A Brief on Constraint Solving

Computer-Aided Design and Applications

Volumn 2, Issue 5, 2005, Pages 655-663

  Hoffmann, Christoph M ^a   Joan Arinyo, Robert ^b  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Constraint solving; Geometric constraints; Parametric design

Indexed keywords

CONSTRAINT THEORY; LOGIC PROGRAMMING;

CONSTRAINT SOLVING; GEOMETRIC CONSTRAINT; GEOMETRIC CONSTRAINT SOLVING; PARAMETRIC DESIGN; STATE OF THE ART;

CODES (SYMBOLS);

EID: 33750700588     PISSN: 16864360     EISSN: None     Source Type: Journal    
DOI: 10.1080/16864360.2005.10738330     Document Type: Article

References (38)

1. S., Bhansali, G., Kramer, and T.J., Hoar. A principled approach towards symbolic geometric constraint Satisfaction. Journal of Artificial Intelligence Research, 4:419–443, 1996.
2. A. H., Borning. The programming language aspects of ThingLab, a constrained oriented simulation laboratory. ACM Trans. on Prog. Lang. and Systems, 3 (4):353–387, 1981.
3. A., Borning, R., Anderson, and B., Freeman-Benson. Indigo:A local propagation algorithm for inequality constraints. In UIST’96, pages 129–136, Seattle, Washington, USA, November 6–8 1996. ACM.
4. W., Bouma, I., Fudos, C., Hoffmann, J., Cai, and R., Paige. A geometric constraint solver. Computer Aided Design, 27 (6):487–501, 1995.
5. B. D., Brüderlin. Constructing three-dimensional geometric objects defined by constraints. Workshop on Interactive 3D Graphics, pages 111–129. ACM, October 1986.
6. C., Durand. Symbolic and numerical techniques for constraint solving. PhD thesis, Comp. Sci., Purdue Univ., 1998.
7. B., Freeman-Benson, J., Maloney, and A., Borning. An incremental constraint solver. Comm.ACM, 33 (1):54–63, 1990.
8. I., Fudos. Constraint Solving for Computer Aided Design. PhD thesis, Purdue University, Department of Computer Sciences, 1995.
9. I., Fudos and C. M., Hoffmann. Correctness proof of a geometric constraint solver. Intl J Computational Geometry and Applications, 6 (4):405420, 1996.
10. I., Fudos and C., Hoffmann. A graph-constructive approach to solving systems of geometric constraints. ACM Trans. On Graphics 16, p.179–216, 1997.
11. C. M., Hoffmann and R., Joan-Arinyo. Symbolic constraints in constructive geometric constraint solving. J. Symbolic Comp. 23, p.287–300, 1997.
12. 3. In D.-Z., Du and F., Hwang, editors, Computing in Euclidean Geometry, p.266–298. World Scientific Publishing, 1995.
13. C. M., Hoffmann and P. J., Vermeer. A spatial constraint problem. In J. P., Merlet and B., Ravani, editors, Computaional Kinematics ’95, p. 183–92. Kluwer Academic Publishers, 1995.
14. C. M., Hoffmann, A., Lomonosov, and M., Sitharam. Finding solvable subsets of constraint graphs. In Principles and Practice of Constraint Programming, 463–477, Schloss Hagenberg, Austria, 1977.
15. C. M., Hoffmann, A., Lomonosov, and M., Sitharam. Decompostion Plans for Geometric Constraint Problems, Part I:Performance Measurements for CAD. Journal of Symbolic Computation, 31:367–408, 2001.
16. C. M., Hoffmann, A., Lomonosov, and M., Sitharam. Decompostion Plans for Geometric Constraint Problems, Part II:New Algorithms. Journal of Symbolic Computation, 31:409–427, 2001.
17. C.-Y., Hsu. Graph-Based Approach for Solving Geometric Constraint Problems.PhD thesis, Department of Computer Science. The University of Utah, June 1996.
18. C.-Y., Hsu and B. D., Brüderlin. A hybrid constraint solver using exact and iterative geometric constructions. In D., Roller and P., Brunet, eds, CAD Systems Development:Tools and Methods, 265–279, 1997. Springer-Verlag.
19. C., Jermann. Resolution de constraints géométriques par rigidification recursive et propagation d’intervalles. PhD thesis, Université de Nice-Sophia Antipolis, 2002.
20. R., Joan-Arinyo and A., Soto-Riera. Combining constructive and geometric constraint solving techniques. ACM Trans. On Graphics 18, p.35–55, 1999.
21. R., Joan-Arinyo, A., Soto-Riera, S., Vila-Marta, and J., Vilaplana. On the domain of constructive geometric constraint solving techniques. In R., Duricovic and S., Czanner, editors, Spring Conference on Computer Graphics, pages 49–54, Budmerice, Slovakia, April 25–28 2001. IEEE Computer Society, Los Alamitos, CA.
22. R., Joan-Arinyo, A., Soto-Riera, S., Vila-Marta, and J., Vilaplana. Declarative characterization of a general architecture for constructive geometric constraint solvers. In D.—Plemenos, editor, Fifth Intl Conf on Computer Graphics and Artificial Intelligence, pages 63–76, Limoges, France, May 2002. Universitè de Limoges.
23. U., Kortenkamp. Foundations of Dynamic Geometry. PhD thesis, ETH Zurich, 1999
24. G., Kramer. Solving Geometric Constraints Systems. MIT Press, 1992.
25. G., Kramer Using degrees of freedom analysis to solve geometric constraint systems. In J., Rossignac and J., Turner, editors, Symposium on Solid Modeling Foundations and CAD/CAM Applications, 371–378, Austin, TX, 1991. ACM Press.
26. G., Kramer. A geometric constraint engine. Artificial Intelligence, 58(1–3):327–360, 1992.
27. G., Kwaiter, V., Gaildrat, and R., Caubet. Interactive constraint system for solid modeling objects. In C., Hoffmann and W., Bronsvoort, editors, Fourth Symposium on Solid Modeling and Applications, 265–270. ACM 1997.
28. R. S., Latham and A. E., Middleditch. Connectivity analysis:a tool for processing geometric constraints. Computer Aided Design, 28(11):917–928, 1996.
29. J. Y., Lee and K., Kim. Geometric reasoning for knowledge-based parametric design using graph representations. Computer-Aided Design, 28(10):831–841, 1996.
30. Leler W., Constraint Programming Languages:Their Specification and Generation. Addison Wesley, 1988.
31. J. C., Owen. Algebraic solution for geometry from dimensional constraints. In R., Rossignac and J., Turner, editors, Symposium on Solid Modeling Foundations and CAD/CAM Applications, 397–407, Austin, TX, 1991.
32. M., Sannella The Sky Blue constraint solver. Technical Report 92–07–02, University of Washington, Dep of Computer Science and Engineering, 1993.
33. P., Todd. A k-tree generalization that characterizes consistency of dimensioned engineering drawings. SIAM J. Disc. Math, 2 (2):255–261, 1989.
34. R. C., Veltkamp and F., Arbab. Geometric constraint propagation with quantum labels. In B., Falcidieno, I., Herman, and C., Pienovi, editors, Eurographics Workshop on Computer Graphics and Mathematics, 211–228. Springer, 1992.
35. A., Verroust Etude de Problemes Lies a Ia Definition Ia Visualisation et l’Animation d’Objects Complexes en Informatique Graph ique. PhD thesis, Universite de Paris-Sud, Centre d’Orsay, 1990.
36. A., Verroust, F., Schonek, and D., Roller. Rule-oriented method for parameterized computer-aided design. Computer Aided Design, 24 (10):531–540, 1992.
37. W.-T., Wu. Basic principles of mechanical theorem proving in geometries. J. of Systems Sciences and Mathematical Sciences, 4:207–235, 1986.
38. W.-T., Wu. Mechanical theorem proving in geometries. In B., Buchberger and G. E., Collins, editors, Texts and Monographs in Symbolic Computations. Springer-Verlag, 1994.