### Examinando por Autor "Ferreira, Placid M."

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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/CAEMás... Mechanical 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 polynomialsMás... Ítem 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/CAEMás... Geometric 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 mechanismsMás... Ítem 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/CAEMás...