Skip to main content
SpringerLink
Log in
Book cover

Proceedings of the 19th International Meshing Roundtable pp 23–34Cite as

Q-TRAN: A New Approach to Transform Triangular Meshes into Quadrilateral Meshes Locally

  • Conference paper

Summary

Q-Tran is a new indirect algorithmto transform triangular tessellation of bounded three-dimensional surfaces into all-quadrilateralmeshes. The proposed method is simple, fast and produces quadrilaterals with provablygood quality and hence it does not require a smoothing post-processing step. The method is capable of identifying and recovering structured regions in the input tessellation. The number of generated quadrilaterals tends to be almost the same as the number of the triangles in the input tessellation. Q-Tran preserves the vertices of the input tessellation and hence the geometry is preserved even for highly curved surfaces. Several examples of Q-Tran are presented to demonstrate the efficiency of the proposed method.

This is a preview of subscription content, 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   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover 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. Chew, L.P.: Constrained Delaunay triangulations. Algorithmica 4, 97–108 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  2. Dey, T.K., Bajaj, C.L., Sugihara, K.: On good triangulations in three dimensions. Int. J. Comput. Geom. & App. 2, 75–95 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  3. Miller, G.L., Talmor, D., Teng, S.-H., Walkington, N.: A Delaunay based numerical method for three dimensions: generation, formulation, and partition. In: 27th Annual ACM Symposium on the Theory of Computing, pp. 683–692 (1995)

    Google Scholar 

  4. Cohen-Steiner, D., Colin, E., Yvinec, M.: Conforming Delaunay triangulations in 3D. In: 18th Annual Symposium on Computational Geometry, pp. 199–208 (2002)

    Google Scholar 

  5. George, P.L., Seveno, E.: The advancing front mesh generation method revisited. Int. J. Numer. Meth. Engng. 37, 3605–3619 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  6. Mavriplis, D.J.: An advancing front Delaunay triangulation algorithm designed for robustness. J. of Comput. Phys. 117, 90–101 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  7. Lohner, R.: Extensions and improvements of the advancing front grid generation technique. Commun. Numer. Meth. Engng. 12, 683–702 (1996)

    Article  MathSciNet  Google Scholar 

  8. Lau, T.S., Lo, S.H.: Finite element mesh generation over analytical surfaces. Comput. Struct. 59, 301–309 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  9. Heighwayl, E.A.: A mesh generator for automatically subdividing irregular polygons into quadrilaterals. IEEE Transactions on Magnetics Mag-19, 2535–2538 (1983)

    Article  Google Scholar 

  10. Itoh, T., Inoue, K., Yamada, A., Shimada, K., Furuhata, T.: Automated conversion of 2D triangular Mesh into quadrilateral mesh with directionality control. In: 7th International Meshing Roundtable, pp. 77–86 (1998)

    Google Scholar 

  11. Lo, S.H.: Generating quadrilateral elements on plane and over curved surfaces. Comput. Struct. 31, 421–426 (1989)

    Article  Google Scholar 

  12. Johnston, B.P., Sullivan Jr., J.M., Kwasnik, A.: Automatic conversion of triangular finite element meshes to quadrilateral elements. Int. J. Numer. Meth. Engng. 31, 67–84 (1991)

    Article  MATH  Google Scholar 

  13. Lee, C.K., Lo, S.H.: A new scheme for the generation of a graded quadrilateral mesh. Comput. Struct. 52, 847–857 (1994)

    Article  MATH  Google Scholar 

  14. Velho, L.: Quadrilateral meshing using 4-8 clustering. In: CILANCE 2000, pp. 61–64 (2000)

    Google Scholar 

  15. Owen, S.J., et al.: Q-Morph: An indirect approach to advancing front quad meshing. Int. J. Numer. Meth. Engng. 44, 1317–1340 (1999)

    Article  MATH  Google Scholar 

  16. Blacker, T.D., Stephenson, M.B.: Paving: A new approach to automated quadrilateral mesh generation. Int. J. Numer. Meth. Engng. 32, 811–847 (1991)

    Article  MATH  Google Scholar 

  17. Miyazaki, R., Harada, K.: Transformation of a closed 3D triangular mesh to a quadrilateral mesh based on feature edges. Int. J. Comput. Sci. Network Security. 9, 30–36 (2009)

    Google Scholar 

  18. Baehmann, P.L., Wittchen, S.L., Shephard, M.S., Grice, K.R., Yerry, M.A.: Robust geometrically based, automatic two-dimensional mesh generation. Int. J. Numer. Meth. Engng. 24, 1043–1078 (1987)

    Article  MATH  Google Scholar 

  19. Tam, T.K.H., Armstrong, C.G.: 2D finite element mesh generation by medial axis subdivision. Adv. Engng. Software 13, 313–324 (1991)

    Article  MATH  Google Scholar 

  20. Joe, B.: Quadrilateral mesh generation in polygonal regions. Comput. Aid. Des. 27(3), 209–222 (1991)

    Article  Google Scholar 

  21. Zhu, J.Z., Zienkiewicz, O.C., Hinton, E., Wu, J.: A new approach to the development of automatic quadrilateral mesh generation. Int. J. Numer. Meth. Engng. 32, 849–866 (1991)

    Article  MATH  Google Scholar 

  22. White, D.R., Kinney, P.: Redesign of the paving algorithm: Robustness enhancements through element by element meshing. In: 6th International Meshing Roundtable, pp. 323–335 (1997)

    Google Scholar 

  23. Zhang, Y., Bajaj, C.: Adaptive and quality quadrilateral/hexahedral meshing from volumetric Data. Comput. Meth. in Appl. Mech. Engng. 195, 942–960 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  24. Bern, M., Eppstein, D.: Quadrilateral meshing by circle packing. Int. J. Comp. Geom. & Appl. 10(4), 347–360 (2000)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Org. 1414, Applied Math and Applications, Sandia National Laboratories,  

    Mohamed S. Ebeida

  2. Code 7130, Physical Acoustics Branch, Naval Research Laboratories,  

    Kaan Karamete, Eric Mestreau & Saikat Dey

Authors
  1. Mohamed S. Ebeida
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kaan Karamete
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eric Mestreau
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Saikat Dey
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Pennsylvania State University, 343J IST Building, 16802, University Park, PA, USA

    Suzanne Shontz

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ebeida, M.S., Karamete, K., Mestreau, E., Dey, S. (2010). Q-TRAN: A New Approach to Transform Triangular Meshes into Quadrilateral Meshes Locally. In: Shontz, S. (eds) Proceedings of the 19th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15414-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-15414-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15413-3

  • Online ISBN: 978-3-642-15414-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation