Skip to main content
SpringerLink
Log in

Geometric constraint solving with geometric transformation

  • Scientific Papers
  • Published:
Science in China Series F Information Sciences Aims and scope Submit manuscript

Abstract

This paper proposes two algorithms for solving geometric constraint systems. The first algorithm is for constrained systems without loops and has linear complexity. The second algorithm can solve constraint systems with loops. The latter algorithm is of quadratic complexity and is complete for constraint problems about simple polygons. The key to it is to combine the idea of graph based methods for geometric constraint solving and geometric transformations coming from rule-based methods.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Gao, X. S., Automated geometry diagram construction and intelligent CAD, in Automated Deduction in Geometry, 1999, Berlin: Springer-Verlag, 232–257.

    Chapter  Google Scholar 

  2. Fudos, I., Hoffmann, C. M., A graph-constructive approach to solving systems of geometric constraints, ACM Transactions on Graphics, 1997, 16(2): 179.

    Article  Google Scholar 

  3. Owen, J. C., Algebraic solution for geometry from dimensional constraints, in Proc. 1st Symp. Solid Modeling Foundations & CAD/CAM Applications, New York: ACM Press, 1991, 379–407.

    Google Scholar 

  4. Latheam, R. S., Middleditch, A. E., Connectivity analysis: a tool for processing geometric constraints, Computer Aided Design, 1994, 28(11), 917.

    Article  Google Scholar 

  5. Yuan, B., Sun, J. G., A graph based approach to design decomposition, The Sixth International Conference on CAD & CG, Dec. 1999, Shanghai-China, 984–988.

  6. Gao, X. S., Chou, S. C., Solving geometric constraint systems I. A global propagation approach, Computer-Aided Design, 1998, 30(1): 47.

    Article  Google Scholar 

  7. Lee, J. Y., A 2D Geometric constraint solver for parametric design using graph reduction and analysis, Automated Deduction in Geometry, New York: Springer-Verlag, 1999, 258–274.

    Chapter  Google Scholar 

  8. Kramer, G., Solving Geometric Constraint Systems, New York: MIT Press, 1992.

    Google Scholar 

  9. Verroust, A., Schonek, F., Roller, D., Rule-oriented method for parameterized computer-aided design, Computer-Aided Design, 1992, 24(2): 531.

    Article  MATH  Google Scholar 

  10. Joan-Arinyo, T., Soto-Riera, A., Combining constructive and educational geometric constraint-solving techniques, ACM Trans. on Graphics, 1999, 18(1): 35.

    Article  Google Scholar 

  11. Ge, J. X., Chou, S. C., Gao, X. S., Geometric constraint satisfaction using optimization methods, CAD, 1999, 31(14): 867.

    MATH  Google Scholar 

  12. Heydon, A., Nelson, G., The juno-2 constraint-based drawing editor, SRC Research Report 131a, 1994.

  13. Lamure, H., Michelucci, D., Solving geometric constraints by homotopy, IEEE Trans., on Visualization and Computer Graphics, 1996, 2(1): 28.

    Article  Google Scholar 

  14. Light, R., Gossard, D., Modification of geometric models through variational geometry, Geometric Aided Design, 1982, 14: 208.

    Google Scholar 

  15. Gao, X. S., Chou, S. C., Solving geometric constraint problems, II. A symbolic approach and decision of Rc-constructibility, Computer Aided Design, 1998, 30(2): 115.

    Article  Google Scholar 

  16. Kondo, K., Algebraic method for manipulation of dimensional relationships in geometric models, Geometric Aided Design, 1992, 24(3): 141.

    Article  MATH  MathSciNet  Google Scholar 

  17. Hoffmann, C. M., Lomonosov, A., Sitharam, M., Finding solvable subsets of constraint graphs, LNCS, 1997, (1330): 163.

  18. Chou, S. C., Mechanical Geometry Theorem Proving, Dordrecht: D. Reidel Publishing Company, 1988.

    MATH  Google Scholar 

  19. Chou, S. C., Gao X. S., Zhang, J. Z., Machine Proofs in Geometry, Singapore: World Scientific, 1994.

    MATH  Google Scholar 

  20. Wu, W. T., Toward mechanization of geometry—Some comments on Hilbert’s “Grundlagen der Geometrie”, Acta Math. Sci., 1982, 2: 125.

    MATH  Google Scholar 

  21. Wang, D., On Wu’s method for proving constructive geometric theorems, in Proc. IJCAI 89 (Detroit, August 20–25, 1989), 1989, 419–424.

  22. Chou, S. C., Gao, X. S., Zhang, J. Z., Automated generation of readable proofs with geometric invariants, I. Multiple and shortest proof generation, J. of Automated Reasoning, 1996, 17: 325.

    Article  MATH  MathSciNet  Google Scholar 

  23. Li, H. B., Cheng, M. T., Automated ordering for automated theorem proving in elementary geometry, MM-Preprints, 1999, (18): 84.

  24. Chou, S. C., Gao, X. S., Zhang, J. Z., Machine Proof in Geometry, Singapore: World Scientific, 1994.

    Google Scholar 

  25. Wang, D., Reasoning about geometric problems using an elimination method, In Automated practical reasoning: Algebraic approaches (eds. Pfalzgraf, J., Wang, D.), New York: Springer Verlag, 1995, 147–185.

    Google Scholar 

  26. Dong, J. X., Ge, J. X., Gao, Y. et al., New ideas for constraint solving in parametric drawing systems, CAD and Graphics, 1997, 9(6): 513.

    Google Scholar 

  27. Wu, W. T., Basical principles of mechanical geometry theorem proving, New York: Springer-Verlag, 1994.

    Google Scholar 

  28. Chen, L. P., Tu, C., Luo, H., and Zhou, J., A New parametric oriented drawing technique, Ruanjian Xue-Bao (in Chinese), 1996, 7(7): 394.

    Google Scholar 

  29. Wu, W. T., A mechanization method of geometry and its applications I. Distances, areas, and volumes, J. Sys. Sci. and Math. Scis., 1986, 6: 204.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Systems Science, AMSS, Chinese Academy of Sciences, 100080, Beijing, China

    Gao Xiaoshan, Huang Leidong & Jiang Kun

Authors
  1. Gao Xiaoshan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huang Leidong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiang Kun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gao Xiaoshan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gao, X., Huang, L. & Jiang, K. Geometric constraint solving with geometric transformation. Sci China Ser F 44, 50–59 (2001). https://doi.org/10.1007/BF02713939

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02713939

Keywords

Search

Navigation