Skip to main content
SpringerLink
Log in

A fast and practical method to pack spheres for mesh generation

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Sphere packing is an attractive way to generate high quality mesh. Several algorithms have been proposed in this topic, however these algorithms are not sufficiently fast for large scale problems. The paper presents an efficient sphere packing algorithm which is much faster and appears to be the most practical among all sphere packing methods presented so far for mesh generation. The algorithm packs spheres inside a domain using advancing front method. High efficiency has resulted from a concept of 4R measure, which localizes all the computations involved in the whole sphere packing process.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Liu, J.F.: Automatic triangulation of n-D domains. In: Proceedings of CAD/Graphics’91, pp. 238–241. Hangzhou, China (1991)

  2. Liu J.F.: Automatic mesh generation of 3D geometric models. Acta Mech. Sin. 19(3), 285–288 (2003)

    Article  Google Scholar 

  3. Shimada, K., Gossard, D.C.: Bubble mesh: Automated triangular meshing of non-manifold geometry by sphere packing. In: Proceedings of Solid Modeling’95, pp. 409–419. Salt Lake City, Utah, USA (1995)

  4. Shimada K., Yamada A., Itoh T.: Anisotropic triangulation of parametric surfaces via close packing of ellipsoids. Int. J. Comput. Geom. Appl. 10(4), 417–440 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Yamakawa S., Shimada K.: Anisotropic tetrahedral meshing via bubble packing and advancing front. Int. J. Num. Methods Eng. 57(13), 1923–1942 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Shimada K., Gossard D.C.: Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis. Comput. Aided Geom. Des. 15(3), 199–222 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Li X.Y., Teng S.H., Ungor A.: Biting: advancing front meets sphere packing. Int. J. Numer. Methods Eng. 49(1–2), 61–81 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Li, X.Y., Teng, S.H., Ungor, A.: Biting Spheres in 3D. In: Proceedings of 8th International Meshing Roundtable, pp. 85–95. South Lake Tahoe, CA, USA (1999)

  9. Lo S.H., Wang W.X.: Generation of finite element mesh with variable size over an unbounded 2D domain. Comput. Methods Appl. Mech. Eng. 194, 4668–4684 (2005)

    Article  MATH  Google Scholar 

  10. Lo S.H., Wang W.X.: Generation of tetrahedral mesh of variable element size by sphere packing over an unbounded 3D domain. Comput. Methods Appl. Mech. Eng. 194, 5002–5018 (2005)

    Article  MATH  Google Scholar 

  11. Wang W.X., Ming C.Y., Lo S.H.: Generation of triangular mesh with specified size by circle packing. Adv. Eng. Softw. 38(2), 133–142 (2007)

    Article  Google Scholar 

  12. Bern M., Mitchell S., Ruppert J.: Linear-size nonobtuse triangulation of polygons. Discr. Computat. Geom. 14(4), 411–428 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  13. Eppstein D.: Faster spheres packing with application to nonobtuse triangulation. Int. J. Comput. Geom. Appl. 7(5), 485–491 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  14. Bern M., Eppstein D.: Quadrilateral meshing by sphere packing. Int. J. Comput. Geom. Appl. 10(4), 347–360 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kim J.H., Kim H.G., Lee B.C., Im S.: Adaptive mesh generation by bubble packing method. Struct. Eng. Mech. 15(1), 135–149 (2003)

    Google Scholar 

  16. Chung S.W., Kim S.J.: A remeshing algorithm based on bubble packing method and its application to large deformation problems. Finite Elem. Anal. Des. 39(4), 301–324 (2003)

    Article  MATH  Google Scholar 

  17. Feng Y.T., Han K., Owen D.R.J.: Filling domains with disks: an advancing front approach. Int. J. Num. Methods Eng. 56(5), 699–713 (2003)

    Article  MATH  Google Scholar 

  18. Horn W.P., Taylor D.L.: A theorem to determine the spatial containment of a point in a planar polygon. Comput. Vis. Graph. Image Process. 45, 106–116 (1989)

    Article  Google Scholar 

  19. Ollivier-Gooch C., Boivin C.: Guaranteed-quality simplical mesh generation with cell size and grading control. Eng. Comput. 17, 269–286 (2001)

    Article  MATH  Google Scholar 

  20. Quadros W.R., Shimada K., Owen S.J.: Skeleton-based computational method for the generation of a 3D finite element mesh sizing function. Eng. Comput. 20, 249–264 (2004)

    Article  Google Scholar 

  21. Liu J.F., Sun S.L., Wang D.C.: Optimal tetrahedralization for small polyhedron: a new local transformation strategy for 3D mesh generation and mesh improvement. CMES: Comput. Model. Eng. Sci. 14(1), 31–43 (2006)

    MathSciNet  Google Scholar 

  22. Liu, J.F., Sun, S.L.: Small polyhedron re-connection: A new way to eliminate poorly-shaped tetrahedra. In: Proceedings of the 15th International Meshing Roundtable, pp. 85–95. South Lake Tahoe, CA, USA (1999)

  23. Lo S.H.: Optimization of tetrahedral meshes based on element shape measures. Comput. Struct. 63(5), 951–961 (1997)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LTCS, College of Engineering, Peking University, Beijing, 100871, China

    Jianfei Liu, Shuixiang Li & Yongqiang Chen

Authors
  1. Jianfei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shuixiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yongqiang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shuixiang Li.

Additional information

The project supported by the National Natural Science Foundation of China (10602002 and 10772005).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, J., Li, S. & Chen, Y. A fast and practical method to pack spheres for mesh generation. Acta Mech Sin 24, 439–447 (2008). https://doi.org/10.1007/s10409-008-0165-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-008-0165-y

Keywords

Search

Navigation