Physics-Based Animation

Yahan Zhou, Zhaoliang Lun, Evangelos Kalogerakis, Rui Wang

We present a novel particle-based method for stable simulation of elasto-plastic materials. The main contribution of our method is an implicit numerical integrator, using a physically-based model, for computing particles that undergo both elastic and plastic deformations. The main advantage of our implicit integrator is that it allows the use of large time steps while still preserving stable and physically plausible simulation results. As a key component of our algorithm, at each time step we compute the particle positions and velocities based on a sparse linear system, which we solve efficiently on the graphics hardware. Compared to existing techniques, our method allows for a much wider range of stiffness and plasticity settings. In addition, our method can significantly reduce the computation cost for certain range of material types. We demonstrate fast and stable simulations for a variety of elasto-plastic materials, ranging from highly stiff elastic materials to highly plastic ones.

Implicit Integration for Particle-based Simulation of Elasto-plastic Solids

Eder Miguel, Rasmus Tamstorf, Derek Bradley, Sara C. Schvartzman, Bernhard Thomaszewski, Bernd Bickel, Wojciech Matusik, Steve Marschner, Miguel A. Otaduy

Force-deformation measurements of cloth exhibit significant hysteresis, and many researchers have identified internal friction as the source of this effect. However, it has not been incorporated into computer animation models of cloth. In this paper, we propose a model of internal friction based on an augmented reparameterization of Dahl’s model, and we show that this model provides a good match to several important features of cloth hysteresis even with a minimal set of parameters. We also propose novel parameter estimation procedures that are based on simple and inexpensive setups and need only sparse data, as opposed to the complex hardware and dense data acquisition of previous methods. Finally, we provide
an algorithm for the efficient simulation of internal friction, and we demonstrate it on simulation examples that show disparate behavior with and without internal friction.

Modeling and Estimation of Internal Friction in Cloth

Yubo Zhang, Kwan-Liu Ma

We introduce a novel spatio-temporal extrapolation technique for fluid simulation designed to improve the results without using higher resolution simulation grids. In general, there are rigid demands associated with pushing fluid animations to higher resolutions given limited computational capabilities. This results in tradeoffs between implementing high-order numerical methods and increasing the resolution of the simulation in space and time. For 3D problems, such challenges rapidly become cost-ineffective. The extrapolation method we present improves the flow features without using higher resolution simulation grids. In this paper, we show that simulation results from our extrapolation are comparable to those from higher resolution simulations. In addition, our method differs from high-order numerical methods because it does not depend on the equation or specific solver. We demonstrate that it is easy to implement and can significantly improve the fluid animation results.

Spatio-temporal Extrapolation for Fluid Animation

Christoph von Tycowicz, Christian Schulz, Hans-Peter Seidel, Klaus Hildebrandt

Many efficient computational methods for physical simulation are based on model reduction. We propose new model reduction techniques for the approximation of reduced forces and for the construction of reduced shape spaces of deformable objects that accelerate the construction of a reduced dynamical system, increase the accuracy of the approximation, and simplify the implementation of model reduction. Based on the techniques, we introduce schemes for real-time simulation of deformable objects and interactive deformation-based editing of triangle or tet meshes. We demonstrate the effectiveness of the new techniques in different experiments with elastic solids and shells and compare them to alternative approaches.

An Efficient Construction of Reduced Deformable Objects

Alexandre Derouet-Jourdan, Florence Bertails-Descoubes, Gilles Daviet, Joelle Thollot

In the latest years, considerable progress has been achieved for accurately acquiring the geometry of human hair, thus largely improving the realism of virtual characters. In parallel, rich and robust physics-based simulators have been successfully designed to capture the intricate dynamics of hair due to contact and friction. However, at the moment there exists no consistent pipeline for converting a given hair geometry into a realistic physics-based hair model. Current approaches simply initialize the hair simulator with the input geometry in the absence of external forces. This results in an undesired sagging effect when the dynamic simulation is started, which basically ruins all the efforts put into the accurate design and/or capture of the input hairstyle. In this paper we propose the first method which consistently and robustly accounts for surrounding forces — gravity and frictional contacts, including hair self-contacts — when converting a geometric hairstyle into a physics-based hair model. Taking an arbitrary hair geometry as input together with a corresponding body mesh, we interpret the hair shape as a static equilibrium configuration of a hair simulator, in the presence of gravity as well as hair-body and hair-hair frictional contacts. Assuming hair parameters are homogeneous and lie in a plausible range of physical values, we show that this large, underdetermined inverse problem can be formulated as a well-posed constrained optimization problem, which can be robustly and efficiently solved by leveraging the frictional contact solver of the direct hair simulator. Our method was successfully applied to the animation of various hair geometries, ranging from synthetic hairstyles manually designed by an artist to the most recent human hair data reconstructed from capture.

Inverse Dynamic Hair Modeling with Frictional Contact

Dan Gerzewski, Adam Bargteil

Fluid simulation has been one of the greatest successes of physics-based animation, generating hundreds of research papers and a great many special effects over the last fifteen years. However, the animation of large-scale, splashing liquids remains challenging. In this paper, we show that a novel combination of unilateral incompressibility, mass-full FLIP, and blurred boundaries is extremely well-suited to the animation of large-scale, violent, splashing liquids.

Physics-Based Animation of Large-scale Splashing Liquids

Libin Liu, KangKang Yin, Bin Wang, Baining Guo

In this paper we present a physics-based framework for simulation and control of human-like skeleton-driven soft body characters. We couple the skeleton dynamics and the soft body dynamics to enable two-way interactions between the skeleton, the skin geometry, and the environment. We propose a novel pose-based plasticity model that extends the corotated linear elasticity model to achieve large skin deformation around joints. We further reconstruct controls from reference trajectories captured from human subjects by augmenting a sampling-based algorithm. We demonstrate the effectiveness of our framework by results not attainable with a simple combination of previous methods.

Simulation and Control of Skeleton-Driven Soft Body Characters

Tiantian Liu, Adam Bargteil, James F. O’Brien, Ladislav Kavan

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.

Fast Simulation of Mass-Spring Systems

Jia Pan, Xinyu Zhang, Dinesh Manocha

We present a new method for efficiently computing the global penetration depth between two rigid objects using machine learning techniques. Our approach consists of two phases: offline learning and performing run-time queries. In the learning phase, we pre-compute an approximation of the contact space of a pair of intersecting objects from a set of samples in the configuration space. We use active and incremental learning algorithms to accelerate the pre-computation and improve the accuracy. During the run-time phase, our algorithm performs a nearest-neighbor query based on translational or rotational distance metrics. The run-time query has a small overhead and computes an approximation to global penetration depth in a few milliseconds. We use our algorithm for collision response computations in Box2D and Bullet game physics engines and observe more than an order of magnitude improvement over prior PD computation techniques.

Efficient Penetration Depth Approximation using Active Learning

Alexey Stomakhin, Craig Schroeder, Lawrence Chai, Joseph Teran, Andrew Selle

Snow is a challenging natural phenomenon to visually simulate. While the graphics community has previously considered accumulation and rendering of snow, animation of snow dynamics has not been fully addressed. Additionally, existing techniques for solids and fluids have difficulty producing convincing snow results. Specifically, wet or dense snow that has both solid- and fluid-like properties is difficult to handle. Consequently, this paper presents a novel snow simulation method utilizing a usercontrollable elasto-plastic constitutive model integrated with a hybrid Eulerian/Lagrangian Material Point Method. The method is continuum based and its hybrid nature allows us to use a regular Cartesian grid to automate treatment of self-collision and fracture. It also naturally allows us to derive a grid-based semi-implicit integration scheme that has conditioning independent of the number of Lagrangian particles. We demonstrate the power of our method with a variety of snow phenomena including complex character interactions.

A Material Point Method for Snow Simulation