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Dual joints for 3D-structures

Producing skins for skeletons by exploring duality

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Abstract

The increasing popularity of 3D printing is drawing the interest of the research community to the possibilities and challenges of this manufacturing method. Amongst its many uncertainties, we are concerned here with one of its certainties—that reduction of the material required in 3D printing is critical for efficiency and affordability. In this paper, we propose a solution to the computer graphics problem of, given a volume boundary, automatically defining the mesh of a low density internal structure that is 3D-printable. The proposed solution involves two steps. The first step is to define a cell complex partition for the internal space of a volume defined by its boundaries. The second step, is to apply the Skin4Skeleton algorithm, which uses the cell complex dual to produce a 3D-printable cell-complex mesh with a parametrised thickness.

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References

  1. Sá, A.M., Echavarria, K.R., Griffin, M., Covill, D., Kaminski, J., Arnold, D.: Parametric 3D-fitted frames for packaging heritage artefacts. In: VAST: International Symposium on Virtual Reality, Archaeology and Intelligent Cultural Heritage, 2012, Brighton, UK. pp. 105–112. Eurographics Associassion, Brighton (2012)

    Google Scholar 

  2. Bitzer, T.: Honeycomb Technology: Materials, Design, Manufacturing, Applications and Testing. Chapman & Hall, London (1997)

    Book  Google Scholar 

  3. Chen, Y.: A mesh-based geometric modeling method for general structures. ASME Conf. Proc. 2006(42578), 269–281 (2006)

    Google Scholar 

  4. Christensen, R.M.: Mechanics of cellular and other low-density materials. Int. J. Solids Struct. 37(1–2), 93–104 (2000)

    Article  MATH  Google Scholar 

  5. Conway, J.H., Jiao, Y., Torquato, S.: New family of tilings of three-dimensional euclidean space by tetrahedra and octahedra. Proc. Natl. Acad. Sci. 108(27), 11009–11012 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Deshpande, V.S., Fleck, N.A., Ashby, M.F.: Effective properties of the octet-truss lattice material. J. Mech. Phys. Solids 49(8), 1747–1769 (2001)

    Article  MATH  Google Scholar 

  7. Freedom of creation (2013). http://www.freedomofcreation.com

  8. Friedrichs, O.D., Huson, D.H.: Tiling space by platonic solids, I. Discrete Comput. Geom. 21(2), 299–315 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Gibson, I., Rosen, D.W., Stucker, B.: Additive Manufacturing Technologies: Rapid Prototyping to Direct Digital Manufacturing. Springer, Berlin (2009)

    Google Scholar 

  10. Greiner, G., Grosso, R.: Hierarchical tetrahedral-octahedral subdivision for volume visualization. Vis. Comput. 16, 357–369 (2000)

    Article  MATH  Google Scholar 

  11. Hutmacher, D.W., Sittinger, M., Risbud, M.V.: Scaffold-based tissue engineering: rationale for computer-aided design and solid free-form fabrication systems. Trends Biotechnol. 22(7), 354–362 (2004)

    Article  Google Scholar 

  12. Kang, H., Lin, C.-Y., Hollister, S.J.: Topology optimization of three dimensional tissue engineering scaffold architectures for prescribed bulk modulus and diffusivity. Struct. Multidiscip. Optim. 42, 633–644 (2010)

    Article  Google Scholar 

  13. Kawamoto, A.: Prototyping lightweight car seat structures using topology optimization and additive manufacturing. In: Additive Manufacturing Conference Proceedings (2012)

    Google Scholar 

  14. Kowalski, N., Ledoux, F., Staten, M.L., Owen, S.J.: Fun sheet matching: towards automatic block decomposition for hexahedral meshes. Eng. Comput. 28, 241–253 (2012)

    Article  Google Scholar 

  15. Ledoux, H., Gold, C.M.: Simultaneous storage of primal and dual three-dimensional subdivisions. Comput. Environ. Urban Syst. 31(4), 393–408 (2007)

    Article  Google Scholar 

  16. Takashi, M.: An overview of offset curves and surfaces. Comput. Aided Des. 31(3), 165–173 (1999)

    Article  MATH  Google Scholar 

  17. Murdoch, P., Benzley, S., Blacker, T., Mitchell, S.A.: The spatial twist continuum: a connectivity based method for representing all-hexahedral finite element meshes. Finite Elem. Anal. Des. 28(2), 137–149 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  18. Netfabb (2013). http://www.netfabb.com/structure.php

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

    Article  Google Scholar 

  20. OpenSG. Open source scenegraph OpenSG. http://www.opensg.org/

  21. Owen, S.J.: A survey of unstructured mesh generation technology. In: IMR, pp. 239–267 (1998)

    Google Scholar 

  22. Patrikalakis, N.M., Maekawa, T.: Shape Interrogation for Computer Aided Design and Manufacturing. Springer, Berlin (2010)

    Book  MATH  Google Scholar 

  23. Pavic, D., Kobbelt, L.: High-resolution volumetric computation of offset surfaces with feature preservation. Comput. Graph. Forum 27(2), 165–174 (2008)

    Article  Google Scholar 

  24. Pham, B.: Offset curves and surfaces: a brief survey. Comput. Aided Des. 24(4), 223–229 (1992)

    Article  Google Scholar 

  25. Rosen, D.W.: Computer-aided design for additive manufacturing of cellular structures. Comput-Aided Des. Appl. 4(1–6), 585–594 (2007)

    Google Scholar 

  26. Schneiders, R.: Algorithms for quadrilateral and hexahedral mesh generation. Lect. Ser. - Kareman Inst. Fluid Dyn. 5, L1–L56 (2000)

    Google Scholar 

  27. Schneiders, R.: Mesh generators (2013). http://www.robertschneiders.de/meshgeneration/software.html

  28. Si, H.: TetGen: a quality tetrahedral mesh generator and three-dimensional Delaunay triangulator. http://tetgen.berlios.de/

  29. Srinivasan, V., Mandal, E., Akleman, E.: Solidifying wireframes (2005)

  30. Wadley, H.N.G.: Multifunctional periodic cellular metals. Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci. 364(1838), 31–68 (2006)

    Article  Google Scholar 

  31. Wang, H., Chen, Y., Rosen, D.W.: A hybrid geometric modeling method for large scale conformal cellular structures. ASME Conf. Proc. 2005(47403), 421–427 (2005)

    Google Scholar 

  32. Yoo, D.J.: Porous scaffold design using the distance field and triply periodic minimal surface models. Biomaterials 32(31), 7741–7754 (2011)

    Article  Google Scholar 

  33. Yoo, D.-J., Kwon, H.-H.: Shape reconstruction, shape manipulation, and direct generation of input data from point clouds for rapid prototyping. Int. J. Precis. Eng. Manuf. 10, 103–113 (2009)

    Article  Google Scholar 

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Correspondence to Asla Medeiros e Sá.

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A.M.S. supported by CAPES—Brazil.

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Medeiros e Sá, A., Rodriguez Echavarria, K. & Arnold, D. Dual joints for 3D-structures. Vis Comput 30, 1321–1331 (2014). https://doi.org/10.1007/s00371-013-0883-4

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