Skip to main content
SpringerLink
Log in

Curved Edge Routing

  • Conference paper
  • First Online:
Fundamentals of Computation Theory (FCT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2138))

Included in the following conference series:

Abstract

We consider the problem of drawing a graph where edges are represented by smooth curves between the associated nodes. Previously curved edges were drawn as splines defined by carefully calculated control points. We present a completely different approach where finding an edge is reduced to solving a differential equation. This approach allows to represent the graph drawing aesthetics directly, even the most complex ones denoting the dependencies among the paths.

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. G. Di Battista, P. Eades, R. Tamassia, I. G. Tollis. Algorithms for drawing graphs: an annotated bibliography, Computational Geometry: Theory and Applications, vol. 4, no. 5, 1994, pp. 235–282.

    MATH  MathSciNet  Google Scholar 

  2. G. Di Battista, P. Eades, R. Tamassia, I. G. Tollis. Graph Drawing. Prentice Hall, 1999.

    Google Scholar 

  3. A. Bicchi, G. Casalino, C. Santilli. Planning Shortest Bounded-Curvature Paths for a Class of Nonholonomic Vehicles among Obstacles. Proc. IEEE Int. Conf. on Robotics and Automation, pp.1349–1354, 1995.

    Google Scholar 

  4. C. C. Cheng, C. A. Duncan, M. T. Goodrich, S. G. Koburov. Drawing Planar Graphs with Circular Arcs. Symp. on Graph Drawing GD’99, Lecture Notes in Computer Science, vol.1731, pp.117–126, 1999.

    Chapter  Google Scholar 

  5. T. H. Cormen, C. E. Leiserson, R. L. Rivest, Introduction to Algorithms. MIT Press. Cambridge, Massachusetts. xvii, 1990.

    Google Scholar 

  6. D.P. Dobkin, E.R. Gansner, E. Koutsofios, Stephen C. North. Implementing a General-Purpose Edge Router. Symp. on Graph Drawing GD’97, Lecture Notes in Computer Science, vol.1353, pp.262–271, 1998.

    Chapter  Google Scholar 

  7. J. D. Foley, A. vanDam, S. K. Feiner, J. F. Huges, Computer Graphics: principles and practice, Addison-Wesley, 1993.

    Google Scholar 

  8. E. R. Gansner, E. Koutsofios, Stephen C. North, Kiem-Phong Vo. A Technique for Drawing Directed Graphs. TSE 19(3), pp.214–230 (1993)

    Google Scholar 

  9. M. T. Goodrich, C. G. Wagner. A Framework for Drawing Planar Graphs with Curves and Polylines. Symp. on Graph Drawing GD’98, Lecture Notes in Computer Science, vol.1547, pp.153–166, 1998.

    Chapter  Google Scholar 

  10. J.C. Latombe. Robot Motion Planning. Kluwer Academic Publishers, Boston, 1991.

    Google Scholar 

  11. T. Lengauer. Combinatorial Algorithms for Integrated Circuit Layout. John Wiley & Sons, 1990.

    Google Scholar 

  12. H. Lerchs, I. G. Grossmann. Optimum Design of Open-Pit Mines. Transactions, C.I.M., Volume LXVIII, 1965, pp.17–24.

    Google Scholar 

  13. K. Miriyala, S. W. Hornick, R. Tamassia. An Incremental Approach to Aesthetic Graph Layout, Proc. International Workshop on Computer-Aided Software Engineering, 1993.

    Google Scholar 

  14. G. Sander. Graph Layout through the VCG Tool. Technical Report A03-94, Universität des Saarlandes, FB 14 Informatik, 1994.

    Google Scholar 

  15. J.A. Sethian. Level Set Methods. Cambridge University Press, 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, University of Latvia, Raina blvd. 29, LV-1459, Riga, Latvia

    Kārlis Freivalds

Authors
  1. Kārlis Freivalds
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Latvia, Raiņa bulvaris 29, LV-1459, Riga, Latvia

    Rūsiņš Freivalds

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Freivalds, K. (2001). Curved Edge Routing. In: Freivalds, R. (eds) Fundamentals of Computation Theory. FCT 2001. Lecture Notes in Computer Science, vol 2138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44669-9_14

Download citation

  • DOI: https://doi.org/10.1007/3-540-44669-9_14

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42487-1

  • Online ISBN: 978-3-540-44669-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation