Skip to main content

Constrained Triangulation of 2D Shapes

  • 2177 Accesses

Part of the Advances in Intelligent Systems and Computing book series (AISC,volume 448)

Abstract

Algorithms for triangulating two dimensional shapes have been used as sub-problems in many application areas that include finite element analysis, geographic information systems, and geometric compression. We consider a constrained version of triangulation problem in which the objective is to increase the proportion of even degree vertices. We present an effective approach for generating triangulated polygons with increased number of even degree vertices. The proposed approach is based on the convex decomposition of polygon followed by ‘diagonal flipping’ operation.

Keywords

  • Constrained triangulation
  • Mesh generation
  • Polygon decomposition

This is a preview of subscription content, access via your institution.

Buying options

Chapter
EUR   29.95
Price includes VAT (Finland)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR   117.69
Price includes VAT (Finland)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR   164.99
Price includes VAT (Finland)
  • 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. Auer, T., Held, M.: Heuristics for the generation of random polygons. In: Fiala, F., Kranakis, E., Sack, J.-R. (eds.) Proceedings of the 8th Canadian Conference on Computational Geometry, Carleton University, Ottawa, Canada, August 12–15, 1996, pp. 38–43. Carleton University Press (1996)

    Google Scholar 

  2. de Berg, M., Cheong, O., van Kreveld, M., Overmars, M.: Computational Geometry: Theory and Applications, 3rd edn. Springer (2008)

    Google Scholar 

  3. Chazelle, B.: Triangulating a simple polygon in linear time. Discrete Comput. Geom. 6, 485–524 (1991)

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Fortune, S.: A sweepline algorithm for voronoi diagrams. Algorithmica 2, 153–174 (1987)

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Gyawali, R.: MS Thesis, Department of Computer Science, University of Nevada, Las Vegas, August 2012

    Google Scholar 

  6. David, J.F., George, P.-L.: Mesh-Generation: Application to Finite Elements, 2nd edn. Wilet (2010)

    Google Scholar 

  7. Guibas, L.J., Knuth, D.E., Sharir, M.: Randomized incremental construction of delaunay and voronoi diagrams. Algorithmica 7(4), 381–413 (1992)

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Hertel, S., Mehlhorn, K.: Fast triangulation of simple polygons. In: Proceedings of the 1983 International FCT-Conference on Fundamentals of Computation Theory, pp. 207–218. Springer-Verlag, London (1983)

    Google Scholar 

  9. Hurtado, F., Noy, M., Urrutia, J.: Flipping edges in triangulations. In: Proceedings of the Twelfth Annual Symposium on Computational Geometry, SCG 1996, pp. 214–223. ACM, New York (1996)

    Google Scholar 

  10. Lawson, C.L.: Software for c1 surface interpolation. Mathematical Software III, pp. 161–194 (1977)

    Google Scholar 

  11. Meisters, G.H.: Polygons have ears. American Mathematical Monthly 82, 648651 (1975)

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. O’Rourke, J.: Art gallery theorems and algorithms. Oxford University Press Inc., New York (1987)

    MATH  Google Scholar 

  13. O’Rourke, J.: Computational Geometry in C, 2nd edn. Cambridge University Press (1998)

    Google Scholar 

  14. Osherovich, E., Bruckstein, A.M.: All triangulations are reachable via sequences of edge-flips: an elementary proof. Comput. Aided Geom. Des. 25(3), 157–161 (2008)

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Urrutia, J., Pelez, C., Ramrez-Viguer, A.: Triangulations with many points of even degree. In: Proceedings of the 22nd Annual Canadian Conference on Computational Geometry, Winnipeg, Manitoba, Canada, August 9–11, 2010, pp. 103–106 (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Laxmi P. Gewali .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Gewali, L.P., Gyawali, R. (2016). Constrained Triangulation of 2D Shapes. In: Latifi, S. (eds) Information Technology: New Generations. Advances in Intelligent Systems and Computing, vol 448. Springer, Cham. https://doi.org/10.1007/978-3-319-32467-8_104

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-32467-8_104

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32466-1

  • Online ISBN: 978-3-319-32467-8

  • eBook Packages: EngineeringEngineering (R0)