint Satisfaction or Scene Feasibility (GCS/SF) problem consists of a basic scenario containing geometric entities, whose context is used to propose constraining relations among still undefined entities -- If the constraint specification is consistent, the answer of the problem is one of finitely or infinitely many solution scenarios satisfying the prescribed constraints -- Otherwise, a diagnostic of inconsistency is expected -- The three main approaches used for this problem are numerical, procedural or operational and mathematical -- Numerical and procedural approaches answer only part of the problem, and are not complete in the sense that a failure to provide an answer does not preclude the existence of one -- The mathematical approach previously presented by the authors describes the problem using a set of polynomial equations -- The common roots to this set of polynomials characterizes the solution space for such a problem -- That work presents the use of Groebner basis techniques for verifying the consistency of the constraints -- It also integrates subgroups of the Special Euclidean Group of Displacements SE(3) in the problem formulation to exploit the structure implied by geometric relations -- Although theoretically sound, these techniques require large amounts of computing resources -- This work proposes Divide-and-Conquer techniques applied to local GCS/SF subproblems to identify strongly constrained clusters of geometric entities -- The identification and preprocessing of these clusters generally reduces the effort required in solving the overall problem -- Cluster identification can be related to identifying short cycles in the Spatial Con straint graph for the GCS/SF problem -- Their preprocessing uses the aforementioned Algebraic Geometry and Group theoretical techniques on the local GCS/SF problems that correspond to these cycles -- Besides improving theefficiency of the solution approach, the Divide-and-Conquer techniques capture the physical essence of the problem -- This is illustrated by applying the discussed techniques to the analysis of the degrees of freedom of mechanismsÍtem Graphs of optimally fit features in assessment of geometric tolerances(2014) Ruíz, Óscar E.; Congote, John; Acosta, Diego A.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEThis article presents an industrial application case of geometric constraint graphs, whose nodes are statistically optimal instances of manufacturing or design features and whose edges are usual geometric relations used in tolerance applications -- The features might be virtual ones -- As a consequence, they may lie beyond the piece’s extents -- The geometric constraint graph may have cyclic topology -- Contrary to deterministic geometric constraint graphs, tolerance constraint graphs admit numerical slacks, due to their stochastic nature -- The methodology has been applied in industrial scenarios, showing superiority to traditional material features for the assessment of tolerancesÍtem A new evaluation framework and image dataset for keypoint extraction and feature descriptor matching(2013-02) Barandiaran, Iñigo; Cortes, Camilo; Nieto, Marcos; Graña, Manuel; Ruíz, Óscar E.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEKey point extraction and description mechanisms play a crucial role in image matching, where several image points must be accurately identified to robustly estimate a transformation or to recognize an object or a scene -- New procedures for keypoint extraction and for feature description are continuously emerging -- In order to assess them accurately, normalized data and evaluation protocols are required -- In response to these needs, we present a (1) new evaluation framework that allow assessing the performance of the state-of-the-art feature point extraction and description mechanisms, (2) a new image dataset acquired under controlled affine and photometric transformations and (3) a testing image generator -- Our evaluation framework allows generating detailed curves about the performance of different approaches, providing a valuable insight about their behavior -- Also, it can be easily integrated in many research and development environments -- The contributions mentioned above are available on-line for the use of the scientific communityÍtem Using Gröbner Bases in Kinematic Analysis of Mechanisms(Birkhäuser Verlag, 1996) Ruíz, Óscar E.; Ferreira, Placid M.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE