CageIK: Dual-Laplacian Cage-Based Inverse Kinematics

  • Yann Savoye
  • Jean-Sébastien Franco
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6169)


Cage-based deformation techniques are widely used to control the deformation of an enclosed fine-detail mesh. Achieving deformation based on vertex constraints has been extensively studied for the case of pure meshes, but few works specifically examine how such vertex constraints can be used to efficiently deform the template and estimate the corresponding cage pose. In this paper, we show that this can be achieved very efficiently with two contributions: (1) we provide a linear estimation framework for cage vertex coordinates; (2) the regularization of the deformation is expressed on the cage vertices rather than the enclosed mesh, yielding a computationally efficient solution which fully benefits from cage-based parameterizations. We demonstrate the practical use of this scheme for two applications: animation edition from sparse screen-space user-specified constraints, and automatic cage extraction from a sequence of meshes, for animation re-edition.


Inverse Kinematics Space Deformation Positional Constraint Mesh Deformation Model Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Lipman, Y., Sorkine, O., Cohen-Or, D., Levin, D., Rössl, C., Seidel, H.P.: Differential coordinates for interactive mesh editing. In: Proceedings of Shape Modeling International, pp. 181–190. IEEE Computer Society Press, Los Alamitos (2004)Google Scholar
  2. 2.
    Sorkine, O.: Differential representations for mesh processing. Computer Graphics Forum 25, 789–807 (2006)CrossRefGoogle Scholar
  3. 3.
    Lipman, Y., Sorkine, O., Alexa, M., Cohen-Or, D., Levin, D., Rössl, C., Seidel, H.P.: Laplacian framework for interactive mesh editing. International Journal of Shape Modeling (IJSM) 11, 43–61 (2005)CrossRefGoogle Scholar
  4. 4.
    Au, O.K.C., Tai, C.L., Liu, L., Fu, H.: Dual laplacian editing for meshes. IEEE Transactions on Visualization and Computer Graphics 12, 386–395 (2006)CrossRefGoogle Scholar
  5. 5.
    Luo, Q., Liu, B., Ma, Z.g., Zhang, H.b.: Mesh editing in roi with dual laplacian. In: CGIV ’07: Proceedings of the Computer Graphics, Imaging and Visualisation, pp. 195–199. IEEE Computer Society Press, Los Alamitos (2007)CrossRefGoogle Scholar
  6. 6.
    Sorkine, O., Alexa, M.: As-rigid-as-possible surface modeling. In: Proceedings of Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 109–116 (2007)Google Scholar
  7. 7.
    Meyer, M., Lee, H., Barr, A., Desbrun, M.: Generalized barycentric coordinates on irregular polygons. Journal of Graphics Tools 7, 13–22 (2002)CrossRefzbMATHGoogle Scholar
  8. 8.
    Ju, T., Schaefer, S., Warren, J.: Mean value coordinates for closed triangular meshes. In: SIGGRAPH ’05: ACM SIGGRAPH 2005 Papers, pp. 561–566. ACM Press, New York (2005)CrossRefGoogle Scholar
  9. 9.
    Joshi, P., Meyer, M., DeRose, T., Green, B., Sanocki, T.: Harmonic coordinates for character articulation. ACM Trans. Graph. 26, 71 (2007)CrossRefGoogle Scholar
  10. 10.
    Ben-Chen, M., Weber, O., Gotsman, C.: Variational harmonic maps for space deformation. In: SIGGRAPH ’09: ACM SIGGRAPH 2009 papers, pp. 1–11. ACM, New York (2009)CrossRefGoogle Scholar
  11. 11.
    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, New York (2009)CrossRefGoogle Scholar
  12. 12.
    Lipman, Y., Levin, D., Cohen-Or, D.: Green coordinates. In: ACM SIGGRAPH 2008 papers, pp. 78:1–78:10. ACM, New York (2008), doi:10.1145/1399504.1360677CrossRefGoogle Scholar
  13. 13.
    Ju, T., Zhou, Q.Y., van de Panne, M., Cohen-Or, D., Neumann, U.: Reusable skinning templates using cage-based deformations. ACM Trans. Graph. 27, 1–10 (2008)CrossRefGoogle Scholar
  14. 14.
    Xian, C., Hongwei Lin, S.G.: Automatic generation of coarse bounding cages from dense meshes. In: IEEE International Conference on Shape Modeling and Applications (Shape Modeling International 2009) (2009)Google Scholar
  15. 15.
    Sumner, R.W., Zwicker, M., Gotsman, C., Popović, J.: Mesh-based inverse kinematics. ACM Trans. Graph. 24, 488–495 (2005)CrossRefGoogle Scholar
  16. 16.
    Der, K.G., Sumner, R.W., Popović, J.: Inverse kinematics for reduced deformable models. In: SIGGRAPH ’06: ACM SIGGRAPH 2006 Papers, pp. 1174–1179. ACM, New York (2006)CrossRefGoogle Scholar
  17. 17.
    Shi, X., Zhou, K., Tong, Y., Desbrun, M., Bao, H., Guo, B.: Mesh puppetry: cascading optimization of mesh deformation with inverse kinematics. ACM Trans. Graph. 26, 81 (2007)CrossRefGoogle Scholar
  18. 18.
    Zhou, K., Huang, J., Snyder, J., Liu, X., Bao, H., Guo, B., Shum, H.Y.: Large mesh deformation using the volumetric graph laplacian. ACM Trans. Graph. 24, 496–503 (2005)CrossRefGoogle Scholar
  19. 19.
    Huang, J., Shi, X., Liu, X., Zhou, K., Wei, L.-Y., Teng, S.H., Bao, H., Guo, B., Shum, H.Y.: Subspace gradient domain mesh deformation. ACM Trans. Graph. 25(3), 1126–1134 (2006)CrossRefGoogle Scholar
  20. 20.
    Cohen-Or, D.: Space deformations, surface deformations and the opportunities in-between. J. Comput. Sci. Technol. 24, 2–5 (2009)CrossRefGoogle Scholar
  21. 21.
    Borosan, P., Howard, R., Zhang, S., Nealen, A.: Hybrid mesh editing. to appear in Proc. of Eurographics 2010 (short papers), Norrkoping, Sweden (2010)Google Scholar
  22. 22.
    Chen, L., Huang, J., Sun, H., Bao, H.: Cage-based deformation transfer. Computers & Graphics (2010)Google Scholar
  23. 23.
    Rustamov, R.M.: Boundary element formulation of harmonic coordinates. Technical report (2008)Google Scholar
  24. 24.
    Sorkine, O., Cohen-Or, D.: Least-squares meshes. In: Proceedings of Shape Modeling International, pp. 191–199. IEEE Computer Society Press, Los Alamitos (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yann Savoye
    • 1
  • Jean-Sébastien Franco
    • 1
  1. 1.LaBRI-INRIA Sud-OuestUniversity of BordeauxFrance

Personalised recommendations