Skip to main content
SpringerLink
Log in

HexDom: Polycube-Based Hexahedral-Dominant Mesh Generation

  • Chapter
  • First Online:
Mesh Generation and Adaptation

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 30))

Abstract

In this paper, we extend our earlier polycube-based all-hexahedral mesh generation method to hexahedral-dominant mesh generation, and present the HexDom software package. Given the boundary representation of a solid model, HexDom creates a hex-dominant mesh by using a semi-automated polycube-based mesh generation method. The resulting hexahedral dominant mesh includes hexahedra, tetrahedra, and triangular prisms. By adding non-hexahedral elements, we are able to generate better quality hexahedral elements than in all-hexahedral meshes. We explain the underlying algorithms in four modules including segmentation, polycube construction, hex-dominant mesh generation and quality improvement, and use a rockerarm model to explain how to run the software. We also apply our software to a number of other complex models to test their robustness. The software package and all tested models are available in github (https://github.com/CMU-CBML/HexDom).

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

Access this chapter

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 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
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

Institutional subscriptions

References

  1. Ahrens, J., Geveci, B., Law, C.: Paraview: an end-user tool for large data visualization. Visualization Handbook, vol. 717 (2005)

    Google Scholar 

  2. Blacker, T.D., Stephenson, M.B.: Paving: a new approach to automated quadrilateral mesh generation. Int. J. Numer. Methods Eng. 32(4), 811–847 (1991)

    Article  MATH  Google Scholar 

  3. Corporation, L.S.T.: Ls-dyna keyword user’s manual (2007)

    Google Scholar 

  4. Delaunay, B.N.: Sur la sphere vide. Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskikh I Estestvennykh Nauk 7(793–800), 1–2 (1934)

    MATH  Google Scholar 

  5. Eck, M., DeRose, T., Duchamp, T., Hoppe, H., Lounsbery, M., Stuetzle, W.: Multiresolution analysis of arbitrary meshes. In: Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, pp. 173–182 (1995)

    Google Scholar 

  6. Floater, M.S.: Parametrization and smooth approximation of surface triangulations. Comput. Aided Geom. Design 14(3), 231–250 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Folwell, N., Mitchell, S.: Reliable whisker weaving via curve contraction. Eng. Comput. 15(3), 292–302 (1999)

    Article  MATH  Google Scholar 

  8. Frey, P.J., Borouchaki, H., George, P.L.: Delaunay tetrahedralization using an advancing-front approach. In: 5th International Meshing Roundtable, pp. 31–48. Citeseer (1996)

    Google Scholar 

  9. Gregson, J., Sheffer, A., Zhang, E.: All-Hex mesh generation via volumetric polycube deformation. Comput. Graph. Forum 30(5), 1407–1416 (2011)

    Article  Google Scholar 

  10. Guennebaud, G., Jacob, B.: Eigen v3 (2010). http://eigen.tuxfamily.org

  11. He, Y., Wang, H., Fu, C., Qin, H.: A divide-and-conquer approach for automatic polycube map construction. Comput. Graph. 33(3), 369–380 (2009)

    Article  Google Scholar 

  12. Hu, K., Zhang, Y., Liao, T.: Surface segmentation for polycube construction based on generalized centroidal Voronoi tessellation. Comput. Methods Appl. Mech. Eng. 316, 280–296 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hu, K., Zhang, Y.J.: Centroidal Voronoi tessellation based polycube construction for adaptive all-hexahedral mesh generation. Comput. Methods Appl. Mech. Eng. 305, 405–421 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hu, K., Zhang, Y.J., Xu, G.: CVT-based 3D image segmentation and quality improvement of tetrahedral/hexahedral meshes using anisotropic Giaquinta-Hildebrandt operator. Comput. Methods Biomech. Biomed. Eng. Imaging Vis. 6(3), 331–342 (2018)

    Article  Google Scholar 

  15. Khan, D., Plopski, A., Fujimoto, Y., Kanbara, M., Jabeen, G., Zhang, Y., Zhang, X., Kato, H.: Surface remeshing: a systematic literature review of methods and research directions. IEEE Trans. Vis. Comput. Graph. (2020). https://doi.org/10.1109/TVCG.2020.3016645

  16. Lai, Y., Liu, L., Zhang, Y.J., Chen, J., Fang, E., Lua, J.: Rhino 3D to Abaqus: a T-spline based isogeometric analysis software framework. In: Advances in Computational Fluid-Structure Interaction and Flow Simulation, pp. 271–281 (2016)

    Google Scholar 

  17. Lai, Y., Zhang, Y.J., Liu, L., Wei, X., Fang, E., Lua, J.: Integrating CAD with Abaqus: a practical isogeometric analysis software platform for industrial applications. Comput. Math. Appl. 74(7), 1648–1660 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  18. Li, A., Chai, X., Yang, G., Zhang, Y.J.: An isogeometric analysis computational platform for material transport simulation in complex neurite networks. Mol. Cell. Biomech. 16(2), 123 (2019)

    Article  Google Scholar 

  19. Liang, X., Zhang, Y.: An octree-based dual contouring method for triangular and tetrahedral mesh generation with guaranteed angle range. Eng. Comput. 30(2), 211–222 (2014)

    Article  Google Scholar 

  20. Lin, J., Jin, X., Fan, Z., Wang, C.: Automatic polycube-maps. In: Advances in Geometric Modeling and Processing. Lecture Notes in Computer Science, vol. 4975, pp. 3–16. Springer Berlin/Heidelberg (2008)

    Google Scholar 

  21. Liu, L., Zhang, Y., Hughes, T.J., Scott, M.A., Sederberg, T.W.: Volumetric T-spline construction using Boolean operations. Eng. Comput. 30(4), 425–439 (2014)

    Article  Google Scholar 

  22. Liu, L., Zhang, Y., Liu, Y., Wang, W.: Feature-preserving T-mesh construction using skeleton-based polycubes. Comput. Aided Design 58, 162–172 (2015)

    Article  Google Scholar 

  23. Lohner, R., Parikh, P.: Three-dimensional grid generation by the advancing front method. Int. J. Numer. Methods Fluids 8, 1135–1149 (1988)

    Article  MATH  Google Scholar 

  24. Meshkat, S., Talmor, D.: Generating a mixed mesh of hexahedra, pentahedra and tetrahedra from an underlying tetrahedral mesh. Int. J. Numer. Methods Eng. 49(1–2), 17–30 (2000)

    Article  MATH  Google Scholar 

  25. Meyers, R.J., Tautges, T.J., Tuchinsky, P.M.: The “hex-tet” hex-dominant meshing algorithm as implemented in cubit. In: International Meshing Roundtable, pp. 151–158. Citeseer (1998)

    Google Scholar 

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

    Article  Google Scholar 

  27. Owen, S.J.: A survey of unstructured mesh generation technology. In: International Meshing Roundtable, Dearborn, MI, vol. 194, pp. 4135–4195 (1998)

    Google Scholar 

  28. Owen, S.J., Saigal, S.: H-morph: An indirect approach to advancing front hex meshing. Int. J. Numer. Methods Eng. 49(1–2), 289–312 (2000)

    Article  MATH  Google Scholar 

  29. Pan, Q., Xu, G., Zhang, Y.: A unified method for hybrid subdivision surface design using geometric partial differential equations. In: A Special Issue of Solid and Physical Modeling 2013 in Computer Aided Design, vol. 46, pp. 110–119 (2014)

    Google Scholar 

  30. Price, M.A., Armstrong, C.G.: Hexahedral mesh generation by medial surface subdivision: part II. Solids with flat and concave edges. Int. J. Numer. Methods Eng. 40(1), 111–136 (1997)

    Article  Google Scholar 

  31. Price, M.A., Armstrong, C.G., Sabin, M.A.: Hexahedral mesh generation by medial surface subdivision: Part I. Solids with convex edges. Int. J. Numer. Methods Eng. 38(19), 3335–3359 (1995)

    Article  MATH  Google Scholar 

  32. Qian, J., Zhang, Y.: Automatic unstructured all-hexahedral mesh generation from B-Reps for non-manifold CAD assemblies. Eng. Comput. 28(4), 345–359 (2012)

    Article  Google Scholar 

  33. Qian, J., Zhang, Y., O’Connor, D.T., Greene, M.S., Liu, W.K.: Intersection-free tetrahedral meshing from volumetric images. Comput. Methods Biomech. Biomed. Eng. Imaging Vis. 1(2), 100–110 (2013)

    Article  Google Scholar 

  34. Qian, J., Zhang, Y., Wang, W., Lewis, A.C., Qidwai, M.A.S., Geltmacher, A.B.: Quality improvement of non-manifold hexahedral meshes for critical feature determination of microstructure materials. Int. J. Numer. Methods Eng. 82(11), 1406–1423 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  35. Schneiders, R.: A grid-based algorithm for the generation of hexahedral element meshes. Eng. Comput. 12(3–4), 168–177 (1996)

    Article  Google Scholar 

  36. Schneiders, R.: An algorithm for the generation of hexahedral element meshes based on an octree technique. In: 6th International Meshing Roundtable pp. 195–196 (1997)

    Google Scholar 

  37. Seveno, E., et al.: Towards an adaptive advancing front method. In: 6th International Meshing Roundtable, pp. 349–362 (1997)

    Google Scholar 

  38. Shephard, M.S., Georges, M.K.: Automatic three-dimensional mesh generation by the finite octree technique. Int. J. Numer. Methods Eng. 32(4), 709–749 (1991)

    Article  MATH  Google Scholar 

  39. Staten, M., Kerr, R., Owen, S., Blacker, T.: Unconstrained paving and plastering: progress update. Proceedings of 15th International Meshing Roundtable pp. 469–486 (2006)

    Google Scholar 

  40. Tarini, M., Hormann, K., Cignoni, P., Montani, C.: Polycube-maps. ACM Trans. Graph. 23(3), 853–860 (2004)

    Article  Google Scholar 

  41. Teng, S.H., Wong, C.W.: Unstructured mesh generation: theory, practice, and perspectives. Int. J. Comput. Geom. Appl. 10(3), 227–266 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  42. Wang, W., Zhang, Y., Liu, L., Hughes, T.J.R.: Trivariate solid T-spline construction from boundary triangulations with arbitrary genus topology. Comput. Aided Design 45(2), 351–360 (2013)

    Article  MathSciNet  Google Scholar 

  43. Wang, W., Zhang, Y., Scott, M.A., Hughes, T.J.R.: Converting an unstructured quadrilateral mesh to a standard T-spline surface. Comput. Mech. 48(4), 477–498 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  44. Wang, W., Zhang, Y., Xu, G., Hughes, T.J.R.: Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline. Comput. Mech. 50(1), 65–84 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  45. Wei, X., Zhang, Y., Hughes, T.J.R.: Truncated hierarchical tricubic C0 spline construction on unstructured hexahedral meshes for isogeometric analysis applications. Comput. Math. Appl. 74(9), 2203–2220 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  46. Wei, X., Zhang, Y.J., Toshniwal, D., Speleers, H., Li, X., Manni, C., Evans, J.A., Hughes, T.J.: Blended B-spline construction on unstructured quadrilateral and hexahedral meshes with optimal convergence rates in isogeometric analysis. Comput. Methods Appl. Mech. Eng. 341, 609–639 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  47. Xie, J., Xu, J., Dong, Z., Xu, G., Deng, C., Mourrain, B., Zhang, Y.J.: Interpolatory Catmull-Clark volumetric subdivision over unstructured hexahedral meshes for modeling and simulation applications. Comput. Aided Geom. Design 80, 101867 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  48. Xu, G., Ling, R., Zhang, Y.J., Xiao, Z., Ji, Z., Rabczuk, T.: Singularity structure simplification of hexahedral meshes via weighted ranking. Comput. Aided Design 130, 102946 (2021)

    Article  MathSciNet  Google Scholar 

  49. Yamakawa, S., Shimada, K.: Fully-automated hex-dominant mesh generation with directionality control via packing rectangular solid cells. Int. J. Numer. Methods Eng. 57(15), 2099–2129 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  50. Yu, Y., Liu, H., Qian, K., Yang, H., McGehee, M., Gu, J., Luo, D., Yao, L., Zhang, Y.J.: Material characterization and precise finite element analysis of fiber reinforced thermoplastic composites for 4D printing. Comput. Aided Design 122, 102817 (2020)

    Article  MathSciNet  Google Scholar 

  51. Yu, Y., Wei, X., Li, A., Liu, J., He, J., Zhang, Y.J.: HexGen and Hex2Spline: polycube-based hexahedral mesh generation and spline modeling for isogeometric analysis applications in LS-DYNA. In: Springer INdAM Series: Proceedings of INdAM Workshop “Geometric Challenges in Isogeometric Analysis.” (2021)

    Google Scholar 

  52. Yu, Y., Zhang, Y.J., Takizawa, K., Tezduyar, T.E., Sasaki, T.: Anatomically realistic lumen motion representation in patient-specific space–time isogeometric flow analysis of coronary arteries with time-dependent medical-image data. Comput. Mech. 65(2), 395–404 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  53. Zhang, Y.: Challenges and advances in image-based geometric modeling and mesh generation. In: Image-Based Geometric Modeling and Mesh Generation, pp. 1–10. Springer, Berlin (2013)

    Google Scholar 

  54. Zhang, Y.: Geometric Modeling and Mesh Generation from Scanned Images. Chapman and Hall/CRC (2016)

    Google Scholar 

  55. Zhang, Y., Bajaj, C.L.: Adaptive and quality quadrilateral/hexahedral meshing from volumetric data. Comput. Methods Appl. Mech. Eng. 195(9–12), 942–960 (2006)

    Article  MATH  Google Scholar 

  56. Zhang, Y., Bajaj, C.L., Sohn, B.S.: 3D finite element meshing from imaging data. Comput. Methods Appl. Mech. Eng. 194(48–49), 5083–5106 (2005)

    Article  MATH  Google Scholar 

  57. Zhang, Y., Bajaj, C.L., Xu, G.: Surface smoothing and quality improvement of quadrilateral/hexahedral meshes with geometric flow. Commun. Numer. Methods Eng. 25(1), 1–18 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  58. Zhang, Y., Bazilevs, Y., Goswami, S., Bajaj, C.L., Hughes, T.J.R.: Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow. Comput. Methods Appl. Mech. Eng. 196(29–30), 2943–2959 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  59. Zhang, Y., Hughes, T.J.R., Bajaj, C.L.: An automatic 3D mesh generation method for domains with multiple materials. Comput. Methods Appl. Mech. Eng. 199(5–8), 405–415 (2010)

    Article  MATH  Google Scholar 

  60. Zhang, Y., Liang, X., Ma, J., Jing, Y., Gonzales, M.J., Villongco, C., Krishnamurthy, A., Frank, L.R., Nigam, V., Stark, P., Others: An atlas-based geometry pipeline for cardiac Hermite model construction and diffusion tensor reorientation. Med. Image Anal. 16(6), 1130–1141 (2012)

    Article  Google Scholar 

  61. Zhang, Y., Liang, X., Xu, G.: A robust 2-refinement algorithm in octree and rhombic dodecahedral tree based all-hexahedral mesh generation. Comput. Methods Appl. Mech. Eng. 256, 562–576 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  62. Zhang, Y., Qian, J.: Resolving topology ambiguity for multiple-material domains. Comput. Methods Appl. Mech. Eng. 247, 166–178 (2012)

    Article  MATH  Google Scholar 

  63. Zhang, Y., Wang, W., Hughes, T.J.R.: Solid T-spline construction from boundary representations for genus-zero geometry. Comput. Methods Appl. Mech. Eng. 249, 185–197 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  64. Zhang, Y., Wang, W., Hughes, T.J.R.: Conformal solid T-spline construction from boundary T-spline representations. Comput. Mech. 51(6), 1051–1059 (2013)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Y. Yu, J. Liu and Y. Zhang were supported in part by Honda funds. We also acknowledge the open source scientific library Eigen and its developers.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA

    Yuxuan Yu, Jialei Ginny Liu & Yongjie Jessica Zhang

Authors
  1. Yuxuan Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jialei Ginny Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yongjie Jessica Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongjie Jessica Zhang .

Editor information

Editors and Affiliations

  1. College of Engineering, Swansea University, Swansea, UK

    Rubén Sevilla

  2. Dipartimento di Matematica, Politecnico di Milano, Milan, Italy

    Simona Perotto

  3. College of Engineering, Swansea University, Swansea, UK

    Kenneth Morgan

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Yu, Y., Liu, J.G., Zhang, Y.J. (2022). HexDom: Polycube-Based Hexahedral-Dominant Mesh Generation. In: Sevilla, R., Perotto, S., Morgan, K. (eds) Mesh Generation and Adaptation. SEMA SIMAI Springer Series, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-92540-6_7

Download citation

Publish with us

Policies and ethics

Search

Navigation