Skip to main content
SpringerLink
Log in

Geometric reasoning in sketch-based volumetric decomposition framework for hexahedral meshing

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

This paper presents a sketch-based volumetric decomposition framework using geometric reasoning to assist in hex meshing. The sketch-based user interface makes the framework user-friendly and intuitive, and the geometric reasoning engine makes the framework smarter and improves the usability. The system first generates a database that contains both the B-rep and 3D medial object to capture the exterior and interior of the input model, respectively. Next, the geometric reasoning process determines sweeping direction and two types of sweepable regions and provides visual aids to assist the user in developing decomposition solutions. The user conducts decomposition via the sketch-based user interface, which understands the user’s intent through freehand stroke inputs for smart decomposition. Imprint and merge operations are then performed on the decomposed model before passing it to the sweeping algorithm to create hex meshes. The proposed framework has been tested on industrial models.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. Steven EB, Ernest P, Karl M, Brett C, Greg S (1995) A comparison of all-hexahedral and all-tetrahedral finite element meshes for elastic and elasto-plastic analysis. In: Proceedings of the 4th International Meshing Roundtable, pp 179–191

  2. Blum H (1967) A transformation for extracting new descriptors of shape. In: Walthem-Dunn (ed) Models for the perception of speech and visual form. MIT Press, Cambridge, MA, pp 362–380

  3. Chong CS, Senthil Kumar A, Lee KH (2004) Automatic solid decomposition and reduction for non-manifold geometric model generation. Comput Aided Des 36(13):1357–1369

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Donaghy RJ, Armstrong CG, Price MA (2000) Dimensional reduction of surface models for analysis. Eng Comput 16:24–35

    Article  Google Scholar 

  6. Folwell NT, Mitchell SA (1998) Reliable whisker weaving via curve contraction. In: Proceedings of the 7th International Meshing Roundtable, pp 365–378

  7. Hardwick M (2005) In DART system analysis presented to simulation sciences seminar

  8. Igarashi T, Matsuoka S, Tanaka H (1999) Teddy: a sketching interface for 3D freeform design. In: Proceeding of the 26th annual conference on computer graphics and interactive, pp 409–416

  9. ITI TranscenData (2013) CAD Translation-CADFix. In: http://www.cadfix.com

  10. Kara LB, Shimada K (2006) Construction and modification of 3D geometry using a sketch-based interface. In: Proceeding of the EUROGRAPHICS Workshop on sketch-based interfaces and modeling, pp 59–66

  11. Li TS, McKeag RM, Armstrong CG (1995) Hexahedral meshing using midpoint subdivision and integer programming. Comput Methods Appl Mech Eng 124(1-2):171–193

    Article  Google Scholar 

  12. Lu JHC, Song I, Quadros WR, Shimada K (2010) Pen-based user interface for geometric decomposition for hexahedral mesh generation. In: Proceedings of the 19th International Meshing Roundtable, pp 263–278

  13. Lu Y, Gadh R, Tautges TJ (2001) Feature based hex meshing methodology: feature recognition and volume decomposition. Comput Aided Des 33(3):221–232

    Article  Google Scholar 

  14. Luo X-J, Shephard MS, Yin L-Z, OBara RM, Nastasi R, Beall MW (2010) Construction of near optimal meshes for 3d curved domains with thin sections and singularities for p-version method. Comput Methods Appl Mech Eng 26:215–229

    Google Scholar 

  15. Makem JE, Armstrong CG, Robinson TT (2012) Automatic decomposition and efficient semi-structured meshing of complex solids. In: Proceeding of the 20th International Meshing Roundtable. Springer, Berlin, Heidelberg, pp 199–215

  16. Masry M, Kang D, Lipson H (2005) A freehand sketching interface for progressive construction of 3D objects. Comput Gr 29(4):563–575

    Article  Google Scholar 

  17. Owen SJ, Clark B, Melander DJ, Brewer ML, Shepherd J, Merkley KG, Ernst C, Morris R (2007) An immersive topology environment for meshing. In: Proceeding of the 16th International Meshing Roundtable, Sandia National Laboratories, pp 553–578

  18. Pointwise Inc (2011) Multi-block grids for axial turbines. In: http://www.pointwise.com/theconnector/March-2011/Gridding-an-Axial-Turbine-Video.shtml

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

    Article  Google Scholar 

  20. Price MA, Armstrong CG, Sabin MA (1995) Hexahedral mesh generation by medial surface subdivision: part I. Solids with convex edges. Int J Numer Methods Eng 38(19):3335–3359

    Article  MATH  Google Scholar 

  21. Quadros WR, Ramaswami K, Prinz FB, Gurumoorthy B (2004) LayTracks: a new approach to automated geometry adaptive quadrilateral mesh generaton using medial axis transform. Int J Numer Meth Eng 61:209–237

    Article  MATH  Google Scholar 

  22. Sampl P (2000) Semi-structured mesh generation based on medial axis. In: Proceeding of the 9th International Meshing Roundtable, pp 21–32

  23. Sandia National Laboratories (2013) Cubit: Geometry and meshing toolkit. In: https://www.cubit.sandia.gov

  24. Schneiders R (1995) Automatic generation of hexahedral finite element meshes. In: Proceedings of the 4th International Meshing Roundtable, pp 103–114

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

    Article  Google Scholar 

  26. Schoof L, Yarberry V (1995) Exodus II a finite element data model. SAND92-2137, Sandia National Laboratories

  27. Sheffer A, Etzion M, Bercovier M (1999) Hexahedral mesh generation using the embedded voronoi graph. In: Proceedings of the 7th International Meshing Roundtable, pp 347–364

  28. Shepherd JF, Johnson CR (2008) Hexahedral mesh generation constraints. Eng Comput 24(3):195–213

    Article  Google Scholar 

  29. Shih BY, Sakurai H (1996) Automated hexahedral mesh generation by swept volume decomposition and recomposition. In: Proceeding of the 5th International Meshing Roundtable, pp 273–280

  30. Shih BY, Sakurai H (1997) Shape recognition and shape-specific meshing for generating all hexahedral meshes. In: Proceeding of the 6th International Meshing Roundtable, pp 197–209

  31. Tam T, Armstrong CG (1991) 2D finite element mesh generation by medial axis subdivision. Adv Eng Softw 13(5–6):313–324

    MATH  Google Scholar 

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

    Google Scholar 

  33. Timothy JT (2000) The common geometry module (CGM): a generic, extensible geometry interface. In: Proceeding of the 9th International Meshing Roundtable, Sandia National Laboratories, pp 337–348

  34. Varley PAC, Suzuki H, Mitani J, Martin RR (2000) Interpretation of Single Sketch Input for Mesh and Solid Models. Int J Shape Model 6:207–240

    Google Scholar 

  35. White D, Mingwu L, Benzley SE, Sjaardema GD (1995) Automated hexahedral mesh generation by virtual decomposition. In: Proceeding of the 4th International Meshing Roundtable, Sandia National Laboratories, pp 165–176

  36. Yamakawa S, Gentilini I, Shimada K (2011) Subdivision templates for converting a non-conformal hex-dominant mesh to a conformal hex-dominant mesh without pyramid elements. Eng Comput 27:51–65

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Dr. Geoffrey Butlin, Mr. Henry Bucklow, Mr. Robin Fairey, Mr. Mark Gammon, Mr. Mike Field, and Mr. John Lamont for assisting with the medial related work in CADFIX.

Author information

Authors and Affiliations

  1. Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA, USA

    Jean Hsiang-Chun Lu, Inho Song & Kenji Shimada

  2. Sandia National Laboratories, Albuquerque, NM, 87185, USA

    William Roshan Quadros

Authors
  1. Jean Hsiang-Chun Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Inho Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. William Roshan Quadros
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kenji Shimada
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jean Hsiang-Chun Lu.

Additional information

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lu, J.HC., Song, I., Quadros, W.R. et al. Geometric reasoning in sketch-based volumetric decomposition framework for hexahedral meshing. Engineering with Computers 30, 237–252 (2014). https://doi.org/10.1007/s00366-013-0332-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-013-0332-z

Keywords

Search

Navigation