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A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects

Published:26 July 2019Publication History
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Abstract

We present a unified method to simulate deformable elastic bodies consisting of mixed-dimensional components represented with potentially non-manifold simplicial meshes. Building on well-known simplicial rod, shell, and solid models for elastic continua, we categorize and define a comprehensive palette expressing all possible constraints and elastic energies for stiff and flexible connections between the 1D, 2D, and 3D components of a single conforming simplicial mesh. This palette consists of three categories: point connections, in which simplices meet at a single vertex around which they may twist and bend; curve connections in which simplices share an edge around which they may rotate (bend) relative to one another; and surface connections, in which a shell is embedded on or into a solid. To define elastic behaviors across non-manifold point connections, we adapt and apply parallel transport concepts from elastic rods. To address discontinuous forces that would otherwise arise when large accumulated relative rotations wrap around in the space of angles, we develop an incremental angle-update strategy. Our method provides a conceptually simple, flexible, and highly expressive framework for designing complex elastic objects, by modeling the geometry with a single simplicial mesh and decorating its elements with appropriate physical models (rod, shell, solid) and connection types (point, curve, surface). We demonstrate a diverse set of possible interactions achievable with our method, through technical and application examples, including scenes featuring complex aquatic creatures, children's toys, and umbrellas.

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References

  1. Christopher Batty, Andres Uribe, Basile Audoly, and Eitan Grinspun. 2012. Discrete viscous sheets. ACM Trans. Graph. (SIGGRAPH) 31, 4 (2012), 113. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. G. Beer. 1985. An isoparametric joint/interface element for finite element analysis. Internat. J. Numer. Methods Engrg. 21, 4 (1985), 585--600.Google ScholarGoogle ScholarCross RefCross Ref
  3. Miklos Bergou, Basile Audoly, Etienne Vouga, Max Wardetzky, and Eitan Grinspun. 2010. Discrete viscous threads. ACM Trans. Graph. (SIGGRAPH) 29, 4 (2010), 116. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Miklos Bergou, Max Wardetzky, Stephen Robinson, Basile Audoly, and Eitan Grinspun. 2008. Discrete elastic rods. ACM Trans. Graph. (SIGGRAPH) 27, 3 (2008), 63. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Florence Bertails, Basile Audoly, Marie-Paule Cani, Frédéric Leroy, Bernard Querleux, and Jean-Luc Lévêque. 2006. Super-helices for predicting the dynamics of natural hair. ACM Trans. Graph. (SIGGRAPH) 25, 3 (jul 2006), 1180--1187. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Robert Bridson, Ronald Fedkiw, and John Anderson. 2002. Robust treatment of collisions, contact and friction for cloth animation. ACM Trans. Graph. (SIGGRAPH) 21, 3 (2002), 594--603. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Nuttapong Chentanez, Ron Alterovitz, Daniel Ritchie, Lita Cho, Kris K. Hauser, Ken Goldberg, Jonathan R. Shewchuk, and James F. O'Brien. 2009. Interactive simulation of surgical needle insertion and steering. ACM Trans. Graph. (SIGGRAPH) 28, 3 (2009), 88. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Fehmi Cirak and Quan Long. 2011. Subdivision shells with exact boundary control and non-manifold geometry. Int. J. Numer. Methods Eng. 88, 9 (2011), 897--923.Google ScholarGoogle ScholarCross RefCross Ref
  9. Ye Fan, Joshua Litven, David I. W. Levin, and Dinesh K. Pai. 2013. Eulerian-on-Lagrangian simulation. ACM Trans. Graph. (SIGGRAPH) 32, 3 (2013), 22. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. François Faure, Benjamin Gilles, Guillaume Bousquet, and Dinesh K. Pai. 2011. Sparse meshless models of complex deformable solids. ACM Trans. Graph. (SIGGRAPH) 30, 4 (2011), 73. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Benjamin Gilles, Guillaume Bousquet, François Faure, and Dinesh K. Pai. 2011. Frame-based elastic models. ACM Trans. Graph. 30, 2 (2011), 15. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Yotam Gingold, Adrian Secord, Jefferson Y. Han, Eitan Grinspun, and Denis Zorin. 2004. A discrete model for inelastic deformation of thin shells. Technical Report. New York University. 12 pages.Google ScholarGoogle Scholar
  13. Eitan Grinspun, Anil N. Hirani, Peter Schröder, and Mathieu Desbrun. 2003. Discrete shells. In Symposium on Computer Animation. Eurographics Association, 62--67. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. Paul M Isaacs and Michael F Cohen. 1987. Controlling dynamic simulation with kinematic constraints. ACM SIGGRAPH 21, 4 (1987), 215--224. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. T. Kugelstadt and E. Schömer. 2016. Position and orientation based Cosserat rods. In Symposium on Computer Animation. 169--178. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Faming Li, Xiaowu Chen, Lin Wang, and Qinping Zhao. 2014. Canopy-frame interactions for umbrella simulation. Computers and Graphics 38 (2014), 320--327. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Minchen Li, Ming Gao, Timothy Langlois, Chenfanfu Jiang, and Danny M. Kaufman. 2019. Decomposed Optimization Time Integrator for Large-Step Elastodynamics. ACM Trans. Graph. (SIGGRAPH) 31 (2019). Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Miles Macklin, Matthias Müller, Nuttapong Chentanez, and Tae-Yong Kim. 2014. Unified particle physics for real-time applications. ACM Trans. Graph. (SIGGRAPH) 33, 4 (2014), 153. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Sebastian Martin, Peter Kaufmann, Mario Botsch, Eitan Grinspun, and Markus Gross. 2010. Unified simulation of elastic rods, shells, and solids. ACM Trans. Graph. (SIGGRAPH) 29, 4 (2010), 39. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Matthias Müller and Nuttapong Chentanez. 2011. Solid simulation with oriented particles. ACM Trans. Graph. (SIGGRAPH) 30, 4 (2011), 92. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Matthias Müller, Bruno Heidelberger, Marcus Hennix, and John Ratcliff. 2007. Position based dynamics. Journal of Visual Communication and Image Representation 18, 2 (2007), 109--118.Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. James F. O'Brien and Jessica K. Hodgins. 1999. Graphical modeling and animation of brittle fracture. In SIGGRAPH. ACM Press/Addison-Wesley Publishing Co., 137--146. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. Jesús Pérez, Miguel A. Otaduy, and Bernhard Thomaszewski. 2017. Computational design and automated fabrication of kirchhoff-plateau surfaces. ACM Trans. Graph. (SIGGRAPH) 36, 4 (jul 2017), 1--12. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. 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. 34, 4, Article 138 (July 2015), 12 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. John C Platt and Alan H Barr. 1988. Constraint methods for flexible models. SIGGRAPH 22, 4 (1988), 279--288. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Olivier Rémillard and Paul G. Kry. 2013. Embedded thin shells for wrinkle simulation. ACM Trans. Graph. (SIGGRAPH) 32, 4 (2013), 50. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. J. C.J. Schellekens and René De Borst. 1993. On the numerical integration of interface elements. Internat. J. Numer. Methods Engrg. 36, 1 (1993), 43--66.Google ScholarGoogle ScholarCross RefCross Ref
  28. Eftychios Sifakis, Tamar Shinar, Geoffrey Irving, and Ron Fedkiw. 2007. Hybrid simulation of deformable solids. In Symposium on Computer Animation. 81--90. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Jonas Spillmann and Matthias Teschner. 2007. CORDE: Cosserat rod elements for the dynamic simulation of one-dimensional elastic objects. In Symposium on Computer Animation. 63--72. Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. Jonas Spillmann and Matthias Teschner. 2009. Cosserat nets. IEEE TVCG 15, 2 (2009), 325--338. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. Jos Stam. 2009. Nucleus: Towards a unified dynamics solver for computer graphics. In Computer-Aided Design and Computer Graphics. 1--11.Google ScholarGoogle Scholar
  32. Maxime Tournier, Matthieu Nesme, Benjamin Gilles, and Francois Faure. 2015. Stable constrained dynamics. ACM Trans. Graph. (SIGGRAPH) 34, 4 (2015), 132. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. Christopher D. Twigg and Zoran Kacic-Alesic. 2010. Point cloud glue: Constraining simulations using the Procrustes transform. In Symposium on Computer Animation. 45--54. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Nobuyuki Umetani, Ryan Schmidt, and Jos Stam. 2014. Position-based elastic rods. (2014), 21--30 pages. https://dl.acm.org/citation.cfm?id=2849522 Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. Nicholas J. Weidner, Kyle Piddington, David I. W. Levin, and Shinjiro Sueda. 2018. Eulerian-on-lagrangian cloth simulation. ACM Trans. Graph. (SIGGRAPH) 37, 4 (jul 2018), 1--11. Google ScholarGoogle ScholarDigital LibraryDigital Library
  36. Jane Wilhelms. 1987. Using dynamic analysis for realistic animation of articulated bodies. IEEE Computer Graphics and Applications 7, 6 (1987), 12--27. Google ScholarGoogle ScholarDigital LibraryDigital Library
  37. Andrew Witkin, Kurt Fleischer, and Alan Barr. 1988. Energy constraints on parameterized models. In SIGGRAPH. 225--232. Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. Hongyi Xu, Espen Knoop, Stelian Coros, and Moritz Bächer. 2018. Bend-it: Design and Fabrication of Kinetic Wire Characters. ACM Trans. Graph. 37, 6, Article 239 (Dec. 2018), 15 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. Bo Zhu, Minjae Lee, Ed Quigley, and Ronald Fedkiw. 2015. Codimensional non-Newtonian fluids. ACM Trans. Graph. (SIGGRAPH) 34, 4 (2015), 115. Google ScholarGoogle ScholarDigital LibraryDigital Library
  40. Bo Zhu, Ed Quigley, Matthew Cong, Justin Solomon, and Ronald Fedkiw. 2014. Codimensional surface tension flow on simplicial complexes. ACM Trans. Graph. (SIGGRAPH) 33, 4 (2014), 111. Google ScholarGoogle ScholarDigital LibraryDigital Library

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    • Published in

      cover image Proceedings of the ACM on Computer Graphics and Interactive Techniques
      Proceedings of the ACM on Computer Graphics and Interactive Techniques  Volume 2, Issue 2
      July 2019
      239 pages
      EISSN:2577-6193
      DOI:10.1145/3352480
      Issue’s Table of Contents

      Copyright © 2019 ACM

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 26 July 2019
      Published in pacmcgit Volume 2, Issue 2

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