Deforming Surface Meshes

Abstract

We study the problem of maintaining a deforming surface mesh, specified only by a dense sample of n points that move with the surface. We propose a motion model under which the class of \((\varepsilon,\alpha )\)-meshes can be efficiently maintained by a combination of edge flips and insertion and deletion of vertices. We can enforce bounded aspect ratios and a small approximation error throughout the deformation.

References

  1. 1.
    Adams, B., Pauly, M., Keiser, R., Guibas, L.J.: Adaptively sampled particle fluids. ACM Trans. Graph. 26, 3–48 (2007)CrossRefGoogle Scholar
  2. 2.
    Amenta, N., Bern, M.: Surface reconstruction by Voronoi filtering. Discrete Comput. Geom. 22, 481–504 (1999)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Amenta, N., Choi, S., Dey, T.K., Leekha, N.: A simple algorithm for homeomorphic surface reconstruction. Int. J. Comput. Geom. Appl. 12, 125–141 (2002)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Baraff, D., Witkin, A.: Large steps in cloth simulation. In: SIGGRAPH, pp. 43–54 (1998)Google Scholar
  5. 5.
    Beer, G., Smith, I., Duenser, C.: The Boundary Element Method with Programming. Springer, New York (2008)MATHGoogle Scholar
  6. 6.
    Bredno, J., Lehmann, T.M., Spitzer, K.: A general discrete contour model in two, three, and four dimensions for topology-adaptive multichannel segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 25, 550–563 (2003)CrossRefGoogle Scholar
  7. 7.
    Cheng, S.-W., Jin, J.: Edge flips and deforming surface meshes. In: Proceedings of the 28th Annual Symposium on Computational Geometry, pp. 331–340 (2011)Google Scholar
  8. 8.
    Cheng, S.-W., Jin, J.: Edge flips in surface meshes. Manuscript. http://www.cse.ust.hk/faculty/scheng/pub/deform.pdf (2013)
  9. 9.
    Cheng, S.-W., Jin, J., Lau., M.-K.: A fast and simple surface reconstruction algorithm. In: Proceedings of the 28th Annual Symposium on Computational Geometry, pp. 69–78 (2012)Google Scholar
  10. 10.
    Delingette, H.: Towards realistic soft tissue modeling in medical simulation. In: Proceedings of the IEEE: Special Issue on Surgery Simulation, pp. 512–523 (1998)Google Scholar
  11. 11.
    Dey, T.K.: Curve and Surface Reconstruction: Algorithms with Mathematical Analysis. Cambridge University Press, New York (2006)CrossRefGoogle Scholar
  12. 12.
    Enright, D., Fedkiw, R., Ferziger, J., Mitchell, I.: A hybrid particle level set method for improved interface capturing. J. Comput. Phys. 183, 83–116 (2002)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Giesen, J., Wagner, U.: Shape dimension and intrinsic metric from samples of manifolds. Discrete Comput. Geom. 32, 245–267 (2004)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Glimm, J., Grove, J.W., Li, X.L., Tan, D.C.: Robust computational algorithms for dynamic interface tracking in three dimensions. SIAM J. Sci. Comput. 21, 2240–2256 (1999)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Hall, W.S.: The Boundary Element Method. Kluwer Academic Publishers, Dordrecht (1994)CrossRefMATHGoogle Scholar
  16. 16.
    Jiao, X.: Face offsetting: a unified approach for explicit moving interfaces. J. Comput. Phys. 220, 612–625 (2007)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Jin, J.: Surface reconstruction and deformation. Doctoral Dissertation, The Hong Kong University of Science and Technology (2012)CrossRefGoogle Scholar
  18. 18.
    Khayat, R.E.: Three-dimensional boundary element analysis of drop deformation in confined flow for Newtonian and viscoelastic systems. Int. J. Numer. Methods Fluids 34, 241–275 (2000)CrossRefMATHGoogle Scholar
  19. 19.
    Koch, R.K., Gross, M.H., Carls, F.R., von Büren, D.F., Fankhauser, G., Parish, Y.I.H.: Simulating facial surgery using finite element methods. In: SIGGRAPH, pp. 421–428 (1996)Google Scholar
  20. 20.
    LeVeque, R.J.: High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. Anal. 33, 627–665 (1996)CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Liu, T., Shen, D., Davatzikos, C.: Deformable registration of cortical structures via hybrid volumetric and surface warping. NeuroImage 22, 1790–1801 (2004)CrossRefGoogle Scholar
  22. 22.
    Müller, M., Charypar, D., Gross, M.: Particle-based fluid simulation for interactive applications. In: SIGGRAPH, pp. 154–159 (2003)Google Scholar
  23. 23.
    Osher, S., Sethian, J.: Fronts propagating with curvature-dependent speed: algorithms based on Hamiltonian Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988)CrossRefMATHMathSciNetGoogle Scholar
  24. 24.
    Pauly, M., Keiser, R., Adams, B., Dutré, P., Gross, M., Guibas, L.J.: Meshless animation of fracturing solids. ACM Trans. Graph. 24, 957–964 (2005)CrossRefGoogle Scholar
  25. 25.
    Plantinga, S., Vegter, G.: Isotopic meshing of implicit surfaces. Vis. Comput. 23, 45–58 (2007)CrossRefGoogle Scholar
  26. 26.
    Pons, J., Boissonnat, J.D.: Delaunay deformable models: topology-adaptive meshes based on the restricted Delaunay triangulation. In: CVPR, 1–8 (2007)Google Scholar
  27. 27.
    Sethian, J.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1999)MATHGoogle Scholar
  28. 28.
    Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S., Jan, Y.-J.: A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169(2), 708–759 (2001)CrossRefMATHGoogle Scholar
  29. 29.
    Volino, P., Magnenat-Thalmann, N.: Comparing efficiency of integration methods for cloth simulation. In: Proceedings of the International Conference on Computer Graphics, pp. 265–272 (2001)Google Scholar
  30. 30.
    Wojtan, C., Thüey, N., Gross, M., Turk, G.: Deforming meshes that split and merge. ACM Trans. Graph. 28 (2009). Article 76Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer Science & EngineeringHKUST, Clear Water BayKowloonHong Kong
  2. 2.Google Inc.Mountain ViewUSA

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