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Spectral mesh deformation

Abstract

In this paper, we present a novel spectral method for mesh deformation based on manifold harmonics transform. The eigenfunctions of the Laplace–Beltrami operator give orthogonal bases for parameterizing the space of functions defined on the surfaces. The geometry and motion of the original irregular meshes can be compactly encoded using the low-frequency spectrum of the manifold harmonics. Using the spectral method, the size of the linear deformation system can be significantly reduced to achieve interactive computational speed for manipulating large triangle meshes. Our experimental results demonstrate that only a small spectrum is needed to achieve undistinguishable deformations for large triangle meshes. The spectral mesh deformation approach shows great performance improvement on computational speed over its spatial counterparts.

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References

  1. 1.

    Au, O.K.C., Tai, C.L., Liu, L., Fu, H.: Dual laplacian editing for meshes. IEEE Trans. Vis. Comput. Graph. 12(3), 386–395 (2006)

  2. 2.

    Boier-Martin, I., Ronfard, R., Bernardini, F.: Detail-preserving variational surface design with multiresolution constraints. In: Proceedings of the 2004 Shape Modeling International, pp. 119–128. IEEE Computer Society, Washington, DC (2004)

  3. 3.

    Botsch, M., Kobbelt, L.: An intuitive framework for real-time freeform modeling. ACM Trans. Graph. 23(3), 630–634 (2004)

  4. 4.

    Botsch, M., Pauly, M., Gross, M., Kobbelt, L.: PriMo: coupled prisms for intuitive surface modeling. In: Proceedings of the 4th Eurographics Symposium on Geometry processing, pp. 11–20. Eurographics Association, Aire-la-Ville, Switzerland (2006)

  5. 5.

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

  6. 6.

    Botsch, M., Sumner, R., Pauly, M., Gross, M.: Deformation transfer for detail-preserving surface editing. In: Proceedings of 11th International Fall Workshop Vision, Modeling & Visualization, pp. 357–364. Akademische Verlagsgesellschaft Aka, Aachen (2006)

  7. 7.

    Guo, X., Li, X., Bao, Y., Gu, X., Qin, H.: Meshless thin-shell simulation based on global conformal parameterization. IEEE Trans. Vis. Comput. Graph. 12(3), 375–385 (2006)

  8. 8.

    Guskov, I., Sweldens, W., Schröder, P.: Multiresolution signal processing for meshes. In: Proceedings of ACM SIGGRAPH 99, pp. 325–334. ACM Press/Addison-Wesley Publishing Co., New York, NY (1999)

  9. 9.

    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)

  10. 10.

    Karni, Z., Gotsman, C.: Spectral compression of mesh geometry. In: Proceedings of ACM SIGGRAPH 2000, pp. 279–286. ACM Press/Addison-Wesley Publishing Co., New York, NY (2000)

  11. 11.

    Kobbelt, L., Campagna, S., Vorsatz, J., Seidel, H.P.: Interactive multi-resolution modeling on arbitrary meshes. In: Proceedings of ACM SIGGRAPH 98, pp. 105–114. ACM Press/Addison-Wesley Publishing Co., New York, NY (1998)

  12. 12.

    Lipman, Y., Sorkine, O., Levin, D., Cohen-Or, D.: Linear rotation-invariant coordinates for meshes. ACM Trans. Graph. 24(3), 479–487 (2005)

  13. 13.

    Marinov, M., Botsch, M., Kobbelt, L.: GPU-based multiresolution deformation using approximate normal field reconstruction. J. Graph. Tools 12(1), 27–46 (2007)

  14. 14.

    Meyer, M., Desbrun, M., Schröder, P., Barr, A.H.: Discrete differential geometry operators for triangulated 2-manifolds. In: Hege, H.C., Polthier, K. (eds.) Visualization and Mathematics III, pp. 35–57. Springer, Heidelberg (2002)

  15. 15.

    Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes – The Art of Scientific Computing, 3rd edn. Cambridge University Press, New York, NY (2007)

  16. 16.

    Reuter, M., Wolter, F.E., Peinecke, N.: Laplace–Beltrami spectra as shape-DNA of surfaces and solids. Comput.-Aided Des. 38(4), 342–366 (2006)

  17. 17.

    Sorkine, O., Cohen-Or, D., Lipman, Y., Alexa, M., Rössl, C., Seidel, H.P.: Laplacian surface editing. In: Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 175–184. ACM Press, New York, NY (2004)

  18. 18.

    Sumner, R.W., Popović, J.: Deformation transfer for triangle meshes. ACM Trans. Graph. 23(3), 399–405 (2004)

  19. 19.

    Taubin, G.: A signal processing approach to fair surface design. In: Proceedings of ACM SIGGRAPH 95, pp. 351–358. ACM Press/Addison-Wesley Publishing Co., New York, NY (1995)

  20. 20.

    Terzopoulos, D., Platt, J., Barr, A., Fleischer, K.: Elastically deformable models. Comput. Graph. (Proceedings of ACM SIGGRAPH 90) 21(4), 205–214 (1987)

  21. 21.

    Vallet, B., Lévy, B.: Spectral geometry processing with manifold harmonics. Technical report, ALICE – INRIA Lorraine, Nancy, France (2007)

  22. 22.

    Welch, W., Witkin, A.: Variational surface modeling. Comput. Graph. (Proceedings of ACM SIGGRAPH 92) 26(2), 157–166 (1992)

  23. 23.

    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)

  24. 24.

    Zayer, R., Rössl, C., Karni, Z., Seidel, H.P.: Harmonic guidance for surface deformation. Comput. Graph. Forum 24(3), 601–609 (2005)

  25. 25.

    Zhang, H., van Kaick, O., Dyer, R.: Spectral methods for mesh processing and analysis. In: Proceedings of Eurographics State-of-the-art Report, pp. 1–22. Eurographics Association, Prague (2007)

  26. 26.

    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(3), 496–503 (2005)

  27. 27.

    Zhou, K., Huang, X., Xu, W., Guo, B., Shum, H.Y.: Direct manipulation of subdivision surfaces on GPUs. ACM Trans. Graph. 26(3), 91 (2007)

  28. 28.

    Zorin, D., Schröder, P., Sweldens, W.: Interactive multiresolution mesh editing. In: Proceedings of ACM SIGGRAPH 97, pp. 259–268. ACM Press/Addison-Wesley Publishing Co., New York, NY (1997)

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Correspondence to Guodong Rong.

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Rong, G., Cao, Y. & Guo, X. Spectral mesh deformation. Visual Comput 24, 787–796 (2008) doi:10.1007/s00371-008-0260-x

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Keywords

  • Spectral geometry
  • Manifold harmonics
  • Mesh deformation
  • Interactive manipulation