Decomposition of geometric constraint systems: A survey

International Journal of Computational Geometry and Applications

Volumn 16, Issue 5-6, 2006, Pages 379-414

  Jermann, Christophe ^a   Trombettoni, Gilles ^b   Neveu, Bertrand ^b   Mathis, Pascal ^c  

^a UNIVERSITÉ DE NANTES   (France)

^b INRIA   (France)

^c Faculté de Médecine   (France)

Author keywords

Connectivity analysis; Decomposition techniques; DOF analysis; DR planner; Geometric constraints; Maximum matching; PDOF; Rigidity; WCM

Indexed keywords

EID: 33750727375     PISSN: 02181959     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0218195906002105     Document Type: Conference Paper

References (77)

1. C. M. Hoffmann, A. Lomonosov and M. Sitharam, Decomposition of Geometric Constraints Part I: performance measures & Part II: new algorithms, J. Symb. Comput., 31(4) (2001).
2. C. M. Hoffmann and R. Joan-Arinyo, A brief on constraint solving, Computer-Aided Design and Applications, 2005.
3. M. Sitharam, Combinatorial approaches to geometric constraint solving: problems, progress, directions, in AMS-DIMACS Book on CAD and Manufacturing, 2005.
4. C. Jermann, Résolution de contraintes géométriques par rigidification recursive et propagation d'intervalles, PhD thesis, UNSA, NICE, 2002.
5. L. Henneberg, Die graphische Statik der starren Systeme, Leipzig, 1911.
6. I. Fudos, Constraint Solving for Computer Aided Design, PhD thesis, Purdue University, 1995.
7. J. Graver, B. Servatius and H. Servatius, Combinatorial Rigidity. Graduate Studies in Mathematics (American Mathematical Society, 1993).
8. L. Lovasz and Y. Yemini, On generic rigidity in the plane, SIAM J. Alg. Discr. Methods 3 (1982) 91-98.
9. H. Crapo, On the generic rigidity of plane frameworks, Technical Report 1278, INRIA, 1990.
10. B. Hendrickson, Conditions for unique realizations, SIAM J. Comput. 21(1) (1992) 65-84.
11. W. Whiteley and B. Servatius, Constraining plane configurations in computer-aided design: combinatorics of directions and lengths, SIAM J. Discr. Math. 12(1) (1999) 136-153.
12. Y. Zhou and M. Sitharam, A tractable, approximate characterization of combinatorial rigidity in 3D, in ADG'2004, 2004.
13. M. Sitharam, Frontier, an opensource gnu geometric constraint solver: version3 (2003) for general 2d and 3d systems, 2003. http://www.cise.ufl.edu/ sitharam.
14. C. Jermann, B. Neveu and G. Trombettoni, A new structural rigidity for geometric constraint systems, in Int. Workshop on Automated Deduction in Geometry, ADG'2002, LNCS 2930, 2004, pp. 87-106.
15. G.-F. Zhang and X.-S. Gao, Geometric constraint solving based on connectivity of graph, Technical Report 22, Academia Sinica, Beijing, China, December 2003.
16. A. S. Householder, Principles of Numerical Analysis (McGraw-Hill, New York, NY, USA, 1953).
17. E. Lahaye, Une méthode de résolution d'une catégorie d'équations transcendantes, Compte-rendu des Séances de L'Académie des Sciences 198 (1934) 1840-1842.
18. D. Michelucci and H. Lamure, Résolution de contraintes géométriques par homotopie, in Actes de AFIG 1994, 1994.
19. C. Durand, Symbolic and Numerical Techniques for Constraint Solving, PhD thesis, Purdue University, 1998.
20. R. E. Moore, Interval Analysis (Prentice-Hall, 1966).
21. C. Jermann, G. Trombettoni, B. Neveu and M. Rueher, A constraint programming approach for solving rigid geometric systems, in Constraint Programming, CP'2000, volume 1894 of LNCS, 2000, pp. 233-248.
22. C. Jermann, B. Neveu and G. Trombettoni, Inter-block backtracking: exploiting the structure in continuous CSPs, in Selected papers of the Int. Works. on Global Optim. and constraint satisfaction, COCOS 2003, LNCS 3478, 2005, pp. 15-30.
23. W. Wu, Basic principles of mechanical theorem proving in elementary geometries, J. Automat. Reas. 2 (1986) 221-254.
24. S. G. Chou, Mechanical Theorem Proving (Reidel Publishing Co., 1988).
25. P. Mathis, P. Schreck and J.-F. Dufourd, Yams: a multi-agent system for 2d constraint solving, in Geometric Constraint Solving and Applications, eds. B. Bruderlin and D. Roller (Springer, 1998), pp. 211-233.
26. M. Wilczkowiak, G. Trombettoni, C. Jermann, P. Sturm and P. Boyer, Scene modeling based on constraint system decomposition techniques, in 9th IEEE Int. Conf. Computer Vision, ICCV'03, 2003.
27. J. Owen, Algebraic solution for geometry from dimensional constraints, in Proc. Solid Modeling and CAD/CAM Applications, 1991, pp. 397-407.
28. J.-F. Dufourd, P. Mathis and P. Schreck, Geometric construction by assembling solved subfigures, Artifi. Intell. 99(1) (1998) 73-119.
29. I. Fudos and C. M. Hoffmann, A graph-constructive approach to solving systems of geometric constraints, ACM Trans. Graph. 16(2) (1997) 179-216.
30. R. Joan-Arinyo, A. Soto-Riera, S. Vila-Marta and J. Vilaplana-Pasto, Transforming an under-constrained geometric constraint problem into a well-constrained one, in SM'03: Proc. Solid Modeling and Applications, 2003.
31. R. Joan-Arinyo, A. Soto-Riera, S. Vila-Marta and J. Vilaplana-Pasto, Revisiting decomposition analysis of geometric constraint graphs, Comput. Aided Des. 36 (2004) 123-140.
32. J. E. Hopcroft and R. E. Tarjan, Dividing a graph into triconnected components, SIAM J. Comput. 3 (1973) 135-158.
33. C. M. Hoffmann, A. Lomonosov and M. Sitharam, Finding solvable subsets of constraint graphs, in Proc. Constraint Programming, CP'97, 1997, pp. 463-477.
34. A. Lomonosov, Graph and Combinatorial Algorithms for Geometric Constraint Solving, PhD thesis, University of Florida, 2004.
35. J. J. Oung, M. Sitharam, B. Moro and A. Arbree, Frontier: fully enabling geometric constraints for feature based modeling and assembly, in Proceedings of ACM Solid Modeling Symp., 2001, 2001.
36. C. M. Hoffmann, M. Sitharam and B. Yuan, Making constraint solvers more usable: overconstraint problem, Comput. Aided Des. 36(4) (2004) 377-399.
37. S.-M. Hu, Y.-T. Li and J.-G. Sun, A constructive approach to solving 3D geometric constraint systems using dependence analysis, Comput. Aided Des. 34(2) (2002) 97-108.
38. X.-S. Gao and G.-F. Zhang, Geometric Constraint Solving via C-tree Decomposition, in SM'03, 2003, pp. 45-55.
39. G. Sunde, Specification of shapes by dimensions and other geometric constraints, in IFIP WG 5.2 Geometric Modeling, 1986.
40. A. Verroust, F. Schonek and D. Roller, Rule oriented method for parametrized computer aided design, Comput. Aided Des. 24(6) (1992) 531-540.
41. R Joan-Arinyo and A Soto, A correct rule-based geometric constraint solver, Comput. Graph. 5(21) (1997) 599-609.
42. W. Bouma, I. Fudos, G. M. Hoffmann, J. Cai and R. Paige, Geometric constraint solver, Comput. Aided Des. 27(6) (1995) 487-501.
43. I. Fudos and C. M. Hoffmann, Correctness proof of a geometric constraint solver, Int. J. Computational Geometry and Applications 6 (1996) 405-420.
44. C. M. Hoffmann and R. Joan-Arinyo, Symbolic constraints in constructive geometric constraint solving, J. Symb. Comput. 23 (1997) 287-299.
45. G. Kramer, Solving Geometric Constraint Systems (MIT Press, 1992).
46. M. Gruebler, Getriebelehre (Springer, Berlin, 1917).
47. X. S. Gao, K. Jiang and C.-C. Zhu, Geometric constraint solving with conies and linkages, Comput. Aided Des. 34(6) (2002) 421-433.
48. P. Schreck, Implantation d'un systéme à base de connaissances pour les constructions gé omé triques, Revue d'Intelligence Artificielle 8(3) (1994) 223-247.
49. S. C. Chou, X. S. Gao and J. Z. Zhang, A deductive database approach to automated geometry theorem proving and discovering, J. Automat. Reason. 25(3) (2000) 219-246.
50. B. Aldefeld, Variations of geometries based on a geometric-reasoning method, Comput. Aided Des. 20(3) (1988) 117-126.
51. P. Schreck, Robustness in CAD geometric construction, in Proc. Int. Conf. Information Visualisation, IV'2001, IEEE, 2001, pp. 111-116.
52. E. Schramm and P. Schreck, Solving geometric constraints invariant modulo the similarity group, in Proc. of the 2002 Int. Conf. Computational Science and its Applications, Part II, LNCS 2669 (Part III), 2003, pp. 356-365.
53. P. Schreck and P. Mathis, Geometrical constraint system decomposition: a multigroup approach, Technical report, Université de Strasbourg, France, 2005.
54. D. Serrano, Constraint Management in Conceptual Design, PhD thesis, MIT, 1987.
55. 2.5 algorithm for maximum matching in bipartite graphs, SIAM J. Comput. 2(4) (1973) 225-231.
56. R. E. Tarjan, Depth-first search and linear graph algorithms, SIAM J. Comput. 1(2) (1972) 146-160.
57. D. Koenig, Über Graphen und ihre Anwendung auf Determinantentheorie und Mengenlehre, in Math. Ann. 77, 1916, pp. 453-465.
58. A. Pothen and C. J. Fan, Computing the block triangular form of a sparse matrix, ACM Trans. Math. Soft. 16(4) (1990) 303-324.
59. R. S. Latham and A. E. Middleditch, Connectivity analysis: a tool for processing geometric constraints, Comput. Aided Des. 28(11) (1996) 917-928.
60. I. Sutherland, Sketchpad: A Man-Machine Graphical Communication System, PhD thesis, Department of Electrical Engineering, MIT, 1963.
61. A. Borning, ThingLab: A Constraint-Oriented Simulation Laboratory, PhD thesis, Stanford University, 1979.
62. B. Vander Zanden, An incremental algorithm for satisfying hierarchies of multi-way, dataflow constraints, ACM TOPLAS 18(1) (1996) 30-72.
63. S. Ait Aoudia, Modélisation géométrique par contraintes: quelques méthodes de résolution, PhD thesis, Ecoles des Mines de Saint Etienne, 1994.
64. C. Hsu and B. Brderlin, A degree-of-freedom graph approach, in Geometric Modeling: Theory And Practice, 1997, pp. 132-155.
65. P. Massan Kuzo, Des contraintes projectives en modlisation tridimensionnelle interactive, PhD thesis, Ecole des Mines de Nantes, 1999.
66. E. Eremchenko and A. Ershov, Two new decomposition techniques in geometric constraint solving, Research report Preprint number 11, LEDAS Company, 2004.
67. C. Bliek, B. Neveu and G. Trombettoni, Using graph decomposition for solving continuous CSPs, in Proc. Constraint Programming, CP'98, volume LNCS 1520, 1998, pp. 102-116.
68. G. Trombettoni, A polynomial time local propagation algorithm for general dataflow constraint problems, in Proc. Constraint Programming, volume LNCS 1520, 1998, pp. 432-446.
69. G. Trombettoni and M. Wilczkowiak, GPDOF: a fast algorithm to decompose underconstrained geometric constraint systems: Application to 3D model reconstruction, Int. J. Computational Geometry and Applications, 16, 2006.
70. P. Mathis, Constructions géométriques sous contraintes en modélisation à base topologique, PhD thesis, Université Louis Pasteur, 1997.
71. C. Essert-Villard, P. Schreck and J. F. Dufourd, Sketch-based pruning of a solution space within a formal geo. constraint solver, Artif. Intell. 124 (2000) 139-159.
72. S. Foufou, D. Michelucci and J.-P. Jurzak, Numerical decomposition of geometric constraints, in Proc. Solid and Physical Modeling, SPM, 2005, pp. 143-151.
73. D. Michelucci and S. Foufou, The witness configuration method, Comput. Aided Des., 2005.
74. W. Whiteley, Applications of the geometry of rigid structures, in Computer Aided Geometric Reasoning, eds. H. Crapo, INRIA, 1987, pp. 219-254.
75. H. Lamure and D. Michelucci, Qualitative study of geometric constraints, in Geometric Constraint Solving and Applications, (Springer, 1998), pp. 234-258.
76. J. Graver, Counting on Frameworks: Mathematics to Aid the Design of Rigid Structures, Number 25 (Mathematical Association of America, 2002).
77. W.A. Martin, Determining the equivalence of algebraic expressions by hash coding, J. ACM 18(4) (1971) 549-558.