skip to main content
research-article
Public Access

Interactive Two-Way Shape Design of Elastic Bodies

Published:25 July 2018Publication History
Skip Abstract Section

Abstract

We present a novel system for interactive elastic shape design in both forward and inverse fashions. Using this system, the user can choose to edit the rest shape or the quasistatic shape of an elastic solid, and obtain the other shape that matches under the quasistatic equilibrium condition at the same time. The development of this system is based on the discovery that inverse quasistatic simulation can be immediately solved by Newton's method with a direct solver. To implement our simulator, we propose a Jacobian matrix evaluation scheme for the inverse elastic problem and we present step length and matrix evaluation techniques that improve the simulation performance. While our simulator is efficient, it is still not fast enough for the system to generate the result in real time. Our solution is a shape initialization method using the recent projective dynamics technique. Shape initialization not only works as a fast preview function during the user editing process, but also speeds up the convergence of quasistatic or inverse quasistatic simulation afterwards. The use of a heterogeneous algorithm structure allows the system to further reduce its preview cost, by utilizing the power of both the CPU and the GPU. Our experiment demonstrates that the whole system is fast, robust, and convenient for the designer to use in both forward and inverse elastic shape design. It can handle a variety of nonlinear elastic material models, and its runtime performance has space for more improvement.

References

  1. Aric Bartle, Alla Sheffer, Vladimir G. Kim, Danny M. Kaufman, Nicholas Vining, and Floraine Berthouzoz. 2016. Physics-driven Pattern Adjustment for Direct 3D Garment Editing. ACM Trans. Graph. (SIGGRAPH) 35, 4, Article 50 (July 2016), 11 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Bernd Bickel, Peter Kaufmann, Mélina Skouras, Bernhard Thomaszewski, Derek Bradley, Thabo Beeler, Phil Jackson, Steve Marschner, Wojciech Matusik, and Markus Gross. 2012. Physical Face Cloning. ACM Trans. Graph. (SIGGRAPH) 31, 4, Article 118 (July 2012), 118:1--118:10 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Marc Bonnet and A. Constantinescu. 2005. Inverse problems in elasticity. Inverse Problems 21, 2 (2005), R1-R50.Google ScholarGoogle ScholarCross RefCross Ref
  4. Sofien Bouaziz, Sebastian Martin, Tiantian Liu, Ladislav Kavan, and Mark Pauly. 2014. Projective Dynamics: Fusing Constraint Projections for Fast Simulation. ACM Trans. Graph. (SIGGRAPH) 33, 4, Article 154 (July 2014), 11 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Xiang Chen, Changxi Zheng, Weiwei Xu, and Kun Zhou. 2014. An Asymptotic Numerical Method for Inverse Elastic Shape Design. ACM Trans. Graph. (SIGGRAPH) 33, 4, Article 95 (July 2014), 11 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Alicia Cordero, José L. Hueso, Eulalia Martínez, and Juan R. Torregrosa. 2010. New Modifications of Potra-PtáK's Method with Optimal Fourth and Eighth Orders of Convergence. J. Comput. Appl. Math. 234, 10 (Sept. 2010), 2969--2976. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Stelian Coros, Sebastian Martin, Bernhard Thomaszewski, Christian Schumacher, Robert Sumner, and Markus Gross. 2012. Deformable Objects Alive! ACM Trans. Graph. (SIGGRAPH) 31, 4, Article 69 (July 2012), 9 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Alexandre Derouet-Jourdan, Florence Bertails-Descoubes, Gilles Daviet, and Joëlle Thollot. 2013. Inverse Dynamic Hair Modeling with Frictional Contact. ACM Trans. Graph. (SIGGRAPH Asia) 32, 6, Article 159 (Nov. 2013), 10 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Marco Fratarcangeli, Valentina Tibaldo, and Fabio Pellacini. 2016. Vivace: a Practical Gauss-Seidel Method for Stable Soft Body Dynamics. ACM Trans. Graph. (SIGGRAPH Asia) 35, 6 (Nov. 2016), 214:1--214:9. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Sunil Hadap. 2006. Oriented Strands: Dynamics of Stiff Multi-body System. In Proceedings of SCA. 91--100. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Ryo Kikuuwe, Hiroaki Tabuchi, and Motoji Yamamoto. 2009. An Edge-based Computationally Efficient Formulation of Saint Venant-Kirchhoff Tetrahedral Finite Elements. ACM Trans. Graph. 28, 1, Article 8 (Feb. 2009), 13 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Tae-Yong Kim, Nuttapong Chentanez, and Matthias Müller-Fischer. 2012. Long Range Attachments - A Method to Simulate Inextensible Clothing in Computer Games. In Proceedings of SCA. 305--310. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. Tiantian Liu, Adam W. Bargteil, James F. O'Brien, and Ladislav Kavan. 2013. Fast Simulation of Mass-Spring Systems. ACM Transactions on Graphics 32, 6 (Nov. 2013), 209:1--7. http://cg.cis.upenn.edu/publications/Liu-FMS Proceedings of ACM SIGGRAPH Asia 2013, Hong Kong. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. Tiantian Liu, Sofien Bouaziz, and Ladislav Kavan. 2016. Towards Real-time Simulation of Hyperelastic Materials. arXiv preprint arXiv:1604.07378 (2016).Google ScholarGoogle Scholar
  15. Matthias Müller. 2008. Hierarchical Position Based Dynamics. In Proceedings of VRIPHYS. 1--10.Google ScholarGoogle Scholar
  16. Matthias Müller, N. Chentanez, T.Y. Kim, and M. Macklin. 2014. Strain Based Dynamics. In Proceedings of SCA. 21--23.Google ScholarGoogle Scholar
  17. Matthias Müller, Bruno Heidelberger, Matthias Teschner, and Markus Gross. 2005. Meshless Deformations Based on Shape Matching. ACM Trans. Graph. (SIGGRAPH) 24, 3 (July 2005), 471--478. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. James F. O'Brien, Adam W. Bargteil, and Jessica K. Hodgins. 2002. Graphical modeling and animation of ductile fracture. ACM Trans. Graph. (SIGGRAPH) 21, 3 (July 2002), 291--294. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Théodore Papadopoulo and Manolis I. A. Lourakis. 2000. Estimating the Jacobian of the Singular Value Decomposition: Theory and Applications. In Proceedings of the 6th European Conference on Computer Vision-Part I. 554--570. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Jesús Pérez, Bernhard Thomaszewski, Stelian Coros, Bernd Bickel, José A. Canabal, Robert Sumner, and Miguel A. Otaduy. 2015. Design and Fabrication of Flexible Rod Meshes. ACM Trans. Graph. (SIGGRAPH) 34, 4, Article 138 (July 2015), 12 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Xavier Provot. 1996. Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior. In Proceedings of Graphics Interface. 147--154.Google ScholarGoogle Scholar
  22. Alec R. Rivers and Doug L. James. 2007. FastLSM: Fast Lattice Shape Matching for Robust Real-time Deformation. ACM Trans. Graph. (SIGGRAPH) 26, 3, Article 82 (July 2007). Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. Hijung V. Shin, Christopher F. Porst, Etienne Vouga, John Ochsendorf, and Frédo Durand. 2016. Reconciling Elastic and Equilibrium Methods for Static Analysis. ACM Trans. Graph. 35, 2, Article 13 (Feb. 2016), 13:1--13:16 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. Mélina Skouras, Bernhard Thomaszewski, Bernd Bickel, and Markus Gross. 2012. Computational Design of Rubber Balloons. Comput. Graph. Forum 31, 2pt4 (May 2012). Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Mélina Skouras, Bernhard Thomaszewski, Stelian Coros, Bernd Bickel, and Markus Gross. 2013. Computational Design of Actuated Deformable Characters. ACM Trans. Graph. (SIGGRAPH) 32, 4, Article 82 (July 2013), 10 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. J. Teran, S. Blemker, V. Ng Thow Hing, and R. Fedkiw. 2003. Finite Volume Methods for the Simulation of Skeletal Muscle. In Proceedings of SCA. 68--74. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. Joseph Teran, Eftychios Sifakis, Geoffrey Irving, and Ronald Fedkiw. 2005. Robust Quasistatic Finite Elements and Flesh Simulation. In Proceedings of SCA. 181--190. Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. Demetri Terzopoulos, John Platt, Alan Barr, and Kurt Fleischer. 1987. Elastically Deformable Models. SIGGRAPH Comput. Graph. 21, 4 (Aug. 1987), 205--214. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Bernhard Thomaszewski, Simon Pabst, and Wolfgang Strasser. 2009. Continuum-based Strain Limiting. Computer Graphics Forum (Eurographics) 28, 2 (2009), 569--576.Google ScholarGoogle ScholarCross RefCross Ref
  30. Maxime Tournier, Matthieu Nesme, Benjamin Gilles, and François Faure. 2015. Stable Constrained Dynamics. ACM Trans. Graph. (SIGGRAPH) 34, 4, Article 132 (July 2015), 10 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. Christopher D. Twigg and Zoran Kačić-Alesić. 2011. Optimization for Sag-free Simulations. In Proceedings of SCA. 225--236. Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. Bin Wang, Longhua Wu, KangKang Yin, Uri Ascher, Libin Liu, and Hui Huang. 2015. Deformation Capture and Modeling of Soft Objects. ACM Trans. Graph. (SIGGRAPH) 34, 4, Article 94 (July 2015), 12 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. Huamin Wang. 2015. A Chebyshev Semi-iterative Approach for Accelerating Projective and Position-based Dynamics. ACM Trans. Graph. (SIGGRAPH Asia) 34, 6, Article 246 (Oct. 2015), 9 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Huamin Wang, James O'Brien, and Ravi Ramamoorthi. 2010. Multi-resolution isotropic strain limiting. ACM Trans. Graph. (SIGGRAPH Asia) 29, 6, Article 156 (Dec. 2010), 156:1--156:10 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. Huamin Wang and Yin Yang. 2016. Descent Methods for Elastic Body Simulation on the GPU. ACM Trans. Graph. (SIGGRAPH Asia) 35, 6, Article 212 (Nov. 2016), 10 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  36. Hongyi Xu, Funshing Sin, Yufeng Zhu, and Jernej Barbič. 2015. Nonlinear Material Design Using Principal Stretches. ACM Trans. Graph. (SIGGRAPH) 34, 4, Article 75 (July 2015), 11 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Interactive Two-Way Shape Design of Elastic Bodies

    Recommendations

    Comments

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Sign in

    Full Access

    PDF Format

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader
    About Cookies On This Site

    We use cookies to ensure that we give you the best experience on our website.

    Learn more

    Got it!