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TECHNICAL PAPERS

A Constraint Solving-Based Approach to Analyze 2D Geometric Problems With Interval Parameters

[+] Author and Article Information
R. Joan-Arinyo, N. Mata, A. Soto-Riera

Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Av. Diagonal 647, 8a , E-08028 Barcelona, Catalonia, Spain

J. Comput. Inf. Sci. Eng 1(4), 341-346 (Oct 01, 2001) (6 pages) doi:10.1115/1.1429641 History: Received August 01, 2001; Revised October 01, 2001
Copyright © 2001 by ASME
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References

Mata., N., 2000, “Constructible Geometric Problems with Interval Parameters,” PhD thesis, Dept. LSI, Universitat Politècnica de Catalunya, Barcelona, Spain.
Mata, N., 1997, “Solving Incidence and Tangency Constraints in 2D,” Technical Report LSI-97-3R, Department LSI, Universitat Politècnica de Catalunya, Available at http://www.lsi.upc.es.
Durand, C., 1998, “Symbolic and Numerical Techniques for Constraint Solving,” PhD thesis, Purdue University, Department of Computer Sciences, December.
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Garling, D. J. H., 1986, “A Course in Galois Theory,” Cambridge University Press.
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.
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 Politècnica de Catalunya. Available at http://www.lsi.upc.es.
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.
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Mata, N., 1999, “How to Compute Tight Enclosures for the Range of a Multi-Dimensional Differentiable Function,” Technical Report LSI-99-48-R, Department LSI, Universitat Politècnica de Catalunya. Available at http://www.lsi.upc.es.
Hammer, R., Hocks, M., Kulisch, U., and Ratz, D., 1993, Numerical Toolbox for Verified Computing I. Springer-Verlag.
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).
Hansen, E., 1992, Global Optimization Using Interval Analysis. Marcel Dekker, Inc.
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Ratschek, H., and Rokne, J., 1988, New Computer Methods for Global Optimization. Ellis Horwood Series in Mathematics and its Applications. Ellis Horwood Limited.
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Figures

Grahic Jump Location
Peaucellier’s linkage
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Motion analysis of point P6 for angles in a1[280.692°,360°]
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Feasible values of angle a
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Geometric problem defined by constraints
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Construction plan for the object in Fig. 1
Grahic Jump Location
Computing tight enclosures for the range of a function over narrow intervals

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