Skip to main content
Springer Nature Link
Log in

Solving Dynamic Geometric Constraints Involving Inequalities

  • Conference paper
Artificial Intelligence and Symbolic Computation (AISC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4120))

  • 489 Accesses

Abstract

This paper presents a specialized method for solving dynamic geometric constraints involving equalities and inequalities. The method works by decomposing the system of constraints into finitely many explicit solution representations in terms of parameters with radicals using triangular decomposition and real quantifier elimination. For any given values of the parameters, if they verify some set of computed relations, the values of the dependent variables may be easily computed by direct evaluation of the corresponding explicit expressions. The effectiveness of our method and its experimental implementation is illustrated by some examples of diagram generation.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Brown, C.W., Hong, H.: QEPCAD — Quantifier elimination by partial cylindrical algebraic decomposition (2004), http://www.cs.usna.edu/~qepcad/B/QEPCAD.html

  2. Collins, G.E., Hong, H.: Partial cylindrical algebraic decomposition for quantifier elimination. J. Symb. Comput. 12, 299–328 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dolzmann, A., Sturm, T., Weispfenning, V.: A new approach for automatic theorem proving in real geometry. J. Automat. Reason. 21(3), 357–380 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. González-Vega, L.: A combinatorial algorithm solving some quantifier elimination problems. In: Caviness, B., Johnson, J. (eds.) Quantifier Elimination and Cylindrical Algebraic Decomposition, pp. 300–316. Springer, Wien (1996)

    Google Scholar 

  5. Hong, H.: Quantifier elimination for formulas constrained by quadratic equations via slope resultants. The Computer J. 36(5), 440–449 (1993)

    Google Scholar 

  6. Joan-Arinyo, R., Hoffmann, C.M.: A brief on constraint solving (2005), http://www.cs.purdue.edu/homes/cmh/distribution/papers/Constraints/ThailandFull.pdf

  7. Kim, D., Kim, D.-S., Sugihara, K.: Apollonius tenth problem via radius adjustment and Möbius transformations. Computer-Aided Design 38(1), 14–21 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lewis, R.H., Bridgett, S.: Conic tangency equations and Apollonius problems in biochemistry and pharmacology. Math. Comput. Simul. 61(2), 101–114 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wang, D.: Elimination Methods. Springer, Wien (2001)

    MATH  Google Scholar 

  10. Wang, D.: Automated generation of diagrams with Maple and Java. In: Joswig, M., Takayama, N. (eds.) Algebra, Geometry, and Software Systems, pp. 277–287. Springer, Heidelberg (2003)

    Google Scholar 

  11. Wang, D.: GEOTHER 1.1: Handling and proving geometric theorems automatically. In: Winkler, F. (ed.) ADG 2002. LNCS (LNAI), vol. 2930, pp. 194–215. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Wang, D.: Elimination Practice: Software Tools and Applications. Imperial College Press, London (2004)

    Book  MATH  Google Scholar 

  13. Weispfenning, V.: Quantifier elimination for real algebra — the cubic case. In: Proceedings of the 1994 International Symposium on Symbolic and Algebraic Computation, Oxford, UK, July 20–22, 1994, pp. 258–263. ACM Press, New York (1994)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC, 27695, USA

    Hoon Hong

  2. LMIB – School of Science, Beihang University, Beijing, 100083, China

    Liyun Li & Dongming Wang

  3. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Tielin Liang

  4. Laboratoire d’Informatique de Paris 6, Université Pierre et Marie Curie – CNRS, 8 rue du Capitaine Scott, F-75015, Paris, France

    Dongming Wang

Authors
  1. Hoon Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liyun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tielin Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dongming Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Algorithmen und Kognitive Systeme, Universität Karlsruhe, 76128, Karlsruhe, Germany

    Jacques Calmet

  2. Department of Computer Science, University of Tsukuba, 305-8573, Tsukuba, Japan

    Tetsuo Ida

  3. LMIB – SKLSDE – School of Science, Beihang University, 100083, Beijing, China

    Dongming Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hong, H., Li, L., Liang, T., Wang, D. (2006). Solving Dynamic Geometric Constraints Involving Inequalities. In: Calmet, J., Ida, T., Wang, D. (eds) Artificial Intelligence and Symbolic Computation. AISC 2006. Lecture Notes in Computer Science(), vol 4120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11856290_17

Download citation

  • DOI: https://doi.org/10.1007/11856290_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-39728-1

  • Online ISBN: 978-3-540-39730-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics