We describe a scheme for time integration of mass-spring systems that makes use of a solver based on block coordinate descent. This scheme provides a fast solution for classical linear (Hookean) springs. We express the widely used implicit Euler method as an energy minimization problem and introduce spring directions as auxiliary unknown variables. The system is globally linear in the node positions, and the non-linear terms involving the directions are strictly local. Because the global linear system does not depend on run-time state, the matrix can be pre-factored, allowing for very fast iterations. Our method converges to the same final result as would be obtained by solving the standard form of implicit Euler using Newton's method. Although the asymptotic convergence of Newton's method is faster than ours, the initial ratio of work to error reduction with our method is much faster than Newton's. For real-time visual applications, where speed and stability are more important than precision, we obtain visually acceptable results at a total cost per timestep that is only a fraction of that required for a single Newton iteration. When higher accuracy is required, our algorithm can be used to compute a good starting point for subsequent Newton's iteration. AbstractWe describe a scheme for time integration of mass-spring systems that makes use of a solver based on block coordinate descent. This scheme provides a fast solution for classical linear (Hookean) springs. We express the widely used implicit Euler method as an energy minimization problem and introduce spring directions as auxiliary unknown variables. The system is globally linear in the node positions, and the non-linear terms involving the directions are strictly local. Because the global linear system does not depend on run-time state, the matrix can be pre-factored, allowing for very fast iterations. Our method converges to the same final result as would be obtained by solving the standard form of implicit Euler using Newton's method. Although the asymptotic convergence of Newton's method is faster than ours, the initial ratio of work to error reduction with our method is much faster than Newton's. For real-time visual applications, where speed and stability are more important than precision, we obtain visually acceptable results at a total cost per timestep that is only a fraction of that required for a single Newton iteration. When higher accuracy is required, our algorithm can be used to compute a good starting point for subsequent Newton's iteration.
In this paper, we describe a method for realistically animating ductile fracture in common solid materials such as plastics and metals. The effects that characterize ductile fracture occur due to interaction between plastic yielding and the fracture process. By modeling this interaction, our ductile fracture method can generate realistic motion for a much wider range of materials than could be realized with a purely brittle model. This method directly extends our prior work on brittle fracture [O'Brien and Hodgins, SIGGRAPH 99]. We show that adapting that method to ductile as well as brittle materials requires only a simple to implement modification that is computationally inexpensive. This paper describes this modification and presents results demonstrating some of the effects that may be realized with it.
Figure 1: A bunny is dropped down a flight of stairs. Due to work softening, portions of the bunny become soft and droop. AbstractWe present an extension to Lagrangian finite element methods to allow for large plastic deformations of solid materials. These behaviors are seen in such everyday materials as shampoo, dough, and clay as well as in fantastic gooey and blobby creatures in special effects scenes. To account for plastic deformation, we explicitly update the linear basis functions defined over the finite elements during each simulation step. When these updates cause the basis functions to become ill-conditioned, we remesh the simulation domain to produce a new high-quality finite-element mesh, taking care to preserve the original boundary. We also introduce an enhanced plasticity model that preserves volume and includes creep and work hardening/softening. We demonstrate our approach with simulations of synthetic objects that squish, dent, and flow. To validate our methods, we compare simulation results to videos of real materials.
Figure 1: (a) Coarse simulation, (b) subdivision, (c) our proposed upsampling and (d) fine-scale simulation. Our upsampling operator is learned from a small set of coarse and fine-scale examples, which allows it to achieve higher quality than subdivision while still being linear and therefore very efficient and simple to implement (this example is upsampled in 0.8ms on a single CPU thread). AbstractWe propose a method for learning linear upsampling operators for physically-based cloth simulation, allowing us to enrich coarse meshes with mid-scale details in minimal time and memory budgets, as required in computer games. In contrast to classical subdivision schemes, our operators adapt to a specific context (e.g. a flag flapping in the wind or a skirt worn by a character), which allows them to achieve higher detail. Our method starts by pre-computing a pair of coarse and fine training simulations aligned with tracking constraints using harmonic test functions. Next, we train the upsampling operators with a new regularization method that enables us to learn mid-scale details without overfitting. We demonstrate generalizability to unseen conditions such as different wind velocities or novel character motions. Finally, we discuss how to re-introduce high frequency details not explainable by the coarse mesh alone using oscillatory modes.
In this paper, we describe a method for realistically animating ductile fracture in common solid materials such as plastics and metals. The effects that characterize ductile fracture occur due to interaction between plastic yielding and the fracture process. By modeling this interaction, our ductile fracture method can generate realistic motion for a much wider range of materials than could be realized with a purely brittle model. This method directly extends our prior work on brittle fracture [O'Brien and Hodgins, SIGGRAPH 99]. We show that adapting that method to ductile as well as brittle materials requires only a simple to implement modification that is computationally inexpensive. This paper describes this modification and presents results demonstrating some of the effects that may be realized with it.
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