Skip to main content
Log in

Mesh massage

A versatile mesh optimization framework

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

Abstract

We present a general framework for post-processing and optimizing surface meshes with respect to various target criteria. On the one hand, the framework allows us to control the shapes of the mesh triangles by applying simple averaging operations; on the other hand we can control the Hausdorff distance to some reference geometry by minimizing a quadratic energy. Due to the simplicity of this setup, the framework is efficient and easy to implement, yet it also constitutes an effective and versatile tool with a variety of possible applications. In particular, we use it to reduce the texture distortion in animated mesh sequences, to improve the results of cross-parameterizations, and to minimize the distance between meshes and their remeshes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Alliez, P., Attene, M., Gotsman, C., Ucelli, G.: Recent advances in remeshing of surfaces. In: De Floriani, L., Spagnuolo, M. (eds.) Shape Analysis and Structuring, pp. 53–82. Springer, Berlin Heidelberg New York (2008)

    Chapter  Google Scholar 

  2. Anuar, N., Guskov, I.: Extracting animated meshes with adaptive motion estimation. In: Proceedings of Vision, Modeling, and Visualization 2004, pp. 63–71. IOS Press, Stanford, CA (2004)

    Google Scholar 

  3. Charpiat, G., Maurel, P., Pons, J.P., Keriven, R., Faugeras, O.: Generalized gradients: Priors on minimization flows. Int. J. Comput. Vision 73(3), 325–344 (2007)

    Article  Google Scholar 

  4. Cignoni, P., Rocchini, C., Scopigno, R.: Metro: Measuring error on simplified surfaces. Comput. Graph. Forum 17(2), 167–174 (1998)

    Article  Google Scholar 

  5. Desbrun, M., Meyer, M., Schröder, P., Barr, A.: Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proceedings of SIGGRAPH ’99, pp. 317–324. ACM Press, Los Angeles, CA (1999)

    Chapter  Google Scholar 

  6. Dyn, N., Hormann, K., Kim, S.J., Levin, D.: Optimizing 3D triangulations using discrete curvature analysis. In: Lyche, T., Schumaker, L.L. (eds.) Mathematical Methods for Curves and Surfaces: Oslo 2000, pp. 135–146. Vanderbilt University Press, Nashville (2001)

    Google Scholar 

  7. Eck, M., DeRose, T., Duchamp, T., Hoppe, H., Lounsbery, M., Stuetzle, W.: Multiresolution analysis of arbitrary meshes. In: Proceedings of SIGGRAPH ’95, pp. 173–182. ACM Press, Los Angeles, CA (1995)

    Chapter  Google Scholar 

  8. Fleishman, S., Drori, I., Cohen-Or, D.: Bilateral mesh denoising. ACM Trans. Graph. 22(3), 950–953 (2003)

    Article  Google Scholar 

  9. Floater, M.S.: Mean value coordinates. Comput. Aided Geom. Des. 20(1), 19–27 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Floater, M.S., Hormann, K.: Surface parameterization: a tutorial and survey. In: Dodgson, N.A., Floater, M.S., Sabin, M.A. (eds.) Advances in Multiresolution for Geometric Modelling, pp. 157–186. Springer, Berlin Heidelberg New York (2005)

    Chapter  Google Scholar 

  11. Garland, M.: Multiresolution modeling: Survey & future opportunities. In: Proceedings of Eurographics, STAR – State of The Art Reports, pp. 111–131. Eurographics Association, Milano (1999)

    Google Scholar 

  12. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Mesh optimization. In: Proceedings of SIGGRAPH ’93, pp. 19–26. ACM Press, Anaheim, CA (1993)

    Chapter  Google Scholar 

  13. Jones, T.R., Durand, F., Desbrun, M.: Non-iterative, feature-preserving mesh smoothing. ACM Trans. Graph. 22(3), 943–949 (2003)

    Article  Google Scholar 

  14. Kraevoy, V., Sheffer, A.: Cross-parameterization and compatible remeshing of 3D models. ACM Trans. Graph. 23(3), 861–869 (2004)

    Article  Google Scholar 

  15. Lawson, C.L.: Contributions to the theory of linear least maximum approximation. Ph.D. thesis, University of California, Los Angeles (1961)

  16. Liu, L., Tai, C.L., Ji, Z., Wang, G.: Non-iterative approach for global mesh optimization. Comput. Aided Des. 39(9), 772–782 (2007)

    Article  Google Scholar 

  17. Meyer, M., Lee, H., Barr, A., Desbrun, M.: Generalized barycentric coordinates for irregular polygons. J. Graph. Tools 7(1), 13–22 (2002)

    MATH  Google Scholar 

  18. Motzkin, T.S., Walsh, J.L.: Polynomials of best approximation on a real finite point set. Trans. Am. Math. Soc. 91(2), 231–245 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  19. Nealen, A., Igarashi, T., Sorkine, O., Alexa, M.: Laplacian mesh optimization. In: Proceedings of GRAPHITE 2006, pp. 381–389. ACM Press, Kuala Lumpur (2006)

    Chapter  Google Scholar 

  20. Ohtake, Y., Belyaev, A.: Mesh optimization for polygonized isosurfaces. Comput. Graph. Forum 20(3), 368–376 (2001)

    Article  Google Scholar 

  21. Owen, S.J., White, D.R., Tautges, T.J.: Facet-based surfaces for 3D mesh generation. In: Proceedings of the 11th International Meshing Roundtable, pp. 297–312. Ithaca, NY (2002)

  22. Pinkall, U., Polthier, K.: Computing discrete minimal surfaces and their conjugates. Exp. Math. 2(1), 15–36 (1993)

    MATH  MathSciNet  Google Scholar 

  23. Pottmann, H., Huang, Q.X., Yang, Y.L., Hu, S.M.: Geometry and convergence analysis of algorithms for registration of 3D shapes. Int. J. Comput. Vis. 67(3), 277–296 (2006)

    Article  Google Scholar 

  24. Schreiner, J., Asirvatham, A., Praun, E., Hoppe, H.: Inter-surface mapping. ACM Trans. Graph. 23(3), 870–877 (2004)

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. Surazhsky, V., Alliez, P., Gotsman, C.: Isotropic remeshing of surfaces: a local parameterization approach. In: Proceedings of the 12th International Meshing Roundtable, pp. 215–224. Santa Fe, NM (2003)

  27. Surazhsky, V., Gotsman, C.: Explicit surface remeshing. In: Proceedings of SGP 2003, pp. 20–30. Eurographics Association, Aachen (2003)

    Google Scholar 

  28. Taubin, G.: A signal approach to fair surface design. In: Proceedings of SIGGRAPH ’95, pp. 351–358. ACM Press, Los Angeles, CA (1995)

    Chapter  Google Scholar 

  29. Toledo, S.: TAUCS: A library of sparse linear solvers, version 2.2. http://www.tau.ac.il/∼stoledo/taucs/ (2003). Accessed 2008

  30. Van Damme, R., Alboul, L.: Tight triangulations. In: Daehlen, M., Lyche, T., Schumaker, L.L. (eds.) Mathematical Methods for Curves and Surfaces, pp. 517–526. Vanderbilt University Press, Nashville (1995)

    Google Scholar 

  31. Wachspress, E.L.: A Rational Finite Element Basis. Academic, New York (1975)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kai Hormann.

Electronic Supplementary Material

Movie 1 2.9MB

Movie 2 4.5MB

Movie 3 2.5MB

Movie 4 4.5MB

Movie 5 1.9MB

Movie 6 4.4MB

Movie 7 1.3MB

Movie 8 4.1MB

Rights and permissions

Reprints and permissions

About this article

Cite this article

Winkler, T., Hormann, K. & Gotsman, C. Mesh massage. Visual Comput 24, 775–785 (2008). https://doi.org/10.1007/s00371-008-0259-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-008-0259-3

Keywords

Navigation