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  • Decomposition of geometric constraint graphs based on computing fundamental circuits. Correctness and complexity

     Joan Arinyo, Robert; Tarres Puertas, Marta Isabel; Vila Marta, Sebastian
    Computer Aided Design
    Vol. 52, p. 1-16
    DOI: 10.1016/j.cad.2014.02.006
    Date of publication: 2014-07-01
    Journal article

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    In geometric constraint solving, Decomposition Recombination solvers (DR-solvers) refer to a general solving approach where the problem is divided into a set of sub-problems, each sub-problem is recursively divided until reaching basic problems which are solved by a dedicated equational solver. Then the solution to the starting problem is computed by merging the solutions to the sub-problems.; Triangle- or tree-decomposition is one of the most widely used approaches in the decomposition step in DR-solvers. It may be seen as decomposing a graph into three subgraphs such that subgraphs pairwise share one graph vertex. Shared vertices are called hinges. Then a merging step places the geometry in each sub-problem with respect to the other two.; In this work we report on a new algorithm to decompose biconnected geometric constraint graphs by searching for hinges in fundamental circuits of a specific planar embedding of the constraint graph. We prove that the algorithm is correct. (C) 2014 Elsevier Ltd. All rights reserved.

  • The Reachability problem in constructive geometric constraint solving based dynamic geometry

     Hidalgo Garcia, Marta; Joan Arinyo, Robert
    Journal of automated reasoning
    p. 1-24
    DOI: 10.1007/s10817-013-9280-y
    Date of publication: 2013-03
    Journal article

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    An important issue in dynamic geometry is the reachability problem that asks whether there is a continuous path that, from a given starting geometric configuration, continuously leads to an ending configuration. In this work we report on a technique to compute a continuous evaluation path, if one exists, that solves the reachability problem for geometric constructions with one variant parameter. The technique is developed in the framework of a constructive geometric constraint-based dynamic geometry system, uses the A¿*¿ algorithm and minimizes the variant parameter arc length.

    An important issue in dynamic geometry is the reachability problem that asks whether there is a continuous path that, from a given starting geometric configuration, continuously leads to an ending configuration. In this work we report on a technique to compute a continuous evaluation path, if one exists, that solves the reachability problem for geometric constructions with one variant parameter. The technique is developed in the framework of a constructive geometric constraintbased dynamic geometry system, uses the A∗ algorithm and minimizes the variant parameter arc length.

  • Geometric constraint solving in a dynamic geometry framework.  Open access

     Hidalgo Garcia, Marta Rosa
    Department of Computer Science, Universitat Politècnica de Catalunya
    Theses

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    La resolució de restriccions geomètriques és un tema principal en diferents àrees com el modelatge paramètric de sòlids o el disseny assistit per computador. Un problema geomètric en restriccions consisteix en un conjunt d'objectes geomètrics sobre el qual es defineix un conjunt de restriccions. Resoldre el problema geomètric en restriccions significa trobar un emplaçament per als elements geomètrics de forma que el conjunt de restriccions es compleixi.L'objectiu principal de la resolució de restriccions geomètriques és definir estructures rígides. És interessant, però, preguntar-se si té sentit permetre que el valor de les restriccions canviï amb el temps. La resposta és afirmativa. Si assumim un canvi continu en els paràmetres motors, el resultat de la resolució de restriccions geomètriques amb paràmetres motors resulta en la generació de famílies de diferents formes construïdes amb els mateixos elements geomètrics però regit per un conjunt fix derestriccions. Estudiar el problema on diferents paràmetres canvien simultàniament seria una gran fita. Malgrat això, la potencialcomplexitat combinatòria ens obliga a considerar problemes amb un sol paràmetre motor. Basant-nos en el treball d'altres autors, hem desenvolupat un nou algorisme basat en una nova eina anomenada h-graf que resol correctament el problema geomètric en restriccions amb un paràmetre motor. Oferim una demostració completa de la correctesa del mètode que mancava a l'obra original.La geometria dinàmica és una tecnologia desenvolupada per ensenyar geometria als computadors en l'escola, que proporciona als usuaris eines per definir contruccions geomètriques i interactuar amb elles. L'objectiu del sistema és mostrar en la pantalla del computador com la geometria canvia en temps real quan l'usuari interactúa amb el sistema. Aquest tipus d'interacció encoratja l'interés dels estudiants en experimentar i provar les seves idees. L'inconvenient més important de la geometria dinàmica és que és l'usuari el que ha de saber com resoldre el problema geomètric. Basant-nos en el fet que la interacció entre l'usuari i el computador bàsicament permet a l'usuari moure un sol element a la vegada, hem desenvolupat una nova metodologia en geometria dinàmica basada en dues idees: 1) el problema subjacent és simplement un problema geomètric en restriccions amb un paràmetre motor, i, 2) la responsabilitat de resoldre el problema geomètric recau en el resoledor de geometria en restriccions.Dos problemes clàssics i interessants en molts models computacionals són els problemes d'alcançabilitat i traçabilitat. L'alcançabilitat consisteix a decidir si es pot aconseguir transformar un estat inicial del sistema en un determinat estat mitjançant un conjunt de transformacions permeses. Aquest problema és primordial en diferents àrees com robòtica, xarxes de Petri, etc. Quan es trasllada a geometria dinàmica apareixen dos problemes específics: 1) en intersectar elements geomètrics on almenys un d'ells té grau 2 o superior, la solució no és única, i, 2) per als valors donats de les restriccions, podria ser que el problema geomètric no tinguera solució. Per exemple, trobar el punt d'intersecció entre dues rectes paral·leles. Hem desenvolupat un mètode específic en el nostre sistema de geometria dinàmica basada en restriccions que resol tant el problema d'alcançabilitat com el de traçabilitat aplicant eines de teoria de sistemes dinàmics.Finalment considerem grafs de Henneberg, de Laman i tree-decomposables, que són una eina fonamental en la resolució deproblemes en restriccions i les seves aplicacions. Estudiem quines relacions es poden establir entre ells i trobem les condicions sota les quals les construccions de Henneberg conserven la tree-decomposabilitat dels grafs. Per últim desenvolupem un algorisme que genera automàticament grafs de Laman tree-decomposables d'un ordre donat usant construccions de Henneberg.

    Geometric constraint solving is a central topic in many fields such as parametric solid modeling, computer-aided design or chemical molecular docking. A geometric constraint problem consists of a set geometric objects on which a set of constraints is defined. Solving the geometric constraint problem means finding a placement for the geometric elements with respect to each other such that the set of constraints holds. Clearly, the primary goal of geometric constraint solving is to define rigid shapes. However an interesting problem arises when we ask whether allowing parameter constraint values to change with time makes sense. The answer is in the positive. Assuming a continuous change in the variant parameters, the result of the geometric constraint solving with variant parameters would result in the generation of families of different shapes built on top of the same geometric elements but governed by a fixed set of constraints. Considering the problem where several parameters change simultaneously would be a great accomplishment. However the potential combinatorial complexity make us to consider problems with just one variant parameter. Elaborating on work from other authors, we develop a new algorithm based on a new tool we have called h-graphs that properly solves the geometric constraint solving problem with one variant parameter. We offer a complete proof for the soundness of the approach which was missing in the original work. Dynamic geometry is a computer-based technology developed to teach geometry at secondary school, which provides the users with tools to define geometric constructions along with interaction tools such as drag-and-drop. The goal of the system is to show in the user's screen how the geometry changes in real time as the user interacts with the system. It is argued that this kind of interaction fosters students interest in experimenting and checking their ideas. The most important drawback of dynamic geometry is that it is the user who must know how the geometric problem is actually solved. Based on the fact that current user-computer interaction technology basically allows the user to drag just one geometric element at a time, we have developed a new dynamic geometry approach based on two ideas: 1) the underlying problem is just a geometric constraint problem with one variant parameter, which can be different for each drag-and-drop operation, and, 2) the burden of solving the geometric problem is left to the geometric constraint solver. Two classic and interesting problems in many computational models are the reachability and the tracing problems. Reachability consists in deciding whether a certain state of the system can be reached from a given initial state following a set of allowed transformations. This problem is paramount in many fields such as robotics, path finding, path planing, Petri Nets, etc. When translated to dynamic geometry two specific problems arise: 1) when intersecting geometric elements were at least one of them has degree two or higher, the solution is not unique and, 2) for given values assigned to constraint parameters, it may well be the case that the geometric problem is not realizable. For example computing the intersection of two parallel lines. Within our geometric constraint-based dynamic geometry system we have developed an specific approach that solves both the reachability and the tracing problems by properly applying tools from dynamic systems theory. Finally we consider Henneberg graphs, Laman graphs and tree-decomposable graphs which are fundamental tools in geometric constraint solving and its applications. We study which relationships can be established between them and show the conditions under which Henneberg constructions preserve graph tree-decomposability. Then we develop an algorithm to automatically generate tree-decomposable Laman graphs of a given order using Henneberg construction steps.

  • Computing parameter ranges in constructive geometric constraint solving: Implementation and correctness proof

     Hidalgo, Marta; Joan Arinyo, Robert
    Computer Aided Design
    Vol. 44, num. 7, p. 709-720
    DOI: 10.1016/j.cad.2012.02.012
    Date of publication: 2012-07
    Journal article

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    In parametric design, changing values of parameters to get different solution instances to the problem at hand is a paramount operation. One of the main issues when generating the solution instance for the actual set of parameters is that the user does not know in general which is the set of parameter values for which the parametric solution is feasible. Similarly, in constraint-based dynamic geometry, knowing the set of critical points where construction feasibility changes would allow to avoid unexpected and unwanted behaviors. We consider parametric models in the Euclidean space with one internal degree of freedom. In this scenario, in general, the set of values of the variant parameter for which the parametric model is realizable and defines a valid shape is a set of intervals on the real line. In this work we report on our experiments implementing the van der Meiden Approach to compute the set of parameter values that bound intervals for which the parametric object is realizable. The implementation is developed on top of a constructive, ruler-and-compass geometric constraint solver. We formalize the underlying concepts and prove that our implementation is correct, that is, the approach exactly computes all the feasible interval bounds.

  • A scalable architecture for 3D map navigation on mobile devices

     Noguera, José María; Segura, Rafael; Ogáyar, Carlos; Joan Arinyo, Robert
    Personal and ubiquitous computing
    p. 1-16
    DOI: 10.1007/s00779-012-0598-y
    Date of publication: 2012
    Journal article

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  • Special issue on geometric constraints and reasoning

     Gao, Xiao-Shang; Joan Arinyo, Robert; Michelucci, Dominique
    Computational geometry: theory and applications
    Vol. 45, num. 8, p. 383-384
    DOI: 10.1016/j.comgeo.2012.01.008
    Date of publication: 2012-09
    Journal article

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  • Navigating large terrains using commodity mobile devices

     Noguera, José María; Segura, Rafael; Ogáyar, Carlos; Joan Arinyo, Robert
    Computers and geosciences
    Vol. 37, num. 9, p. 1218-1233
    DOI: 10.1016/j.cageo.2010.08.007
    Date of publication: 2011-09
    Journal article

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  • Modeling the performance of evolutionary algorithms on the root identification problem: A case study with PBIL and CHC algorithms

     YEGUAS BOLÍAVAR, ENRIQUE; Joan Arinyo, Robert; Luzón, M.V.
    Evolutionary computation
    Vol. 19, num. 1, p. 107-135
    DOI: 10.1162/EVCO_a_00017
    Date of publication: 2011
    Journal article

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  • A constraint-based dynamic geometry system

     Freixas Boleda, Marc; Joan Arinyo, Robert; Soto Riera, Antoni
    Computer Aided Design
    Vol. 42, num. 2, p. 151-161
    DOI: 10.1016/j.cad.2009.02.016
    Date of publication: 2010-02
    Journal article

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    Dynamic geometry systems are tools for geometric visualization. They allow the user to define geometric elements, establish relationships between them and explore the dynamic behavior of the remaining geometric elements when one of them is moved. The main problem in dynamic geometry systems is the ambiguity that arises from operations that lead to more than one possible solution. Most dynamic geometry systems deal with this problem in such a way that the solution selection method leads to a fixed dynamic behavior of the system. This is specially annoying when the behavior observed is not the one the user intended. In this work we propose a modular architecture for dynamic geometry systems built upon a set of functional units which will allow us to apply some well-known results from the Geometric Constraint Solving field. A functional unit called filter will provide the user with tools to unambiguously capture the expected dynamic behavior of a given geometric problem.

  • Performance of Evolutionary Algorithms on the Root Identification Problem in Geometric Constraint Solving

     Joan Arinyo, Robert; Luzón, M.V.; YEGUAS BOLÍAVAR, ENRIQUE
    Computer-aided design and applications
    Vol. 7, num. 1, p. 45-57
    DOI: 10.3722/cadaps.2010.45-57
    Date of publication: 2010-01
    Journal article

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  • Issues on Behavior in Dynamic Geometry

     Joan Arinyo, Robert
    International Workshop on Automated Deduction in Geometry
    Presentation's date: 2010-07-22
    Presentation of work at congresses

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  • A Hybrid Rendering Technique to Navigate in Large Terrains Using Mobile Devices

     Noguera, José María; Segura, Rafael; Ogáyar, Carlos; Joan Arinyo, Robert
    Computer Graphics International
    Presentation's date: 2010-06-11
    Presentation of work at congresses

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    We describe a hybrid client-server technique for remote adaptive streaming and rendering of large terrains in resource-limited mobile devices. The technique has been designed to achieve an interactive rendering performance on a mobile device connected to a low-bandwidth wireless network. The rendering workload is split between the client and the server. The terrain area close to the viewer is rendered in real-time by the client. The terrain located far from the viewer is portrayed as view-dependent impostors, rendered by the server on demand. A prototype has been built and an exhaustive set of experiments covering several platforms, wireless networks and a wide range of viewer velocities has been conducted. Results show that the approach is feasible, effective and robust.

  • Search Space Pruning to Solve the Root Identification Problem in Geometric Constraint Solving

     Joan Arinyo, Robert; Luzón, M.V.; YEGUAS BOLÍAVAR, ENRIQUE
    Computer-aided design and applications
    Vol. 6, num. 1, p. 15-25
    DOI: 10.3722/cadaps.2009.15-25
    Date of publication: 2009-07-08
    Journal article

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  • Parameter tunning of PBIL and CHC evolutionary algorithms applied to solve the Root Identification Problem

     Joan Arinyo, Robert; Luzón, M.V.; YEGUAS BOLÍAVAR, ENRIQUE
    Applied soft computing
    DOI: 10:1016/j.asoc.2009.12.037
    Date of publication: 2009-12-01
    Journal article

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    Evolutionary algorithms are among the most successful approaches for solving a number of problems where systematic searches in huge domains must be performed. One problem of practical interest that falls into this category is known as The Root Identification Problem in Geometric Constraint Solving, where one solution to the geometric problem must be selected among a number of possible solutions bounded by an exponential number. In previous works we have shown that applying genetic algorithms, a category of evolutionary algorithms, to solve the Root Identification Problem is both feasible and effective. In this work, we report on an empirical statistical study conducted to establish the influence of the driving parameters in the PBIL and CHC evolutionary algorithms when they are used to solve the Root Identification Problem. We identify a set of values that optimize algorithms performance. The driving parameters considered for the PBIL algorithm are population size, mutation probability, mutation shift and learning rate. For the CHC algorithm we studied population size, divergence rate, differential threshold and the set of best individuals. In both cases we applied unifactorial and multifactorial analysis, post hoc tests and best parameter level selection. Experimental results show that CHC outperforms PBIL when applied to solve the Root Identification Problem.

  • Access to the full text
    Treedecomposition of geometric constraint graphs based on computing graph circuits  Open access

     Tarres Puertas, Marta Isabel; Vila Marta, Sebastian; Joan Arinyo, Robert
    SIAM/ACM Joint Conference on Geometric and Physical Modeling
    p. 113-122
    DOI: /doi.acm.org/10.1145/1629255.1629270
    Presentation's date: 2009-10-06
    Presentation of work at congresses

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    The graph-based geometric constraint solving technique works in two steps. First the geometric problem is translated into a graph whose vertices represent the set of geometric elements and whose edges are the constraints. Then the constraint problem is solved by decomposing the graph into a collection of subgraphs each representing a standard problem which is solved by a dedicated equational solver. In this work we report on an algorithm to decompose biconnected tree-decomposable graphs representing either underor wellconstrained 2D geometric constraint problems. The algorithm recursively first computes a set of fundamental circuits in the graph then splits the graph into a set of subgraphs each sharing exactly three vertices with the fundamental circuit. Practical experiments show that the reported algorithm clearly outperforms the treedecomposition approach based on identifying subgraphs by applying specific decomposition rules.

    Postprint (author’s final draft)

  • The Grounded Heightmap Tree. A New Data Structure for Terrain Representation

     Alonso Alonso, Jesus; Joan Arinyo, Robert; Solano Albajes, Luis
    Date: 2008-10
    Report

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  • Applying CAD tools to virtual reality: Parametric modeling and rendering in dynamic environments

     Joan Arinyo, Robert; Soto Riera, Antoni; Vila Marta, Sebastian; Vilaplana Pastó, Josep; Solano Albajes, Luis; Pérez Vidal, Luis; Freixas Boleda, Marc
    Competitive project

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  • PARAMETER TUNING FOR PBIL ALGORITHM IN GEOMETRIC CONSTRAINT SOLVING SYSTEMS

     Joan Arinyo, Robert
    GENETIC AND EVOLUTIONARY METHODS, CONFERENCE ON
    Presentation's date: 2008-07-14
    Presentation of work at congresses

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  • A Constraint-Based Dynamic Geometry System

     Freixas Boleda, Marc; Joan Arinyo, Robert; Soto Riera, Antoni
    ACM Symposium on Solid Modeling Foundations and CAD/CAM Applications
    p. 37-46
    DOI: 10.1145/1364901.1364909
    Presentation's date: 2008-07-02
    Presentation of work at congresses

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  • Parameter tuning for pbil algorithm in geometric constraint solving systems

     Joan Arinyo, Robert; Luzon, M V; YEGUAS, E
    GENETIC AND EVOLUTIONARY METHODS, CONFERENCE ON
    p. 69-75
    Presentation of work at congresses

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  • The Grounded Heightmap Tree. A New Data Structure for Terrain Representation

     Alonso Alonso, Jesus; Joan Arinyo, Robert; Solano Albajes, Luis
    International Conference on Computer Graphics Theory and Applications
    Presentation's date: 2008-01-22
    Presentation of work at congresses

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    Terrain modeling is a fast growing field with many applications such as computer graphics, resource management, Earth and environmental sciences, civil and military engineering, surveying and photogrammetry and games programming. One of the most widely used terrain model is the Digital Elevation Model (DEM). A DEM is a simple regularly spaced grid of elevation points that represent the continuous variation of relief over space. DEMs require simple storage and are compatible with satellite data. However, they do not easily account for overhangs. In this work we report on the Grounded Heightmap Tree, a new data structure for terrain representation built as a generalization of the DEM. The new data structure allows to naturally represent terrain overhangs. We illustrate the performance of the Grounded Heightmap Tree when applied to represent terrains that undergo big changes.

  • Elements for a modular dynamic geometry system

     Freixas Boleda, Marc; Joan Arinyo, Robert; Soto Riera, Antoni
    ACM Symposium on Applied Computing
    p. 1816-1820
    Presentation's date: 2008-03-16
    Presentation of work at congresses

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  • Parameter Tunning for PBIL Algorithm in Geometric Constraint Solving Systems

     Joan Arinyo, Robert; Luzón, M.V.; YEGUAS BOLÍAVAR, ENRIQUE
    International Conference on Genetic and Evolutionary Methods
    p. 37-47
    Presentation's date: 2008-07-14
    Presentation of work at congresses

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  • Geometric constraint graphs decomposition based on computing graph circuits

     Joan Arinyo, Robert; Tarres Puertas, Marta Isabel; Vila Marta, Sebastian
    International Workshop on Automated Deduction in Geometry
    p. 96-101
    Presentation's date: 2008-09-22
    Presentation of work at congresses

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    Geometric constraint solving is a growing field which plays a paramount role in industrial applications and that is deeply rooted in automated deduction in geometry. In this work we report on an algorithm to solve geometric constraint-based problems by decomposing biconnected graphs. The algorithm is based on recursively splitting the graph through sets with three vertices located on fundamental circuits of the graph. Preliminary practical experiments suggest that the algorithm runtime is at worst quadratic with the total number of vertices in the graph.

  • The grounded heigtmap tree. a new data structure for terrain representation

     Alonso Alonso, Jesus; Joan Arinyo, Robert
    International Conference on Computer Graphics Theory and Applications
    p. 80-85
    Presentation of work at congresses

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  • Decomposition of geometric constraint graphs based on computing fundamental circuits

     Joan Arinyo, Robert; Soto Riera, Antoni; Tarres Puertas, Marta Isabel; Vila Marta, Sebastian
    Date: 2007-09
    Report

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  • Volume Cutting to Simulate Transurethral Resection of the Prostate

     Joan Arinyo, Robert; Vilaplana Pastó, Josep
    Date: 2006-02
    Report

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  • Constrained-Based techniques to support collaborative design

     Joan Arinyo, Robert; Soto Riera, Antoni; Vila Marta, Sebastian
    Journal of computing and information science in engineering
    Vol. 6, num. 2, p. 139-148
    Date of publication: 2006-06
    Journal article

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  • Interactive cutting in voxel-based objects. Applications to simulate transurethral resection of the prostate

     Joan Arinyo, Robert; Vilaplana Pastó, Josep
    Ibero-American Symposium on Computer Graphics
    p. 61-68
    Presentation of work at congresses

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  • Interactive cutting in voxel-based objects. Applications to simulate transurethral resection of the prostate

     Joan Arinyo, Robert
    Ibero-American Symposium on Computer Graphics
    Presentation's date: 2006-07-06
    Presentation of work at congresses

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  • Basic Concepts for Geometric Constraint Solving

     Joan Arinyo, Robert
    Algebraic Geometry and Geometric Modeling
    p. 3
    Presentation of work at congresses

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  • Searching the solution space in constructive geometric constraint solving

     Joan Arinyo, Robert; Soto Riera, Antoni
    Applied intelligence
    Vol. 22, num. 2, p. 109-124
    Date of publication: 2005-04
    Journal article

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  • A brief on constraint solving

     Joan Arinyo, Robert
    Computer Aided Design
    Vol. 2, num. 5, p. 655-663
    Date of publication: 2005-06
    Journal article

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  • A brief on constraint solving

     Hoffmann, C M; Joan Arinyo, Robert
    Computer-aided design and applications
    Vol. 2, num. 5, p. 655-663
    Date of publication: 2005-05
    Journal article

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  • Geometric Constraint Solving

     Joan Arinyo, Robert
    International CAD Conference and Exhibition
    Presentation's date: 2005-06-22
    Presentation of work at congresses

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  • Geometric Constraint Solving

     Joan Arinyo, Robert
    International CAD Conference and Exhibition
    p. 655-663
    Presentation of work at congresses

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  • Plataforma avanzada de modelado parametrico en cad

     Joan Arinyo, Robert; Soto Riera, Antoni; Vila Marta, Sebastian; Vilaplana Pastó, Josep
    Date of publication: 2004-06-30
    Book

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  • A brief on constraint solving

     Joan Arinyo, Robert
    Date: 2004-11
    Report

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