Hierarchical Delaunay Triangulation for Meshing

  • Shu Ye
  • Karen Daniels
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6630)


This paper discusses an elliptical pad structure and its polygonal approximation. The elliptical pad is a part of via model structures, which are important and critical components on today’s multilayered Printed Circuit Board (PCB) and electrical packaging. To explore meshing characterization of the elliptical pad helps mesh generation over 3D structures for electromagnetic modeling (EM) and simulation on PCB and electrical packaging. Because elliptical structures are often key PCB features, we introduce a hierarchical mesh construct and show that it has several useful Delaunay quality characteristics. Then we show experimentally that Computational Geometry Algorithm Library’s (CGAL) meshing of an elliptical structure at different resolution levels and with various aspect ratios produces patterns similar to our construct. In particular, our experiment also shows that the result of meshing is not only constrained Delaunay triangulation but also Delaunay triangulation.


constrained Delaunay triangulation mesh generation CGAL 


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  1. 1.
    Botsch, M., et al.: ACM SIGGRAPH 2007 course 23: Geometric modeling based on polygonal meshes. Association for Computing Machinery (2007)Google Scholar
  2. 2.
    CGAL User and Reference Manual,
  3. 3.
    Edelsbrunner, H.: Geometry and Topology for Mesh Generation. Cambridge University Press, Cambridge (2001)CrossRefzbMATHGoogle Scholar
  4. 4.
    Frey, P.J., George, P.-L.: Mesh Generation: application to finite elements. Oxford and HERMES Science Publishing, Paris (2000)zbMATHGoogle Scholar
  5. 5.
    Goodman, J.E., O’Rourke, J. (eds.): Handbook of Discrete and Computational Geometry, 2nd edn. CRC Press, Boca Raton (2004)zbMATHGoogle Scholar
  6. 6.
    Hall, S.H., Hall, G.W., McCall, J.A.: High-Speed Digital System Design: A Handbook of Interconnect Theory and Design Practices. John Wiley & Sons, Inc./A Wiley-Interscience Publication (2000)Google Scholar
  7. 7.
    Holzbecher, E., Si, H.: Accuracy Tests for COMSOL – and Delaunay Meshes,
  8. 8.
    Hwang, C.-T., et al.: Partially Prism-Gridded FDTD Analysis for Layered Structures of Transversely Curved Boundary. IEEE Transactions of Microwave Theory and Techniques 48(3), 339–346 (2000)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lee, S.: Efficient Finite Element Electromagnetic Analysis for High-Frequency/High Speed Circuits and Multiconductor Transmission Lines. Doctoral Dissertation, University of Illinois at Urbana-Champaign, Urbana Illinois (2009)Google Scholar
  10. 10.
    Ramahi, O.M.: Analysis of Conventional and Novel Delay Lines: A Numerical Study. Journal of Applied Computational Electromagnetic Society 18(3), 181–190 (2003)Google Scholar
  11. 11.
    Rodger, D., et al.: Finite Element Modelling of Thin Skin Depth Problems using Magnetic Vector Potential. IEEE Transactions on Magnetics 33(2), 1299–1301 (1997)CrossRefGoogle Scholar
  12. 12.
    Thompson, J.F., Soni, B.K., Weatherill, N.P. (eds.): Handbook of Grid Generation. CRC Press, Boca Raton (1999)zbMATHGoogle Scholar
  13. 13.
    Tsukerman, I.: A General Accuracy Criterion for Finite Element Approximation. IEEE Transactions on Magnetics 34(5), 1–4 (1998)CrossRefGoogle Scholar
  14. 14.
    Tummala, R.R.: SOP: What Is It and Why? A New Microsystem-Integration Technology Paradigm-Moore’s Law for System Integration of Miniaturized Covergent Systems of the New Decade. IEEE Transactions on Advanced Packaging 27(2), 241–249 (2004)CrossRefGoogle Scholar
  15. 15.
    Ye, S., Daniels, K.: Triangle-based Prism Mesh Generation for Electromagnetic Simulations. In: Research Note for the 17th International Meshing Roundtable, Pittsburgh, Pennsylvania, October 12-15 (2008)Google Scholar
  16. 16.
    Ye, S., Daniels, K.: Triangle-based Prism Mesh Generation on Interconnect Models for Electromagnetic Simulations. In: 19th Annual Fall Workshop on Computational Geometry (sponsored by NSF), Tufts University, Medford, MA, November 13-14 (2009)Google Scholar
  17. 17.
    Yvinec, M.: Private communication regarding CGAL’s 2D constrained Delaunay algorithm (November 2009)Google Scholar
  18. 18.
    Miller, G., Phillips, T., Sheehy, D.: Linear-Sized Meshes. In: Canadian Conference on Computational Geometry, Montreal, Quebec, August 13-15 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Shu Ye
    • 1
  • Karen Daniels
    • 1
  1. 1.Department of Computer ScienceUniversity of MassachusettsLowellUSA

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