On the impulse method for cloth animation
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
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The animation of cloth in a visually plausible and attractive manner plays an essential role in the special effects industry, such as feature films and 3D games. For the result to be realistic, cloth is usually simulated using physically-based models. With a physically-based method, the motion of cloth evolves according to the law of dynamics. A typical process consists of a dynamics model, an ordinary differential equation (ODE) solver, and a collision detection/resolution mechanism. This dissertation is concerned with the over-deformation problem, which is related to issues in which cloth is being over-stretched (making the cloth appear unrealistic and possibly causing the computation to become unstable). An impulse-based method is put forward, by which the energy of local high deformations is dissipated properly; the resulting non-linear system is approximated by a set of linear equations, whose matrix is proved to be symmetric positive definite. To solve this system efficiently, reordering is performed to the matrix before applying the Cholesky decomposition in order to speed-up the computation and decrease the round-off error. Constraints have been seamlessly incorporated into our impulse method to handle collisions and user interventions, without degrading the performance of the matrix solver. Our method works well with an explicit ODE solver. Other related issues are addressed, such as the internal dynamics of cloth, doing collision detection using octree and interaction between solid objects and cloth. Finally a few experiments, including the simulation of a T-shirt model, are presented.