Skip to main content
Log in

All-hexahedral mesh generation via inside-out advancing front based on harmonic fields

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

The generation of hexahedral meshes is an open problem that has undergone significant research. This paper deals with a novel inside-out advancing front method to generate unstructured all-hexahedral meshes for given volumes. Two orthogonal harmonic fields, principal and radial harmonic fields, are generated to guide the inside-out advancing front process based on a few user interactions. Starting from an initial hexahedral mesh inside the given volume, we advance the boundary quadrilateral mesh along the streamlines of radial field and construct layers of hexahedral elements. To ensure high quality and uniform size of the hexahedral mesh, quadrilateral elements are decomposed in such a way that no non-hexahedral element is produced. For complex volume with branch structures, we segment the complex volume into simple sub-volumes that are suitable for our method. Experimental results show that our method generates high quality all-hexahedral meshes for the given volumes.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Alliez, P., Cohen-Steiner, D., Yvinec, M., Desbrun, M.: Variational tetrahedral meshing. ACM Trans. Graph. 24(3), 617–625 (2005)

    Article  Google Scholar 

  2. Du, Q., Wang, D.: Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations. Int. J. Numer. Methods Eng. 56(9), 1355–1373 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Shewchuk, J.R.: Tetrahedral mesh generation by Delaunay refinement. In: Proceedings of the 14th Annual ACM Symposium on Computational Geometry, pp. 86–95 (1998)

    Google Scholar 

  4. Cifuentes, A.O., Kalbag, A.: A performance study of tetrahedral and hexahedral elements in 3D element structural analysis. Finite Elem. Anal. Des. 12, 313–318 (1992)

    Article  Google Scholar 

  5. Benzley, S.E., Perry, E., Merkley, K.E., Clark, B.W., Sjaardema, G.D.: A comparison of all hexagonal and all tetrahedral finite element meshes for elastic and elasto-plastic analysis. In: Proceedings of the 4th International Meshing Roundtable, pp. 179–191 (1995)

    Google Scholar 

  6. Baker, T.J.: Mesh generation: art or science? Prog. Aerosp. Sci. 41, 29–63 (2005)

    Article  Google Scholar 

  7. Shepherd, J.F., Johnson, C.R.: Hexahedral mesh generation constraints. Eng. Comput. 24(3), 195–213 (2008)

    Article  Google Scholar 

  8. Owen, S.: A survey of unstructured mesh generation technology. In: Proceedings of International Meshing Roundtable, pp. 239–267 (1998)

    Google Scholar 

  9. Canann, S.A.: Plastering: A New Approach to Automated 3-d Hexahedral Mesh Generation. American Institute of Aeronautics and Astronics, Reston (1992)

    Google Scholar 

  10. Blacker, T.D., Meyers, R.J.: Seams and wedges in plastering: a 3D hexahedral mesh generation algorithm. Eng. Comput. 2, 83–93 (1993)

    Article  Google Scholar 

  11. Tautges, T.J., Blacker, T.D., Mitchell, S.A.: The whisker weaving algorithm: a connectivity-based method for constructing all-hexahedral finite element meshes. Int. J. Numer. Methods Eng. 39, 3327–3349 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  12. Staten, M.L., Kerr, R.A., Owen, S.J., Blacker, T.D., Stupazzini, M., Shimada, K.: Unconstrained plastering-hexahedral mesh generation via advancing-front geometry decomposition. Int. J. Numer. Methods Eng. 81, 135–171 (2010)

    MATH  Google Scholar 

  13. Schneiders, R.: A grid-based algorithm for the generation of hexahedral element meshes. Eng. Comput. 12, 168–177 (1996)

    Article  Google Scholar 

  14. Schneiders, R., Schindler, R., Weiler, F.: Octree based generation of hexahedral element meshes. In: 5th International Meshing Roundtable, pp. 205–215 (1996)

    Google Scholar 

  15. Maréchal, L.: Advances in octree-based all-hexahedral mesh generation handling sharp features. In: Proceedings of the 18th International Meshing Roundtable, pp. 65–84 (2009)

    Chapter  Google Scholar 

  16. Vyas, V., Shimada, K.: Tensor-guided hex-dominant mesh generation with targeted all-hex regions. In: Proceedings of the 18th International Meshing Roundtable, pp. 377–396 (2009)

    Chapter  Google Scholar 

  17. Kraevoy, V., Sheffer, A.: Cross-parameterization and compatible remeshing of 3D models. ACM Trans. Graph. 23(3), 861–869 (2004)

    Article  Google Scholar 

  18. Martin, T., Cohen, E., Kirby, R.M.: Volumetric parameterization and trivariate B-spline fitting using harmonic functions. Comput. Aided Geom. Des. 26, 648–664 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Nieser, M., Reitebuch, U., Polthier, K.: CUBECOVER—parameterization of 3D volumes. Comput. Graph. Forum 30(5), 1397–1406 (2011)

    Article  Google Scholar 

  20. Xia, J., He, Y., Yin, X., Han, S., Gu, X.: Direct-product volumetric parameterization of handlebodies via harmonic fields. In: Shape Modeling International Conference, pp. 3–12 (2010)

    Chapter  Google Scholar 

  21. Gregson, J., Sheffer, A., Zhang, E.: All-hex mesh generation via volumetric polycube deformation. Comput. Graph. Forum 30, 1407–1416 (2011)

    Article  Google Scholar 

  22. Shepherd, J.F., Johnson, C.R.: Hexahedral mesh generation for biomedical models in SCIRun. Eng. Comput. 25, 97–114 (2009)

    Article  Google Scholar 

  23. Lai, Y.K., Jin, M., Xie, X., He, Y., Palacios, J., Zhang, E., Hu, S.M., Gu, X.D.: Metric-driven rosy field design and remeshing. IEEE Trans. Vis. Comput. Graph. 16, 95–108 (2010)

    Article  Google Scholar 

  24. Lévy, B., Liu, Y.: Lp centroidal Voronoi tesselation and its applications. ACM Trans. Graph. 29(4) (2010). doi:10.1145/1833349.1778856

  25. Golovinskiy, A., Funkhouser, T.: Randomized cuts for 3D mesh analysis. ACM Trans. Graph. 27(5) (2008). doi:10.1145/1409060.1409098 (Proc. SIGGRAPH ASIA)

  26. Gelfand, N., Guibas, L.J.: Shape segmentation using local slippage analysis. In: SGP’04: Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 214–223 (2004)

    Chapter  Google Scholar 

  27. Attene, M., Falcidieno, B., Spagnuolo, M.: Hierarchical mesh segmentation based on fitting primitives. Vis. Comput. 22(3), 181–193 (2006)

    Article  Google Scholar 

  28. Lai, Y.K., Hu, S.M., Martin, R.R., Rosin, P.L.: Rapid and effective segmentation of 3D models using random walks. Comput. Aided Geom. Des. 26, 665–679 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. Katz, S., Leifman, G., Tal, A.: Mesh segmentation using feature point and core extraction. Vis. Comput. 21, 649–658 (2005)

    Article  Google Scholar 

  30. Attene, M., Katz, S., Mortara, M., Patane, G., Spagnuolo, M., Tal, A.: Mesh segmentation—a comparative study. In: SMI ’06: Proceedings of the IEEE International Conference on Shape Modeling and Applications, pp. 7–19 (2006)

    Chapter  Google Scholar 

  31. Shamir, A.: A survey on mesh segmentation techniques. Comput. Graph. Forum 27, 1539–1556 (2008)

    Article  MATH  Google Scholar 

  32. Chen, X., Golovinskiy, A., Funkhouser, T.: A benchmark for 3D mesh segmentation. ACM Trans. Graph. 28(3) (2009)

  33. Benhabiles, H., Vandeborre, J.P., Lavoué, G., Daoudi, M.: A comparative study of existing metrics for 3D-mesh segmentation evaluation. Vis. Comput. 26(12), 1451–1466 (2010)

    Article  Google Scholar 

  34. Si, H.: Tetgen: a quality tetrahedral mesh generator and three-dimensional Delaunay triangulator. Technical report 1.4, Weierstrass Institute for Applied Analysis and Stochastics (2006)

  35. Wang, Y., Gu, X., Yau, S.T.: Volumetric harmonic map. Commun. Inf. Syst. 3(3), 191–202 (2004)

    MathSciNet  Google Scholar 

  36. Liao, S.H., Tong, R.F., Dong, J.X.: Gradient field based inhomogeneous volumetric mesh deformation for maxillofacial surgery simulation. Comput. Graph. 33, 424–432 (2009)

    Article  Google Scholar 

  37. Knupp, P.M.: Algebraic mesh quality metrics for unstructured initial meshes. Finite Elem. Anal. Des. 39, 217–241 (2003)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

We thank all anonymous reviewers for their valuable comments. This research is supported by the National Basic Research Program (No. 2011CB302205) of China and the National Natural Science Foundation (Nos. 61170141 and 60873126) of China.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ruofeng Tong.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, M., Tong, R. All-hexahedral mesh generation via inside-out advancing front based on harmonic fields. Vis Comput 28, 839–847 (2012). https://doi.org/10.1007/s00371-012-0707-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-012-0707-y

Keywords

Navigation