A constraint solving-based approach to analyze 2d geometric problems with interval parameters

Journal of Computing and Information Science in Engineering

Volumn 1, Issue 4, 2001, Pages 341-346

  Joan Arinyo, R ^a   Mata, N ^a   Soto Riera, A ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Constructive Geometric Constraint Solving; Global optimization; Interval analysis

Indexed keywords

EID: 77955206068     PISSN: 15309827     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1429641     Document Type: Article

References (19)

1. Mata, N., 2000, “Constructible Geometric Problems with Interval Parameters,” PhD thesis, Dept. LSI, Universitat Politecnica de Catalunya, Barcelona, Spain.
2. Mata, N., 1997, “Solving Incidence and Tangency Constraints in 2D,” Technical Report LSI-97-3R, Department LSI, Universitat Politecnica de Catalunya, Available at http://www.lsi.upc.es.
3. Durand, C., 1998, “Symbolic and Numerical Techniques for Constraint Solving,” PhD thesis, Purdue University, Department of Computer Sciences, December.
4. Fudos, I., and Hoffmann, C. M., 1997, “A Graph-Constructive Approach to Solving Systems of Geometric Constraints,” ACM Trans. Graphics, 16, No. 2, pp. 179-216.
5. Laman, G., 1970, “On Graphs and Rigidity of Plane Skeletal Structures,” J. Eng. Math., 4, No. 4, pp. 331-340 October.
6. Garling, D. J. H., 1986, “A Course in Galois Theory,’ Cambridge University Press.
7. Joan-Arinyo, R., and Soto-Riera, A., 1999, “Combining Constructive and Equational Geometric Constraint Solving Techniques,” ACM Trans. Graphics, 18, No. 1, pp. 35-55, January.
8. Joan-Arinyo, R., and Mata, N., 2000, “A Data Structure for Solving Geometric Construction Problems With Interval Parameters,” Technical Report LSI-00-24-R, Department LSI, Universitat Politecnica de Catalunya. Available at http://www.lsi.upc.es.
9. Mata, N., and Kreinovich, V, 1999, “NP-Hardness in Geometric Construction Problems With One Interval Parameter,” In Applications of Interval Analysis to Systems and Control with special emphasis on recent advances in Modal Interval Analysis (MISC’99), pages 85-98, Girona (Spain), Feb. 24-26.
10. Alefeld, G., and Herzberger, J., 1983, Introduction to Interval Computations, Computer Science and Applied Mathematics. Academic Press.
11. Moore, R. E., 1966, Interval Analysis, Series in Automatic Computation, Prentice-Hall, Englewood Cliffs, N.J.
12. Mata, N., 1999, “How to Compute Tight Enclosures for the Range of a MultiDimensional Differentiable Function,” Technical Report LSI-99-48-R, Department LSI, Universitat Politecnica de Catalunya. Available at http://www.lsi.upc.es.
13. Hammer, R., Hocks, M., Kulisch, U., and Ratz, D., 1993, Numerical Toolbox for Verified Computing I. Springer-Verlag.
14. Ratz, D., 1992, “An Inclusion Algorithm for Global Optimization in a Portable PASCAL-XSC Implementation,” In L. Atanassova and J. Herzberger, editors, Computer Arithmetic and Enclosure Methods, pp. 329-338. IMACS, Elsevier Science Publishers B.V (North-Holland).
15. Hansen, E., 1992, Global Optimization Using Interval Analysis. Marcel Dek-ker, Inc.
16. Kearfott, R. B., 1996, Rigorous Global Search: Continuous Problems. Kluwer Academic Publications.
17. Ratschek, H., and Rokne, J., 1988, New Computer Methods for Global Optimization. Ellis Horwood Series in Mathematics and its Applications. Ellis Hor-wood Limited.
18. Cundy, H. M., and Rollett, A. P, 1961, Mathematical Models. Oxford University Press, Second edition.
19. Hilbert, D., and Cohn-Vossen, S., 1983, Geometry and the Imagination. Chelsea Publishing Company, New York.