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FROM:
Rasmus Tamstorf, “Large scale simulation of cloth and hair with contact”, Ph.D dissertation No. 23223, ETH, Switzerland, 2016
ABSTRACT: The goal of this thesis is to develop new methods for robust and scalable simulation of thin objects with contact. This work is motivated by applications in cloth and hair simulation in feature film production, but the results are also applicable in other domains such as in the garment industry, in biology, and in mechanical engineering. The contributions focus primarily on physically correct contact response and ef- ficient implementation thereof. While collision detection has been studied exten- sively, collision response remains a challenging problem. This is due in part to the fact that contact constraints are both nonlinear, non-convex, and non-smooth. Furthermore, the response is inherently coupled to the underlying dynamics, which is often neglected in existing methods. We first develop the necessary details for implementation of the dynamics of orthotropic thin shells undergoing large deformations. This derivation is based on fundamental invariants and symmetry considerations from continuum mechanics and leads to a simple and efficient extension of existing membrane models. We also show how the analytical derivatives for the discrete shell bending model can be computed efficiently to facilitate implicit integration. The next part of the thesis is based on the observation that nonlinear compliance is critical for collision response involving thin objects. This is illustrated with rods (hair), which exhibit the same fundamental problem as shells, but are cheaper to simulate. Taking the nonlinearity into account, we show that simulations can be run with time steps that are 2 3 orders of magnitude larger than with existing methods. Based on this observation, we construct a solver that locally adapts the nonlinear treatment based on the current configuration to ensure stable simulations. We then validate our approach by running simulations with thousands of hairs and millions of contacts. Hair simulation is generally simpler than cloth because the rods can be partitioned into contact groups that can each be handled separately. For shells, all degrees of freedom are inherently coupled, which leads to much larger systems of equations that have to be solved. In pursuit of solving these larger systems of equations, the last part of the thesis investigates the use of algebraic multigrid methods. The first key observation here is that standard multigrid methods (both geometric and algebraic) fail to perform well for thin shell equations even in the absence of contact. To address this difficulty, we introduce the smoothed aggregation method to cloth simulation. This is an algebraic multigrid method designed specifically for vector valued problems. Used as a preconditioner for CG, smoothed aggregation provides substantial speedups for medium and large size problems compared to a diagonally preconditioned CG method. Compared to geometric multigrid methods, it provides both better convergence rates and increased flexibility. Due to the algebraic nature of the method, it can be used for irregular meshes as well as with adaptive tessellations, which is not practical with geometric multigrid methods.
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