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Combining Finite Element Method and L-Systems Using Natural Information Flow Propagation to Simulate Growing Dynamical Systems

  • Jean-Philippe Bernard
  • Benjamin Gilles
  • Christophe Godin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8890)

Abstract

This paper shows how to solve a system of differential equations controlling the development of a dynamical system based on finite element method and L-Systems. Our methods leads to solve a linear system of equations by propagating the flow of information throughout the structure of the developing system in a natural way. The method is illustrated on the growth of a branching system whose axes bend under their own weight.

Keywords

Finite Element Method Integration Point Generalize Curvature Finite Element Method Model Cholesky Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Allen, M., Prusinkiewicz, P., DeJong, T.M.: Using L-systems for modeling source-sink interactions, architecture and physiology of growing trees: the L-PEACH Model. New Phyotologist 166, 869–880 (2005)CrossRefGoogle Scholar
  2. 2.
    Bathe, K.: Finite Element Procedures. Prentice Hall (1996)Google Scholar
  3. 3.
    Boudon, F., Pradal, C., Cokelaer, T., Prusinkiewicz, P., Godin, C.: L-Py: an L-system simulation framework for modeling plant architecture development base on a dynamic language. Frontiers in Plant Science 3(76) (2012)Google Scholar
  4. 4.
    Chou, P.C., Pagano, N.J.: Elasticity: tensor, dyadic, and engineering approaches. Courier Dover Publications (1992)Google Scholar
  5. 5.
    Costes, E., Smith, C., Renton, M., Guédon, Y., Prusinkiewicz, P., Godin, C.: MAppleT: simulation of apple tree development using mixed stochastic and biomechanical models. Functional Plant Biology 35(10) (2008)Google Scholar
  6. 6.
    Featherstone, R.: Efficient Factorization of the Joint-Space Inertia Matrix for Branched Kinematic Trees. The International Journal of Robotics Research 24(6), 487–500 (2005)CrossRefGoogle Scholar
  7. 7.
    Federl, P., Prusinkiewicz, P.: Solving differential equations in developmental models of multicellular structures expressed using L-systems. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2004. LNCS, vol. 3037, pp. 65–72. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Godin, C., Sinoquet, H.: Functional-structural plant modelling. The New Phytologist 166(3), 705–708 (2005)CrossRefGoogle Scholar
  9. 9.
    Hemmerling, R., Evers, J.B., Smoleňova, K., Buck-Sorlin, G., Kurth, W.: Extension of the GroIMP modelling platform to allow easy specification of differential equations describing biological processes within plant models. Computers and Electronics in Agriculture 92(C), 1–8 (2013)CrossRefGoogle Scholar
  10. 10.
    Jirasek, C., Prusinkiewicz, P., Moulia, B.: Integrating biomechanics into developmental plant models expressed using L-systems. Plant Biomechanics 24(9), 614–624 (2000)Google Scholar
  11. 11.
    Peiró, J., Sherwin, S.: Finite Difference, Finite Element and Finite Volume Methods for Partial Differential Equations. In: Springer Netherlands Handbook of Materials Modeling, Dordrecht, pp. 2415–2446 (2005)Google Scholar
  12. 12.
    Press, W.H., Teukolsky, S.A., Vettering, W.T., Flannery, B.P.: Numerical Recipes: The art of scientific computing. Cambridge University Press (1987)Google Scholar
  13. 13.
    Prusinkiewicz, P.: Geometric modeling without coordinates and indices. In: IEEE Computer Society Proceedings of the IEEE Shape Modeling International, pp. 3–4 (2002)Google Scholar
  14. 14.
    Prusinkiewicz, P.: Modeling plant growth and development. Modeling plant growth and development 7(1), 79–83 (2004)Google Scholar
  15. 15.
    Prusinkiewicz, P., Allen, M., Escobar-Gutierrez, A., DeJong, T.M.: Numerical methods for transport-resistance sink-source allocation models. Frontis 22, 123–137 (2007)Google Scholar
  16. 16.
    Prusinkiewicz, P. and Lindenmayer, A.: The algorithmic beauty of plants. Springer (1990)Google Scholar
  17. 17.
    Prusinkiewicz, P., Runions, A.: Computational models of plant development and form. The New Phytologist 193(3), 549–569 (2012)CrossRefGoogle Scholar
  18. 18.
    Taylor-Hell, J.: Incorporating biomechanics into architectural tree models. In: 18th Brazilian Symposium on Computer Graphics and Image Processing, SIBGRAPI 2005. IEEE (2005)Google Scholar
  19. 19.
    Vos, J., Evers, J.B., Buck-Sorlin, G.H., Andrieu, B., Chelle, M., de Visser, P.H.B.: Functional-structural plant modelling: a new versatile tool in crop science. Journal of Experimental Botany 61(8), 2101–2115 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jean-Philippe Bernard
    • 1
  • Benjamin Gilles
    • 2
  • Christophe Godin
    • 1
  1. 1.Inria, Virtual Plants Project-TeamUniversité Montpellier 2Montpellier Cedex 5France
  2. 2.CNRS, Laboratoire d’Informatique, de Robotique et de Microélectronique de MontpellierUniversité Montpellier 2Montpellier Cedex 5France

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