“Enrichment textures for detailed cutting of shells” by Kaufmann, Martin, Botsch, Grinspun and Gross

  • ©Peter Kaufmann, Sebastian Martin, Mario Botsch, Eitan Grinspun, and Markus Gross




    Enrichment textures for detailed cutting of shells



    We present a method for simulating highly detailed cutting and fracturing of thin shells using low-resolution simulation meshes. Instead of refining or remeshing the underlying simulation domain to resolve complex cut paths, we adapt the extended finite element method (XFEM) and enrich our approximation by customdesigned basis functions, while keeping the simulation mesh unchanged. The enrichment functions are stored in enrichment textures, which allows for fracture and cutting discontinuities at a resolution much finer than the underlying mesh, similar to image textures for increased visual resolution. Furthermore, we propose harmonic enrichment functions to handle multiple, intersecting, arbitrarily shaped, progressive cuts per element in a simple and unified framework. Our underlying shell simulation is based on discontinuous Galerkin (DG) FEM, which relaxes the restrictive requirement of C1 continuous basis functions and thus allows for simpler, C0 continuous XFEM enrichment functions.


    1. Abdelaziz, Y., and Hamouine, A. 2008. A survey of the extended finite element. Computers and Structures 86, 11–12, 1141–1151. Google ScholarDigital Library
    2. Arnold, D. N., Brezzi, F., Cockburn, B., and Marini, L. D. 2001. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 5, 1749–1779. Google ScholarDigital Library
    3. Babuska, I., and Melenk, J. M. 1996. The partition of unity finite element method: Basic theory and applications. Comput. Meth. Appl. Mech. Eng., Special Issue on Meshless Methods 139, 289–314.Google ScholarCross Ref
    4. Bao, Z., Mo Hong, J., Teran, J., and Fedkiw, R. 2007. Fracturing rigid materials. IEEE Transactions on Visualization and Computer Graphics 13, 2, 370–378. Google ScholarDigital Library
    5. Baraff, D., and Witkin, A. 1998. Large steps in cloth simulation. In Proc. of ACM SIGGRAPH, 43–54. Google ScholarDigital Library
    6. Belytschko, T., and Black, T. 1999. Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Methods Eng. 45, 5, 601–620.Google ScholarCross Ref
    7. Bielser, D., Maiwald, V., and Gross, M. 1999. Interactive cuts through 3-dimensional soft tissue. Computer Graphics Forum (Proc. Eurographics) 18, 3, 31–38.Google ScholarCross Ref
    8. Bolz, J., Farmer, I., Grinspun, E., and Schröder, P. 2003. Sparse matrix solvers on the GPU: conjugate gradients and multigrid. ACM Trans. on Graphics (Proc. SIGGRAPH) 22, 3, 917–924. Google ScholarDigital Library
    9. Bridson, R., Marino, S., and Fedkiw, R. 2003. Simulation of clothing with folds and wrinkles. In Proc. of Symp. on Computer Animation ’03, 28–36. Google ScholarDigital Library
    10. Choi, K.-J., and Ko, H.-S. 2002. Stable but responsive cloth. ACM Trans. on Graphics (Proc. SIGGRAPH) 21, 3, 604–611. Google ScholarDigital Library
    11. Cirak, F., Ortiz, M., and Schröder, P. 2000. Subdivision surfaces: A new paradigm for thin-shell finite-element analysis. Int. J. Numer. Methods Eng. 47, 12, 2039–2072.Google ScholarCross Ref
    12. Cockburn, B. 2003. Discontinuous Galerkin methods. Z. Angew. Math. Mech. 83, 11, 731–754.Google ScholarCross Ref
    13. De Casson, F. B., and Laugier, C. 2000. Simulating 2D tearing phenomena for interactive medical surgery simulators. In Computer Animation 2000, 9–14. Google ScholarDigital Library
    14. Desbenoit, B., Galin, E., and Akkouche, S. 2005. Modeling cracks and fractures. The Visual Computer 21, 8–10, 717–726.Google ScholarCross Ref
    15. English, E., and Bridson, R. 2008. Animating developable surfaces using nonconforming elements. ACM Trans. on Graphics (Proc. SIGGRAPH) 27, 3, 1–5. Google ScholarDigital Library
    16. Forest, C., Delingette, H., and Ayache, N. 2002. Removing tetrahedra from a manifold mesh. In Proc. of IEEE Computer Animation, 225–229. Google ScholarDigital Library
    17. Gingold, Y., Secord, A., Han, J. Y., Grinspun, E., and Zorin, D. 2004. A discrete model for inelastic deformation of thin shells. Tech. rep., Courant Institute of Mathematical Sciences, New York University.Google Scholar
    18. Goldenthal, R., Harmon, D., Fattal, R., Bercovier, M., and Grinspun, E. 2007. Efficient simulation of inextensible cloth. ACM Trans. on Graphics (Proc. SIGGRAPH) 26, 3, 49:1–49:7. Google ScholarDigital Library
    19. Gracie, R., Wang, H., and Belytschko, T. 2008. Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods. Int. J. Numer. Methods Eng. 74, 11, 1645–1669.Google ScholarCross Ref
    20. Grinspun, E., Krysl, P., and Schröder, P. 2002. CHARMS: A Simple Framework for adaptive simulation. ACM Trans. on Graphics (Proc. SIGGRAPH) 21, 3, 281–290. Google ScholarDigital Library
    21. Grinspun, E., Hirani, A. N., Desbrun, M., and Schröder, P. 2003. Discrete shells. In Proc. of Symp. on Computer Animation’03, 62–67. Google ScholarDigital Library
    22. Gu, X., Gortler, S., and Hoppe, H. 2002. Geometry images. ACM Trans. on Graphics (Proc. SIGGRAPH) 21, 3, 355–361. Google ScholarDigital Library
    23. Guo, X., Li, X., Bao, Y., Gu, X., and Qin, H. 2006. Meshless thin-shell simulation based on global conformal parameterization. IEEE Transactions on Visualization and Computer Graphics 12, 3, 375–385. Google ScholarDigital Library
    24. Huang, R., Sukumar, N., and Prévost, J. 2003. Modeling quasi-static crack growth with the extended finite element method — Part II. Int. J. of Solids and Structures 40, 26, 7539–7552.Google ScholarCross Ref
    25. Hughes, T. J. R. 2000. The Finite Element Method. Linear Static and Dynamic Finite Element Analysis. Dover Publications.Google Scholar
    26. Jerabkova, L., and Kuhlen, T. 2009. Stable cutting of deformable objects in virtual environments using the XFEM. IEEE Computer Graphics and Applications 29, 2, 61–71. Google ScholarDigital Library
    27. Kaufmann, P., Martin, S., Botsch, M., and Gross, M. 2008. Flexible simulation of deformable models using discontinuous Galerkin FEM. In Proc. of Symp. on Computer Animation, 105–115. Google ScholarDigital Library
    28. Kaufmann, P., Martin, S., Botsch, M., and Gross, M. 2009. Implementation of discontinuous Galerkin Kirchhoff-Love shells. Tech. Rep. no. 622, Department of Computer Science, ETH Zurich.Google Scholar
    29. Martin, S., Kaufmann, P., Botsch, M., Wicke, M., and Gross, M. 2008. Polyhedral finite elements using harmonic basis functions. Computer Graphics Forum (Proc. of Symp. on Geometry Processing) 27, 5, 1521–1529. Google ScholarDigital Library
    30. Moës, N., Dolbow, J., and Belytschko, T. 1999. A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46, 1, 131–150.Google ScholarCross Ref
    31. Moës, N., Gravouil, A., and Belytschko, T. 2002. Nonplanar 3d crack growth by the extended finite element and level sets – Part I. Int. J. Numer. Methods Eng. 53, 11, 2549–2568.Google ScholarCross Ref
    32. Molino, N., Bao, Z., and Fedkiw, R. 2004. A virtual node algorithm for changing mesh topology during simulation. ACM Trans. on Graphics (Proc. SIGGRAPH) 23, 3, 385–392. Google ScholarDigital Library
    33. Müller, M. 2008. Hierarchical position based dynamics. In Proc. of Virtual Reality Interactions and Physical Simulations.Google Scholar
    34. Noels, L., and Radovitzky, R. 2008. A new discontinuous Galerkin method for Kirchhoff-Love shells. Computer Methods in Applied Mechanics and Engineering 197, 2901–2929.Google ScholarCross Ref
    35. Noels, L. 2009. A discontinuous Galerkin formulation of nonlinear Kirchhoff-Love shells. Int. J. Numer. Methods Eng. 78, 3, 296–323.Google ScholarCross Ref
    36. O’Brien, J. F., and Hodgins, J. K. 1999. Graphical modeling and animation of brittle fracture. In Proc. of ACM SIGGRAPH, 137–146. Google ScholarDigital Library
    37. O’Brien, J. F., Bargteil, A. W., and Hodgins, J. K. 2002. Graphical modeling and animation of ductile fracture. ACM Trans. on Graphics (Proc. SIGGRAPH) 21, 3, 291–294. Google ScholarDigital Library
    38. Pauly, M., Keiser, R., Adams, B., Dutre, P., Gross, M., and Guibas, L. J. 2005. Meshless animation of fracturing solids. ACM Trans. on Graphics (Proc. SIGGRAPH) 24, 3, 957–964. Google ScholarDigital Library
    39. Réthoré, J., Gravouil, A., and Combescure, A. 2005. An energy-conserving scheme for dynamic crack growth using the extended finite element method. Int. J. Numer. Methods Eng. 63, 5, 631–659.Google ScholarCross Ref
    40. Sethian, J. 1999. Level Set Methods and Fast Marching Methods. Cambridge University Press.Google Scholar
    41. Sifakis, E., Der, K. G., and Fedkiw, R. 2007. Arbitrary cutting of deformable tetrahedralized objects. In Proc. of Symp. on Computer Animation, 73–80. Google ScholarDigital Library
    42. Stazi, F. L., Budyn, E., Chessa, J., and Belytschko, T. 2003. An extended finite element method with higher-order elements for curved cracks. Comput. Mech. 31, 1, 38–48.Google ScholarCross Ref
    43. Steinemann, D., Otaduy, M. A., and Gross, M. 2006. Fast arbitrary splitting of deforming objects. In Proc. of Symp. on Computer Animation, 63–72. Google ScholarDigital Library
    44. Terzopoulos, D., and Fleischer, K. 1988. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. In Proc. of ACM SIGGRAPH, 269–278. Google ScholarDigital Library
    45. Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K. 1987. Elastically deformable models. In Proc. of ACM SIGGRAPH, 205–214. Google ScholarDigital Library
    46. Thomaszewski, B., Wacker, M., and Strasser, W. 2006. A consistent bending model for cloth simulation with corotational subdivision finite elements. In Proc. of Symp. on Computer Animation, 107–116. Google ScholarDigital Library
    47. Toledo, S., Chen, D., and Rotkin, V., 2003. Taucs: A library of sparse linear solvers. http://www.tau.ac.il/~stoledo/taucs.Google Scholar
    48. Wempner, G., and Talaslidis, D. 2003. Mechanics of solids and shells: theories and approximations. CRC Press.Google Scholar
    49. Wicke, M., Steinemann, D., and Gross, M. 2005. Efficient animation of point-sampled thin shells. Computer Graphics Forum (Proc. Eurographics) 24, 667–676.Google ScholarCross Ref
    50. Wicke, M., Botsch, M., and Gross, M. 2007. A finite element method on convex polyhedra. Computer Graphics Forum (Proc. Eurographics) 26, 3, 355–364.Google ScholarCross Ref
    51. Zi, G., and Belytschko, T. 2003. New crack-tip elements for XFEM and applications to cohesive cracks. Int. J. Numer. Methods Eng. 57, 15, 2221–2240.Google ScholarCross Ref

ACM Digital Library Publication:

Overview Page: