Abstract
We present a model for flexible trees using constrained elastic rods, that can be solved implicitly in linear cost. We also demonstrate how to solve frictional hard contacts, as well as the inverse static equilibrium problem.
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Notes
- 1.
As \(\lambda \) is arbitrary up to a scalar factor, we multiplied it by \(h^2\) to obtain a symmetric matrix in (2).
- 2.
Which can be done without any extra normalization, see [11].
- 3.
Kirchhoff’s elasticity model implies that K depends on the rest lengths as well, so is in fact a nonlinear function of \(\sigma _0\).
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Acknowledgments
We would like to thank Alex Nowotny, David Caeiro and Alasdair Coull from Weta Digital for their support, as well as Eitan Grinspun from Columbia University for discussions and comments. We are also grateful to the anonymous reviewers and the editors for their insightful suggestions.
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Aubry, JM., Xian, X. (2015). Fast Implicit Simulation of Flexible Trees. In: Ochiai, H., Anjyo, K. (eds) Mathematical Progress in Expressive Image Synthesis II. Mathematics for Industry, vol 18. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55483-7_5
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DOI: https://doi.org/10.1007/978-4-431-55483-7_5
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