Skip to main content
SpringerLink
Log in

A Hybrid Method for Solving Geometric Constraint Problems

  • Conference paper
  • First Online:
Automated Deduction in Geometry (ADG 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2061))

Included in the following conference series:

Abstract

We propose an algorithm for solving geometric constraint problems. The algorithm has linear complexity for constrained systems without loops, and is of quadratic complexity for constraint problems with loops. This algorithm is complete for constraint problems about simple polygons. The key of the algorithm is to combine the idea of graph based methods for geometric constraint solving and geometric transformations from rule-based methods.

This work is supported in part by a “973” project and by CNSF under an outstanding youth grant (NO. 69725002).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dufourd, J.-F., Mathis, P., and Schreck, P.: Geometric Construction by Assembling Solved Subfigures. Artificial Intelligence, 99(1998), 73–119.

    Article  MATH  MathSciNet  Google Scholar 

  2. Fudos, I. and Hoffmann, C. M.: A Graph-Constructive Approach to Solving Systems of Geometric Constraints. ACM Transactions on Graphics, 16(1997), 179–216.

    Article  Google Scholar 

  3. Gao, X.-S. and Chou, S.-C.: Solving Geometric Constraint Systems I. A Global Propagation Approach. Computer Aided Design, 30(1998), 47–54.

    Article  Google Scholar 

  4. Gao, X.-S. and Chou, S.-C.: Solving Geometric Constraint Systems II. A Symbolic Approach and Decision of Rc-constructibility. Computer Aided Design, 30(1998), 115–122.

    Google Scholar 

  5. Ge, J.-X., Chou, S.-C., and Gao, X.-S.: Geometric Constraint Satisfaction Using Optimization Methods. Computer Aided Design, 31(1999), 867–879.

    Article  MATH  Google Scholar 

  6. Hendrickson, B.: Conditions for Unique Realizations. SIAM J. Computing, 21 (1992), 65–84.

    Article  MATH  MathSciNet  Google Scholar 

  7. Heydon, A. and Nelson, G.: The Juno-2 Constraint-Based Drawing Editor. SRC Research Report 131a (1994).

    Google Scholar 

  8. Hoffmann, C. M., Lomonosov, A., and Sitharam, M.: Finding Solvable Subsets of Constraint Graphs. LNCS, vol. 1330, Springer-Verlag, Berlin Heidelberg (1997), 163–197.

    Google Scholar 

  9. Joan-Arinyo, T. and Soto-Riera, A.: Combining Constructive and Educational Geometric Constraint-Solving Techniques. ACM Trans. on Graphics, 18(1999), 35–55.

    Article  Google Scholar 

  10. Kondo, K.: Algebraic Method for Manipulation of Dimensional Relationships in Geometric Models. Computer Aided Design, 24(1992), 141–147.

    Article  MATH  Google Scholar 

  11. Kramer, G.: Solving Geometric Constraint Systems. MIT Press, Cambridge (1992).

    Google Scholar 

  12. Lamure, H. and Michelucci, D.: Solving Geometric Constraints by Homotopy. IEEE Trans on Visualization and Computer Graphics, 2(1996), 28–34.

    Article  Google Scholar 

  13. Latheam, R. S. and Middleditch, A. E.: Connectivity Analysis: A Tool for Processing Geometric Constraints. Computer Aided Design, 28(1994), 917–928.

    Article  Google Scholar 

  14. Lee, J. Y.: A 2D Geometric Constraint Solver for Parametric Design Using Graph Reduction and Analysis. Automated Deduction in Geometry, LNAI, vol. 1669, Springer-Verlag, Berlin Heidelberg (1999), 258–274.

    Google Scholar 

  15. Light, R. and Gossard, D.: Modification of Geometric Models Through Variational Geometry. Geometric Aided Design, 14(1982), 208–214.

    Google Scholar 

  16. Owen, J.-C.: Algebraic Solution for Geometry from Dimensional Constraints. Proc. 1st Symp. Solid Modeling Foundations & CAD/CAM Applications, ACM Press, New York (1991), 379–407.

    Google Scholar 

  17. Verroust, A., Schonek, F., and Roller, D.: Rule-Oriented Method for Parameterized Computer-Aided Design. Computer Aided Design, 24(1992), 531–540.

    Article  MATH  Google Scholar 

  18. Sunde, G.: Specification of Shape by Dimensions and Other Geometric Constraints. Geometric Modeling for CAD Applications, M. J. Wozny et al., eds., North Holland (1988), 199–213.

    Google Scholar 

  19. Wang, D.: Reasoning about Geometric Problems Using an Elimination Method. Automated Practical Reasoning: Algebraic Approaches, Pfalzgraf, J. and Wang, D., eds., Springer, Wien New York (1995), 147–185.

    Google Scholar 

  20. Wu, W.-T.: Mechanical Theorem Proving in Geometries:Basic Principles. Springer-Verlag, Wien New York (1994).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Systems Science, Academy of Mathematics and System Sciences Academia Sinica, Beijing, 100080, China

    Xiao-Shan Gao, Lei-Dong Huang & Kun Jiang

Authors
  1. Xiao-Shan Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lei-Dong Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kun Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Zentrum Mathematik, SB4, Technische Universität München, 80290, München, Germany

    Jürgen Richter-Gebert

  2. Laboratoire d’Informatique de Paris 6, Université Pierre et Marie Curie — CNRS, 4 place Jussieu, 75252, Paris Cedex 05, France

    Dongming Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gao, XS., Huang, LD., Jiang, K. (2001). A Hybrid Method for Solving Geometric Constraint Problems. In: Richter-Gebert, J., Wang, D. (eds) Automated Deduction in Geometry. ADG 2000. Lecture Notes in Computer Science(), vol 2061. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45410-1_2

Download citation

  • DOI: https://doi.org/10.1007/3-540-45410-1_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42598-4

  • Online ISBN: 978-3-540-45410-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation