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.
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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.
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Hu, S., Chiba, N. & He, D. Realistic animation of interactive trees. Vis Comput 28, 859–868 (2012) doi:10.1007/s00371-012-0694-z
- Natural phenomena
- Physically based animation
- Tree animation
- Lissajous curve
- 1/f β noise