Advertisement

The Visual Computer

, Volume 28, Issue 6–8, pp 859–868 | Cite as

Realistic animation of interactive trees

  • Shaojun HuEmail author
  • Norishige Chiba
  • Dongjian He
Original Article

Abstract

We present a mathematical model for animating trees realistically by taking into account the influence of natural frequencies and damping ratios. To create realistic motion of branches, we choose three basic mode shapes from the modal analysis of a curved beam, and combine them with a driven harmonic oscillator to approximate Lissajous curve which is observed in pull-and-release test of real trees. The forced vibration of trees is animated by utilizing local coordinate transformation before applying the forced vibration model of curved beams. In addition, we assume petioles are flexible to create natural motion of leaves. A wind field is generated by three-dimensional 1/f β noises to interact with the trees. Besides, our animation model allows users to interactively manipulate trees. We demonstrate several examples to show the realistic motion of interactive trees without using pre-computation or GPU acceleration. Various motions of trees can be achieved by choosing different combinations of natural frequencies and damping ratios according to tree species and seasons.

Keywords

Natural phenomena Physically based animation Tree animation Lissajous curve 1/fβ noise 

Notes

Acknowledgements

This work was partially supported by the Doctoral Start-up Funds (2010BSJJ059), the Fundamental Research Funds (QN2011135) of Northwest A&F University, and the National Science & Technology Supporting Plan of China (2011BAD29B08). The authors would like to thank anonymous reviewers for their helpful suggestions.

Supplementary material

(AVI 14.1 MB)

References

  1. 1.
    Diener, J., Rodriguez, M., Baboud, L., Reveret, L.: Wind projection basis for real-time animation of trees. Comput. Graph. Forum 28(2), 533–540 (2009) CrossRefGoogle Scholar
  2. 2.
    Habel, R., Kusternig, A., Wimmer, M.: Physically guided animation of trees. Comput. Graph. Forum 28(2), 523–532 (2009) CrossRefGoogle Scholar
  3. 3.
    Stam, J.: Stochastic dynamics: simulating the effects of turbulence on flexible structures. Comput. Graph. Forum 16(3), 159–164 (1997) CrossRefGoogle Scholar
  4. 4.
    Weber, J.P.: Fast simulation of realistic trees. IEEE Comput. Graph. Appl. 28(3), 67–75 (2008) CrossRefGoogle Scholar
  5. 5.
    Shinya, M., Fournier, A.: Stochastic motion—motion under the influence of wind. Comput. Graph. Forum 11(3), 119–128 (1992) zbMATHCrossRefGoogle Scholar
  6. 6.
    Chuang, Y.Y., Goldman, D.B., Zheng, K.C., Curless, B., Salesin, D., Szeliski, R.: Animating pictures with stochastic motion textures. Proc. ACM SIGGRAPH Conf. 24(3), 853–860 (2005) CrossRefGoogle Scholar
  7. 7.
    Hu, S., Fujimoto, T., Chiba, N.: Pseudo-dynamics model of a cantilever beam for animating flexible leaves and branches in wind field. Comput. Animat. Virtual Worlds 20(2–3), 279–287 (2009) CrossRefGoogle Scholar
  8. 8.
    Akagi, Y., Kitajima, K.: Computer animation of swaying trees based on physical simulation. Comput. Graph. 30(4), 529–539 (2006) CrossRefGoogle Scholar
  9. 9.
    Ota, S., Tamura, M., Fujimoto, T., Muraoka, K., Chiba, N.: A hybrid method for real-time animation of trees swaying in wind field. Vis. Comput. 20(10), 613–623 (2004) CrossRefGoogle Scholar
  10. 10.
    Fujimoto, T., Miyauchi, S., Suzuki, T., Chiba, N.: Noise-based animation of waving phenomena. In: IWAIT 2005, pp. 459–464 (2005) Google Scholar
  11. 11.
    Diener, J., Reveret, L., Fiume, E.: Hierarchical retargeting of 2D motion fields to the animation of 3D plant models. In: ACM-SIGGRAPH/EG Symposium on Computer Animation 2006, pp. 187–195 (2006) Google Scholar
  12. 12.
    Beaudoin, J., Keyser, J.: Simulation levels of detail for plant motion. In: Proceedings of the SIGGRAPH/ Eurographics Symposium on Computer Animation 2004, pp. 297–304 (2004) CrossRefGoogle Scholar
  13. 13.
    Giacomo, T.D., Capo, S., Faure, F.: An interactive forest. In: Proceedings of the Eurographic Workshop on Computer Animation and Simulation 2001, pp. 65–74 (2001) CrossRefGoogle Scholar
  14. 14.
    Zhang, L., Song, C., Tan, Q., Chen, W., Peng, Q.: Quasi-physical simulation of large-scale dynamic forest scenes. In: Computer Graphics International 2006, pp. 735–742 (2006) Google Scholar
  15. 15.
    James, K.R.: Dynamic wind loads on trees. In: ISAAC (2005) Google Scholar
  16. 16.
    James, K.R., Haritos, N., Ades, P.K.: Mechanical stability of trees under dynamic loads. Am. J. Bot. 93(10), 1522–1530 (2006) CrossRefGoogle Scholar
  17. 17.
    Moore, J.R., Maguire, D.A.: Natural sway frequencies and damping ratios of trees: Influence of crown structure. Trees 19(4), 363–373 (2005) CrossRefGoogle Scholar
  18. 18.
    Nealen, A., Müller, M., Keiser, R., Boxerman, E., Carlson, M.: Physically based deformable models in computer graphics. Comput. Graph. Forum 25(4), 809–836 (2005) CrossRefGoogle Scholar
  19. 19.
    Khorloo, O., Gunjee, Z., Sosorbaram, B., Chiba, N.: Wind field synthesis for animating wind-induced vibration. Int. J. Virtual Real. 10(1), 53–60 (2011) Google Scholar
  20. 20.
    James, K.R., Haritos, N.: The role of branches in the dynamics response characteristics of trees. In: Australian Earthquake Engineering Society Conference (2010) Google Scholar
  21. 21.
    Rao, B.N., Rao, G.V.: Large deflections of a non-uniform cantilever beam with end rotational load. J. Sound Vib. 304(24), 969–973 (2007) Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.College of Information EngineeringNorthwest A&F UniversityYanglingChina
  2. 2.Dept. of Computer and Information Sciences, Faculty of EngineeringIwate UniversityMoriokaJapan
  3. 3.Mechanical and Electronic EngineeringNorthwest A&F UniversityYanglingChina

Personalised recommendations