Skip to main content
SpringerLink
Log in

Cage-free local deformations using green coordinates

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

Abstract

Green coordinates require to build an enclosing cage around a shape that is deformed by manipulating the cage. In this paper, we build upon the local differences of Green coordinates and propose a method to deform a shape locally without constructing a cage. Second, we derive linear formulas to directly interpolate points on the shape to desired locations using an umbrella shaped cell. Moreover, we set up an influence region to confine the deformation in a local area. Finally, we suggest a method to automatically construct an umbrella shaped cell and thus update it consecutively while the shape is deforming. Experiments have shown that the suggested approach delivers smooth local deformations and enables shape manipulations at an interactive rate.

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

Similar content being viewed by others

References

  1. Allen, B., Curless, B., Popović, Z.: The space of human body shapes: Reconstruction and parameterization from range scan. ACM Trans. Graph. 22(3), 587–594 (2003)

    Article  Google Scholar 

  2. Au, O.K.-C., Tai, C.-L., Chu, H.-K., Cohen-Or, D., Lee, T.-Y.: Skeleton extraction by mesh contraction. ACM Trans. Graph. 27(3), 44 (2008)

    Article  Google Scholar 

  3. Ben-Chen, M., Weber, O., Gotsman, C.: Spatial deformation transfer. In: SCA ’09: Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 67–74. ACM Press, New York (2009)

    Chapter  Google Scholar 

  4. Ben-Chen, M., Weber, O., Gotsmanm, C.: Variational harmonic maps for space deformation. ACM Trans. Graph. 28(3), 34 (2009)

    Article  Google Scholar 

  5. Botsch, M., Sorkine, O.: On linear variational surface deformation methods. IEEE Trans. Vis. Comput. Graph. 14(1), 213–230 (2008)

    Article  Google Scholar 

  6. Botsch, M., Pauly, M., Wicke, M., Gross, M.: Adaptive space deformations based on rigid cells. Comput. Graph. Forum 26(3), 339–347 (2007)

    Article  Google Scholar 

  7. Joshi, P., Meyer, M., DeRose, T., Green, B., Sanocki, T.: Harmonic coordinates for character articulation. ACM Trans. Graph. 26(3), 71 (2007)

    Article  Google Scholar 

  8. Ju, T., Schaefer, S., Warren, J.: Mean value coordinates for closed triangular meshes. ACM Trans. Graph. 24(3), 561–566 (2005)

    Article  Google Scholar 

  9. Levin, D., Lipman, Y.: Derivation and analysis of green coordinates. Technical Report, Tel-Aviv University (2008)

  10. Lipman, Y., Sorkine, O., Cohen-Or, D., Levin, D., Rössl, C., Seidel, H.-P.: Differential coordinates for interactive mesh editing. In: Shape Modeling International 2004 (SMI’04), pp. 181–190. IEEE Computer Society Press, Los Alamitos (2004)

    Chapter  Google Scholar 

  11. Lipman, Y., Levin, D., Cohen-Or, D.: Green coordinates. ACM Trans. Graph. 27(3), 78 (2008)

    Article  Google Scholar 

  12. Schneider, P.J., Eberly, D.: Geometric Tools for Computer Graphics. Elsevier, New York (2002)

    Google Scholar 

  13. Sorkine, O., Alexa, M.: As-rigid-as-possible surface modeling. In: Proceedings of the fifth Eurographics Symposium on Geometry Processing, pp. 109–116, Barcelona, Spain, 2007. Eurographics Association (2007)

  14. Sorkine, O., Cohen-Or, D., Lipman, Y., Alexa, M., Rössl, C., Seidel, H.-P.: Laplacian surface editing. In: Scopigno, R., Zorin, D. (eds.) The 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing (Nice, France), pp. 175–184. ACM Press, New York (2004)

    Chapter  Google Scholar 

  15. Tagliasacchi, A., Zhang, H., Cohen-Or, D.: Curve skeleton extraction from incomplete point cloud. ACM Transactions on Graphics, 28(3) (2009)

  16. Toledo, S., Chen, D., Rotkin, V.: Taucs: A library of sparse linear solvers, 2003

  17. von Funck, W., Theisel, H., Seidel, H.-P.: Vector field based shape deformations. ACM Trans. Graph. 25(3), 1118–1125 (2006)

    Article  Google Scholar 

  18. Weber, O., Sorkine, O., Lipman, Y., Gotsman, C.: Context-aware skeletal shape deformation. Comput. Graph. Forum 26(3), 265–274 (2007)

    Article  Google Scholar 

  19. Weber, O., Ben-Chen, M., Gotsman, C.: Complex barycentric coordinates with applications to planar shape deformation. Comput. Graph. Forum 28(2), 587–597 (2009)

    Article  Google Scholar 

  20. Yu, Y., Zhou, K., Xu, D., Shi, X., Bao, H., Guo, B., Shum, H.-Y.: Mesh editing with poisson-based gradient field manipulation. ACM Trans. Graph. 23(3), 644–651 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sun Yat-sen University, Guangzhou, 510006, China

    Zheng Li, Zhengjie Deng, Dingyuan Liu & Xiaonan Luo

  2. Tel-Aviv University, Tel-Aviv, 69978, Israel

    David Levin

Authors
  1. Zheng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Levin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhengjie Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dingyuan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiaonan Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zheng Li.

Additional information

This work was supported in part by grants from Israel Science Foundation, China 973 Program (2006CB303106), Production and Research Project of Guangdong-Ministry of Education (2009B090300083), Joint Funds of NSFC–Guangdong (U0735001, U0935004, U0835004), National Project of Sci. & Tech. Supporting Programs (2007BAH13B01), and Cultivation Fund of the Key Sci. & Tech. Inn. Project of Ministry of Education of China (706045).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, Z., Levin, D., Deng, Z. et al. Cage-free local deformations using green coordinates. Vis Comput 26, 1027–1036 (2010). https://doi.org/10.1007/s00371-010-0438-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-010-0438-x

Keywords

Search

Navigation