Skip to main content

On the Decidability of Tracing Problems in Dynamic Geometry

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3763))

Abstract

We investigate two important problems arising in Dynamic Geometry, the Tracing Problem and the Reachability Problem. After presenting purely algebraic algorithms for these problems, we give an alternative approach.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allgower, E.L., Georg, K.: Numerical Continuation Methods. Springer, Heidelberg (1990)

    MATH  Google Scholar 

  2. Basu, S., Pollack, R., Roy, M.-F.: Algorithms in Real Algebraic Geometry. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  3. de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry, vol. 1997. Springer, Heidelberg (2000)

    MATH  Google Scholar 

  4. Blum, L., Cucker, F., Shub, M., Smale, S.: Complexity and Real Computation. Springer, New York (1998)

    Google Scholar 

  5. Ebeling, W.: Funktionentheorie, Differentialtopologie und Singularitäten, Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden (2001)

    Google Scholar 

  6. Forster, O.: Riemannsche Flächen. Springer, Heidelberg (1977)

    MATH  Google Scholar 

  7. Kortenkamp, U.: Foundations of Dynamic Geometry, PhD-thesis, ETH Zürich (1999)

    Google Scholar 

  8. Kortenkamp, U., Richter-Gebert, J.: Decision Complexity in Dynamic Geometry. In: Richter-Gebert, J., Wang, D. (eds.) ADG 2000. LNCS (LNAI), vol. 2061, pp. 193–199. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. Preparata, F.P., Shamos, M.I.: Computational Geometry. Springer, New York (1985)

    Google Scholar 

  10. Richter-Gebert, J., Kortenkamp, U.: Complexity Issues in Dynamic Geometry. In: Proceedings of the Smale Fest 2000 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Denner-Broser, B. (2006). On the Decidability of Tracing Problems in Dynamic Geometry. In: Hong, H., Wang, D. (eds) Automated Deduction in Geometry. ADG 2004. Lecture Notes in Computer Science(), vol 3763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11615798_8

Download citation

  • DOI: https://doi.org/10.1007/11615798_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31332-8

  • Online ISBN: 978-3-540-31363-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics