Skip to main content
SpringerLink
Log in

Optimal strategies for creating paper models from 3D objects

  • Regular Paper
  • Published:
Multimedia Systems Aims and scope Submit manuscript

Abstract

Paper is an underrated medium in multimedia technology. Rather than showing printed information only, it can also be used for creating real paper models from virtual objects by means of glue and scissors. This requires to compute a planar cut-out sheet from a 3D model. However, faces forming a model in 3D will often overlap once unfolded. While 3D space leaves much possibility for a non-intersecting topology of faces, they tend to intersect easily in the planar projection of the cut-out sheet. But overlaps are not the only problem. In some cases, neighboring faces enclose such a small angle that they are difficult to cut out and glue together. Unfolding a virtual model involves to decide which edges of a 3D model to cut first. A carefully chosen order can help to avoid the above mentioned problems in many cases. Finding the optimal order, however, is an NP-complete problem. In this paper, we develop and analyze a number of strategies that generate sheets which can be crafted easily and which yield high quality results.

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

Similar content being viewed by others

Notes

  1. http://www.makerbot.com.

  2. http://dxf2papercraft.sourceforge.net.

  3. http://www.tamasoft.co.jp/pepakura-en/.

  4. http://www.papercraft3d.com.

References

  1. Abelson, H., di Sessa, H.: Turtle Geometry: The Computer as a Medium for Exploring Mathematics. The MIT Press, Cambridge (1980)

    Google Scholar 

  2. Diaz-Gutierrez, P., Bhushan, A., Gopi, M., Pajarola, R.: Constrained strip generation and management for efficient interactive 3d rendering. In: Computer Graphics International, pp. 115–121 (2005)

  3. Dillencourt, M.: Finding hamiltonian cycles in delaunay triangulations in np-complete. In: Canadian conference on computational geometry (CCCG), pp. 223–229 (1992)

  4. Evans, F., Skiena, S., Varshney, A.: Completing sequential triangulations is hard. Tr, State University of New York at Stony Brook (1996)

  5. Evans, F., Skiena, S., Varshney, A.: Optimizing triangle strips for fast rendering. In: IEEE Visualization 96. San Francisco (1996)

  6. Gopi, M., Eppstein, D.: Single-strip triangulation of manifolds with arbitrary topology. In: Computer Graphics Forum, pp. 371–379 (2004)

  7. Julius, D., Kraevoy, V., Sheffer, A.: D-charts: Quasi-developable mesh segmentation. In: Computer Graphics Forum, Eurographics, Dublin, pp. 581–590 (2005)

  8. Kolmanic, S., Guid, N.: A new approach in cad system for designing shoes. J. Comput. Inf. Technol. 4, 319–326 (2003)

    Article  Google Scholar 

  9. Massarwi, F., Gotsman, C., Elber, G.: Papercraft models using generalized cylinders. In: Proceedings of the 15th Pacific conference on computer graphics and applications, pp. 148–157. IEEE Computer Society (2007)

  10. Mitani, J., Suzuki, H.: Making papercraft toys from meshes using strip-based approxi- mate unfolding. In: Proceedings of ACM SIGGRAPH 2004, vol. 23, pp. 259–263 (2004)

  11. Moritsugu, S.: Solving cubic equations by origami. In: Applications of computer algebra (ACA’2005), Nara city (2005)

  12. Read, R.C., Tarjan, R.E.: Bounds on backtrack algorithms for listing cycles, paths, and spanning trees. Networks 5, 237–252 (1975)

    MathSciNet  MATH  Google Scholar 

  13. Sells, E., Smith, Z., Bailard, S., Bowyer, A., Olliver, V.: RepRap: The Replicating Rapid Prototyper—maximizing customizability by breeding the means of production, pp. 568–580. World Scientific (2009)

  14. Shafae, M., Pajarola, R.: Dstrips: dynamic triangle strips for real-time mesh simplification and rendering. In: Pacific Graphics, pp. 271–280 (2003)

  15. Shatz, I., Tal, A., Leifman, G.: Paper craft models from meshes. Vis Comput Int J Comput Graph 22, 825–834 (2006)

    Article  Google Scholar 

  16. Straub, R., Prautzsch, H.: Creating optimized cut-out sheets for paper models from meshes. In: Proceedings of the ninth SIAM conference on geometric design and computing. SIAM (2005). http://www.ibds.uni-karlsruhe.de/papers/cut-out-sheets.pdf

  17. Xiang, X., Abd, J.S.B., Mitchell, M.H.: Fast and effective stripification of polygonal surface models, vol. 3, 71–78 (1999)

  18. Yamauchi, H., Gumhold, S., Zayer, R., Seidel, H.: Mesh segmentation driven by gaussian curvature. Vis Comput 8(10), 659–668 (2005)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Business Informatics and Mathematics, University of Mannheim, A5, 6, 68159, Mannheim, Germany

    Thomas Haenselmann & Wolfgang Effelsberg

Authors
  1. Thomas Haenselmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wolfgang Effelsberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Haenselmann.

Additional information

Communicated by P. Pala.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Haenselmann, T., Effelsberg, W. Optimal strategies for creating paper models from 3D objects. Multimedia Systems 18, 519–532 (2012). https://doi.org/10.1007/s00530-012-0273-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00530-012-0273-1

Keywords

Search

Navigation