“Non-Smooth Developable Geometry for Interactively Animating Paper Crumpling” by Schreck, Rohmer, Hahmann, Cani, Jin, et al. …

  • ©Camille Schreck, Damien Rohmer, Stefanie Hahmann, Marie-Paule Cani, Shuo  Jin, Charlie C. L. Wang, and Jean-Francis Bloch




    Non-Smooth Developable Geometry for Interactively Animating Paper Crumpling

Session/Category Title:   PHYSICAL PHENOMENA




    We present the first method to animate sheets of paper at interactive rates, while automatically generating a plausible set of sharp features when the sheet is crumpled. The key idea is to interleave standard physically based simulation steps with procedural generation of a piecewise continuous developable surface. The resulting hybrid surface model captures new singular points dynamically appearing during the crumpling process, mimicking the effect of paper fiber fracture. Although the model evolves over time to take these irreversible damages into account, the mesh used for simulation is kept coarse throughout the animation, leading to efficient computations. Meanwhile, the geometric layer ensures that the surface stays almost isometric to its original 2D pattern. We validate our model through measurements and visual comparison with real paper manipulation, and show results on a variety of crumpled paper configurations.


    1. M. B. Amar and Y. Pomeau. 1997. Crumpled paper. In Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences.Google Scholar
    2. P. Bo and W. Wang. 2007. Geodesic-controlled developable surfaces for modeling paper bending. Computer Graphics Forum (CGF) 26, 3.Google ScholarCross Ref
    3. S. Bouaziz, M. Deuss, Y. Schwartzburg, T. Weise, and M. Pauly. 2012. Shape-up: Shaping discrete geometry with projections. Computer Graphics Forum (CGF) 31, 5 (Aug.), 1657–1667. Google ScholarDigital Library
    4. R. Bridson, R. Fedkiw, and J. Anderson. 2002. Robust treatment of collisions, contact and friction for cloth animation. ACM Trans. Graph. 21, 3 (July). Google ScholarDigital Library
    5. R. Bridson, R. Marino, and R. Fedkiw. 2003. Simulation of clocloth with folds and wrinkles. In Proceedings of the Symposium on Computer Animation (SCA). Google ScholarDigital Library
    6. C. Bronkhorst. 2003. Modelling paper as a two-dimensional elastic-plastic stochastic network. International Journal of Solids and Structures 40.Google Scholar
    7. R. Burgoon, E. Grinspun, and Z. Wood. 2006. Discrete shells origami. In Proceedings of Computers and Their Applications, 180–187.Google Scholar
    8. A. D. Cambou and N. Menon. 2011. Three-dimensional structure of a sheet crumpled into a ball. Proceedings of the National Academy of Sciences.Google Scholar
    9. E. Cerda and L. Mahadevan. 1998. Conical surfaces and crescent singularities in crumpled sheets. Physical Review Letters 80, 11.Google ScholarCross Ref
    10. C.-H. Chu and C. H. Séquin. 2002. Developable Bézier patches: Properties and design. Computer-Aided Design 34, 7, 511–527.Google ScholarCross Ref
    11. D. W. Coffin. 2009. Developing a deeper understanding of the constitutive behavior of paper. In Advances in Pulp and Paper Research, Transactions of the 14th Fundamental Research Symposium (Oxford, UK), S. J. l’Anson, Ed., 841–876.Google Scholar
    12. P. Decaudin, D. Julius, J. Wither, L. Boissieux, A. Sheffer, and M.-P. Cani. 2006. Virtual garments: A fully geometric approach for cloth design. Computer Graphics Forum (CGF) (Proc. of Eurographics) 25, 3.Google ScholarCross Ref
    13. E. English and R. Bridson. 2008. Animating developable surface using nonconforming elements. ACM Trans. Graph. (Proc. of SIGGRAPH) 27, 3. Google ScholarDigital Library
    14. W. H. Frey. 2004. Modeling buckled developable surfaces by triangulation. Computer Aided Design 36.Google Scholar
    15. Y. Gingold, A. Secord, J. Y. Han, E. Grinspun, and D. Zorin. 2004. A discrete model for inelastic deformation of thin shells. Technical Report.Google Scholar
    16. E. Grinspun, A. N. Hirani, M. Desbrun, and P. Shröder. 2003. Discrete shells. In Proceedings of the Symposium on Computer Animation (SCA) 27, 62–67. Google ScholarDigital Library
    17. D. Harmon, E. Vouga, R. Tamstorf, and E. Grinspun. 2008. Robust treatment of simultaneous collisions. ACM Trans. Graph. (Proc. of SIGGRAPH) 27, 3, 1–4. Google ScholarDigital Library
    18. D. Julius, V. Kraevoy, and A. Sheffer. 2005. D-charts: Quasidevelopable mesh segmentation. Computer Graphics Forum (CGF) (Proc. of Eurographics).Google Scholar
    19. Y.-M. Kang, H.-G. Zhang, and H.-G. Cho. 2009. Plausible virtual paper for real-time application. Computer Animation and Social Agents (CASA), Short Paper.Google Scholar
    20. Y. Kergosien, H. Gotoda, and T. Kunii. 1994. Bending and creasing virtual paper. IEEE Computer Graphics and Applications 14, 1. Google ScholarDigital Library
    21. M. Kilian, S. Floery, Z. Chen, N. Mitra, A. Sheffer, and H. Pottmann. 2008. Curved folding. ACM Trans. Graph. (Proc. of SIGGRAPH) 27, 3. Google ScholarDigital Library
    22. S. Leopoldseder and H. Pottmann. 1998. Approximation of developable surfaces with cone spline surfaces. Computer Aided Design 30.Google Scholar
    23. T. Liu, A. Bargtiel, J. O’Brien, and L. Kavan. 2013. Fast simulation of mass-spring systems. ACM Trans. Graph. (Proc. of SIGGRAPH Asia) 32, 6. Google ScholarDigital Library
    24. Y. Liu, H. Pottmann, J. Wallner, Y.-L. W. Wang, and W. Wang. 2006. Geometric modeling with conical meshes and developable surfaces. ACM Trans. Graph. (Proc. of SIGGRAPH Asia). Google ScholarDigital Library
    25. L. Mahadevan and E. Cerda. 1998. Conical surfaces and crescent singularities in crumpled sheets. Physical Review Letters 80, 11.Google Scholar
    26. P. Makela and S. Ostlund. 2003. Cohesive crack modelling of thin sheet material exhibiting anisotropy, plasticity and large-scale damage evolution. Intern. J. Solids Structures 40, 21.Google Scholar
    27. J. Mitani and T. Igarashi. 2011. Interactive design of planar curved folding by reflection. Pacific Graphics (short paper).Google Scholar
    28. R. Narain, T. Pfaff, and J. F. O’Brien. 2013. Folding and crumpling adaptive sheets. ACM Trans. Graph. (Proc. of SIGGRAPH) 32, 4. Google ScholarDigital Library
    29. R. Narain, A. Samii, and J. F. O’Brien. 2012. Adaptive anisotropic remeshing for cloth simulation. ACM Trans. Graph. (Proc. of SIGGRAPH Asia) 31, 6. Google ScholarDigital Library
    30. M. Peternell. 2004. Developable surface fitting to point clouds. Comput. Aided Geom. Des. 21, 8 (Oct.), 785–803. Google ScholarDigital Library
    31. H. Pottman, Q. Huang, B. Deng, A. Schiftner, M. Kilian, L. Guibas, and J. Wallner. 2010. Geodesic patterns. ACM Trans. Graph. 29, 4, 43:1–43:10. Google ScholarDigital Library
    32. H. Pottman and J. Wallner. 2001. Computational Line Geometry. Springer. Google ScholarDigital Library
    33. X. Provot. 1996. Deformation constraints in a mass-spring model to describe rigid cloth behavior. Graphics Interface, 147–154.Google Scholar
    34. D. Rohmer, M.-P. Cani, S. Hahmann, and Boris Thibert. 2011. Folded paper geometry from 2D pattern and 3D contour. Eurographics Short Paper, 21–24.Google Scholar
    35. D. Rohmer, T. Popa, M.-P. Cani, S. Hahmann, and A. Sheffer. 2010. Animation wrinkling: Augmenting coarse cloth simulations with realistic-looking wrinkles. ACM Trans. Graph. (Proc. of SIGGRAPH Asia) 29, 5. Google ScholarDigital Library
    36. K. Rose, A. Sheffer, J. Wither, M.-P. Cani, and B. Thibert. 2007. Developable surfaces from arbitrary sketched boundaries. In Proceedings of the Symposium on Geometry Processing (SGP). Google ScholarDigital Library
    37. R. D. Schroll, E. Katifori, and B. Davidovitch. 2011. Elastic building blocks for confined sheets. Physical Review Letters 106.Google Scholar
    38. T. J. Simnett, S. D. Laycock, and A. M. Day. 2009. An edge-based approach to adaptively refining a mesh for cloth deformation. In Proceedings of TPCG. 77–84.Google Scholar
    39. J. Solomon, E. Vouga, M. Wardetzky, and E. Grinspun, 2012. Flexible developable surfaces. Computer Graphics Forum (CGF), Proc. of Symposium on Geometry Processing (SGP) 31, 5. Google ScholarDigital Library
    40. B. Steenberg. 1947. Svensk papperstidn. Pappers 50, 6, 127–140.Google Scholar
    41. T. Tachi. 2010. Origamizing polyhedral surfaces. IEEE Transactions on Visualization and Computer Graphics 16, 2, 298–311. Google ScholarDigital Library
    42. M. Tang, D. Manocha, and R. Tong. 2010. Fast continuous collision detection using deforming non-penetration filters. In Proceedings of the Symposium on Interactive 3D Graphics and Games. Google ScholarDigital Library
    43. J.-L. Thorpe and J.-L. 1981. Paper as an orthotropic thin plate. In Proceedings of TAPPI 3, 119–121.Google Scholar
    44. C. Wang. 2008a. Computing length-preserved free boundary for quasi-developable mesh segmentation. IEEE Transactions on Visualization and Computer Graphics 14, 1, 25–36. Google ScholarDigital Library
    45. C. Wang. 2008b. Towards flattenable mesh surfaces. Comput. Aided Des. 40, 1, 109–122. Google ScholarDigital Library
    46. C. Wang and K. Tang. 2004. Achieving developability of a polygonal surface by minimum deformation: A study of global and local optimization approaches. The Visual Computer 20, 8, 521–539. Google ScholarDigital Library
    47. H. Wang, J. F. O’Brien, and R. Ramamoorthi. 2010. Multiresolution isotropic strain limiting. ACM Trans. Graph. (Proc. of SIGGRAPH Asia) 29, 6, 160. Google ScholarDigital Library
    48. T. Witten. 2007. Stress focusing in elastic sheets. Review of Modern Physics 79.Google Scholar
    49. L. Zhu, T. Igarashi, and J. Mitani. 2013. Soft folding. Computer Graphics Forum (Proc. of Pacific Graphics) 32, 7, 167–176.Google ScholarCross Ref

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