Skip to main content

Periodic Planar Straight-Frame Drawings with Polynomial Resolution

  • Conference paper
LATIN 2014: Theoretical Informatics (LATIN 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8392))

Included in the following conference series:

Abstract

We present a new algorithm to compute periodic (planar) straight-line drawings of toroidal graphs. Our algorithm is the first to achieve two important aesthetic criteria: the drawing fits in a straight rectangular frame, and the grid area is polynomial, precisely the grid size is O(n 4×n 4). This solves one of the main open problems in a recent paper by Duncan et al. [3].

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

Access this chapter

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. Chambers, E., Eppstein, D., Goodrich, M., Loffler, M.: Drawing Graphs in the Plane with a Prescribed Outer Face and Polynomial Area. JGAA 16(2), 243–259 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  2. Castelli Aleardi, L., Devillers, O., Fusy, É.: Canonical Ordering for Triangulations on the Cylinder, with Applications to Periodic Straight-Line Drawings. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 376–387. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  3. Duncan, C., Goodrich, M., Kobourov, S.: Planar drawings of higher-genus graphs. Journal of Graph Algorithms and Applications 15, 13–32 (2011)

    Article  MathSciNet  Google Scholar 

  4. de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10(1), 41–51 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  5. Gonçalves, D., Lévêque, B.: Toroidal maps: Schnyder woods, orthogonal surfaces and straight-line representation. arXiv:1202.0911 (2012)

    Google Scholar 

  6. Gotsman, C., Gu, X., Sheffer, A.: Fundamentals of spherical parameterization for 3D meshes. ACM Trans. on Graphics 22(3), 358–363 (2003)

    Article  Google Scholar 

  7. Grimm, C.: Parameterization using Manifolds. Int. J. of Shape Modeling 10(1), 51–82 (2004)

    Article  MATH  Google Scholar 

  8. Kant, G.: Drawing planar graphs using the canonical ordering. Algorithmica 16(1), 4–32 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  9. Kocay, W., Neilson, D., Szypowski, R.: Drawing graphs on the torus. Ars Combinatoria 59, 259–277 (2001)

    MATH  MathSciNet  Google Scholar 

  10. Mohar, B.: Straight-line representations of maps on the torus and other flat surfaces. Discrete Mathematics 15, 173–181 (1996)

    Article  MathSciNet  Google Scholar 

  11. Schnyder, W.: Embedding planar graphs on the grid. In: SODA, pp. 138–148 (1990)

    Google Scholar 

  12. Tutte, W.: How to draw a graph. Proc. of London Math. Soc. 13, 734–767 (1963)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Castelli Aleardi, L., Fusy, É., Kostrygin, A. (2014). Periodic Planar Straight-Frame Drawings with Polynomial Resolution. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-54423-1_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54422-4

  • Online ISBN: 978-3-642-54423-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics