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Solving Over- and Underconstrained Geometric Models [chapter]

Alex Noort, Maurice Dohmen, Willem F. Bronsvoort
1998 Geometric Constraint Solving and Applications  
An implementation of the approaches has been made in a 3D constraint solver based on degrees of freedom analysis.  ...  The concept of storing information about dependencies between model variables in a graph, can be used with all non-iterative constraint satisfaction techniques.  ...  Section 2 presents the concept of degrees of freedom analysis which the constraint solver is based on.  ... 
doi:10.1007/978-3-642-58898-3_6 fatcat:6s5x6d2bpjgb5lhh3hyrpw23ji

A constructive approach to solving 3-D geometric constraint systems using dependence analysis

Yan-Tao Li, Shi-Min Hu, Jia-Guang Sun
2002 Computer-Aided Design  
In this paper, we propose a new DOF-based graph constructive method to geometric constraint systems solving that can ef®ciently handle well-, over-and under-constrained systems based on the dependence  ...  Solving geometric constraint systems in 3-D is much more complicated than that in 2-D because the number of variables is larger and some of the results valid in 2-D cannot be extended for 3-D.  ...  Fudos and Hoffmann [6] presented the correctness proof of a graph-based variational geometric constraint solver.  ... 
doi:10.1016/s0010-4485(01)00054-9 fatcat:kfdounyn4ndhbpexiaefmiwk3m

Geometric constraints solving

Dominique Michelucci, Sebti Foufou, Loic Lamarque, Pascal Schreck
2006 Proceedings of the 2006 ACM symposium on Solid and physical modeling - SPM '06  
This paper presents some important issues and potential research tracks for Geometric Constraint Solving: the use of the simplicial Bernstein base to reduce the wrapping effect in interval methods, the  ...  computation of the dimension of the solution set with methods used to measure the dimension of fractals, the pitfalls of graph based decomposition methods, the alternative provided by linear algebra,  ...  Acknowledgements to our colleagues from the French Group working on geometric constraints and declarative modelling, partly funded by CNRS in 2003-2005.  ... 
doi:10.1145/1128888.1128915 dblp:conf/sma/MichelucciFLS06 fatcat:54htnf6dfzh2tf2lem3yqbxmoe

Tree-decomposable and Underconstrained Geometric Constraint Problems [article]

Ioannis Fudos, Christoph M. Hoffmann, Robert Joan-Arinyo
2017 arXiv   pre-print
The constraint solvers used in MCAD took a quantum leap in the 1990s.  ...  These approaches solve a geometric constraint problem by an initial, graph-based structural analysis that extracts generic subproblems and determines how they would combine to form a complete solution.  ...  The constraint solvers used in MCAD took a quantum leap in the 1990s.  ... 
arXiv:1608.05205v3 fatcat:eoepj4luvfa23h4g4vmii3es34

A Relational Positioning Methodology for Robot Task Specification and Execution

A. Rodriguez, L. Basaez, E. Celaya
2008 IEEE Transactions on robotics  
In order to derive these positions, a geometric constraint solver must be used.  ...  To this end, positioning mobile with respect to fixed (PMF), a geometric constraint solver for the relational positioning of rigid objects in free space is introduced.  ...  Graph-based methods construct a (hyper)graph in which the nodes represent geometric objects and the arcs, constraints.  ... 
doi:10.1109/tro.2008.924263 fatcat:zjcaeltlbrfunn3fldqwokt644


2006 International journal of computational geometry and applications  
In order to tackle problems of industrial size, many solving methods use, as a preprocessing, decomposition techniques that transform a large geometric constraint system into a set of smaller ones.  ...  In this paper, we propose a survey of the decomposition techniques for geometric constraint problems a .  ...  Also thanks to Marc Gouttefarde for useful comments.  ... 
doi:10.1142/s0218195906002105 fatcat:r44sj3f645d2xfi4ile2wqswoe

Software architecture for a constraint-based virtual environment

Terrence Fernando, Norman Murray, Kevin Tan, Prasad Wimalaratne
1999 Proceedings of the ACM symposium on Virtual reality software and technology - VRST '99  
Fa, John Maxfield, M.Munlin, E.Lamounier, T.Tsai who worked hard to realise the initial constraint-based modelling work.  ...  Acknowledgements Thanks goes to Rolls-Royce PLC, British Aerospace, EDS Parasolid and D-Cubed for providing case study material and support for this project. Dr.  ...  The constraint solver is based on the Geometric Constructive approach described in Section 2.  ... 
doi:10.1145/323663.323686 dblp:conf/vrst/FernandoMTW99 fatcat:3le3y5zqdrextdkjrj4s63fmvm

Riemannian Optimization for Distance-Geometric Inverse Kinematics [article]

Filip Marić, Matthew Giamou, Adam W. Hall, Soroush Khoubyarian, Ivan Petrović, Jonathan Kelly
2021 arXiv   pre-print
In this paper, we formalize the equivalence of distance-based inverse kinematics and the distance geometry problem for a large class of articulated robots and task constraints.  ...  We demonstrate that our inverse kinematics solver achieves higher success rates than traditional techniques, and substantially outperforms them on problems that involve many workspace constraints.  ...  We achieve this by defining the following edge weights: d o,x = d o,y = d o,z = 1, d x,y = d x,z = d y,z = √ 2. ( 27 ) This base structure is used in the remainder of the section to specify, in terms of  ... 
arXiv:2108.13720v2 fatcat:7v4yuluwf5d7fhjjpgut3notz4

h-graphs: A new representation for tree decompositions of graphs

Marta Hidalgo, Robert Joan-Arinyo
2015 Computer-Aided Design  
If the graph is tree decomposable, the constraint-based geometric problem can be solved by a Decomposition-Recombination planner based solver.  ...  In geometric constraint solving, well constrained geometric problems can be abstracted as Laman graphs.  ...  In the graph-based constructive geometric constraint solving approach, the solver constructor has figured out a solution to the constraint problem when all the vertices in the graph are placed with respect  ... 
doi:10.1016/j.cad.2015.05.003 fatcat:4ircfu4dqvg63k4zshmagqupxm

A non-rigid cluster rewriting approach to solve systems of 3D geometric constraints

Hilderick A. van der Meiden, Willem F. Bronsvoort
2010 Computer-Aided Design  
We present a new constructive solving approach for systems of 3D geometric constraints.  ...  The solver is based on the cluster rewriting approach, which can efficiently solve large systems of constraints on points, and incrementally handle changes to a system, but can so far solve only a limited  ...  In the DOF-based approach, each constraint corresponds to a DOF reduction, and heuristic rules determine the DOF reduction of combinations of constraints.  ... 
doi:10.1016/j.cad.2009.03.003 fatcat:o45f7j3zdrhtlbjo6r4jv6jnpq

Implicit solutions with consistent additive and multiplicative components

P. Areias, T. Rabczuk, D. Dias-da-Costa, E.B. Pires
2012 Finite elements in analysis and design  
Solutions based on control equations are also directly incorporated as equality constraints. We show that arbitrary constituents can be used as long as the resulting directed graph is acyclic.  ...  This work describes an algorithm and corresponding software for incorporating general nonlinear multiple-point equality constraints in a implicit sparse direct solver.  ...  Acknowledgments The authors gratefully acknowledge financing from the ''Fundacao para a Ciência e a Tecnologia'' under the Project PTDC/EME-PME/ 108751 and the Program COMPETE FCOMP-01-0124-FEDER-010267  ... 
doi:10.1016/j.finel.2012.03.007 fatcat:jhp5o2oi3zbwxocawjg5n2bfci

Modeling Virus Self-Assembly Pathways: Avoiding Dynamics Using Geometric Constraint Decomposition

Meera Sitharam, Mavis Agbandje-Mckenna
2006 Journal of Computational Biology  
The model uses static geometric and tensegrity constraints to represent the driving (weak) forces that cause a viral shell to assemble and hold it together.  ...  Pathways and their properties are carefully defined and computed using computational algebra and geometry, specifically state-of-art concepts in geometric constraint decomposition.  ...  For example, a distance constraint of d between two points (x 1 , y 1 ) and (x 2 , y 2 ) in 2D is written as (x 2 − x 1 ) 2 + (y 2 − y 1 ) 2 = d 2 A solution or realization of a geometric constraint system  ... 
doi:10.1089/cmb.2006.13.1232 pmid:16901239 fatcat:p7ae2s5b5fahxd3wichg24dfw4


2006 International journal of computational geometry and applications  
We have validated our approach by reconstructing, from images, 3D models of buildings using interactively introduced geometrical constraints.  ...  matching based algorithms, and other famous propagation schema are not well-suited or cannot be easily extended to tackle geometric constraint systems that are under-constrained.  ...  Thanks to David Daney, Bertrand Neveu and Théodore Papadopoulo for useful discussions. Thanks to Gilles Chabert for comments. Thanks to Mr. Dominique Chancel for the architectural drawings.  ... 
doi:10.1142/s0218195906002154 fatcat:dvstagz2q5fdhbshgfgd2yiwza

Penetration-free projective dynamics on the GPU

Lei Lan, Guanqun Ma, Yin Yang, Changxi Zheng, Minchen Li, Chenfanfu Jiang
2022 ACM Transactions on Graphics  
IPC exploits a barrier-based formulation, which yields an infinitely large penalty when the constraint is on the verge of being violated.  ...  In addition, we also re-design the CCD root finding procedure by using a new minimum-gradient Newton algorithm.  ...  Acceleration is often achieved using model reduction, which creates a subspace representation of fullspace DOFs.  ... 
doi:10.1145/3528223.3530069 fatcat:hrgtznkqlfcndavawu6ybg7ski

Assembly modelling by geometric constraint satisfaction

Ram Anantha, Glenn A Kramer, Richard H Crawford
1996 Computer-Aided Design  
The approach combines a formalism for representing relationships among features with a new method for geometric constraint satisfaction.  ...  The method employs symbolic reasoning about the geometric structure of parts to solve spatial constraints between the parts, in contrast to other approaches that reduce the geometric relationships to a  ...  Owen handles cases with multiple solutions by maintaining topological relationships among the geometric entities. A commercial constraint solver based on this work is available from D-Cubed Ltd.  ... 
doi:10.1016/0010-4485(96)00001-2 fatcat:pdivh3vr3bhzrmukgvy2wuilbi
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