We propose a fast and robust solver to simulate continuum-based deformable models with constraints, in particular, rigid-body and joint constraints useful for soft articulated characters. Our method embeds degrees of freedom of both articulated rigid bodies and deformable bodies in one unified optimization problem, thus coupling the deformable and rigid bodies. Our method can efficiently simulate character models, with rigid-body parts (bones) being correctly coupled with deformable parts (flesh). Our method is stable because backward Euler time integration is applied to rigid as well as deformable degrees of freedom. Our method is rigorously derived from constrained Newtonian mechanics. In an example simulation with rigid bodies only, we demonstrate that our method converges to the same motion as classical explicitly integrated rigid body simulator.
In this paper we re-examine the idea that implicit integrators with large time steps offer the best stability/performance trade-off for stiff systems. We make the surprising observation that performing a single large time step with n constraint solver iterations is less effective than computing n smaller time steps, each with a single constraint solver iteration. Based on this observation, our approach is to split every visual time step into n substeps of length Δt/n and to perform a single iteration of extended position-based dynamics (XPBD) in each such substep. When compared to a traditional implicit integrator with large time steps we find constraint error and damping are significantly reduced. When compared to an explicit integrator we find that our method is more stable and robust for a wider range of stiffness parameters. This result holds even when compared against more sophisticated implicit solvers based on Krylov methods. Our method is straightforward to implement, and is not sensitive to matrix conditioning nor is it to overconstrained problems.
We propose a novel volume conserving framework for character-water interaction, using a novel volume-of-fluid solver on a skinned tetrahedral mesh, enabling the high degree of the spatial adaptivity in order to capture thin films and hair-water interactions. For efficiency, the bulk of the fluid volume is simulated with a standard Eulerian solver which is two way coupled to our skinned arbitrary Lagrangian-Eulerian mesh using a fast, robust, and straight-forward to implement partitioned approach. This allows for a specialized and efficient treatment of the volume-of-fluid solver, since it is only required in a subset of the domain. The combination of conservation of fluid volume and a kinematically deforming skinned mesh allows us to robustly implement interesting effects such as adhesion, and anisotropic porosity. We illustrate the efficacy of our method by simulating various water effects with solid objects and animated characters.
We present a new formulation of trajectory optimization for articulated bodies. Our approach uses a fully differentiable dynamic model of the articulated body, and a smooth force model that approximates all kinds of internal/external forces as a smooth function of the articulated body's kinematic state. Our formulation is contact-aware and its complexity is not dependent on the contact positions or the number of contacts. Furthermore, we exploit the block-tridiagonal structure of the Hessian matrix and present a highly parallel Newton-type trajectory optimizer that maps well to GPU architectures. Moreover, we use a Markovian regularization term to overcome the local minima problems in the optimization formulation. We highlight the performance of our approach using a set of locomotion tasks performed by characters with 15 -- 35 DOFs. In practice, our GPU-based algorithm running on a NVIDIA TITAN-X GPU provides more than 30x speedup over a multi-core CPU-based implementation running on Intel Xeon E5-1620 CPU. In addition, we demonstrate applications of our method on various applications such as contact-rich motion planning, receding-horizon control, and motion graph construction.
Elastodynamic system simulation is a key procedure in computer graphics and robotics applications. To enable these simulations, the governing differential system is discretized in space (employing FEM) and then in time. For many simulation-based applications keeping the spatial resolution of the computational mesh effectively coarse is crucial for securing acceptable computational efficiency. However, this can introduce numerical stiffening effects that impede visual accuracy.
We propose and demonstrate, for both linear and nonlinear force models, a new method called EigenFit that improves the consistency and accuracy of the lower energy, primary deformation modes, as the spatial mesh resolution is coarsened. EigenFit applies a partial spectral decomposition, solving a generalized eigenvalue problem in the leading mode subspace and then replacing the first several eigenvalues of the coarse mesh by those of the fine one at rest. EigenFit's performance relies on a novel subspace model reduction technique which restricts the spectral decomposition to finding just a few of the leading eigenmodes. We demonstrate its efficacy on a number of objects with both homogenous and heterogenous material distributions.
Data-driven methods for physical simulation are an attractive option for interactive applications due to their ability to trade precomputation and memory footprint in exchange for improved runtime performance. Yet, existing data-driven methods fall short of the extreme memory and performance constraints imposed by modern interactive applications like AAA games and virtual reality. Here, performance budgets for physics simulation range from tens to hundreds of micro-seconds per frame, per object. We present a data-driven physical simulation method that meets these constraints. Our method combines subspace simulation techniques with machine learning which, when coupled, enables a very efficient subspace-only physics simulation that supports interactions with external objects - a longstanding challenge for existing subspace techniques. We also present an interpretation of our method as a special case of subspace Verlet integration, where we apply machine learning to efficiently approximate the physical forces of the system directly in the subspace. We propose several practical solutions required to make effective use of such a model, including a novel training methodology required for prediction stability, and a GPU-friendly subspace decompression algorithm to accelerate rendering.
In grid-based fluid simulation, discrete incompressibility of each cell is enforced by the pressure projection. However, pointwise velocities constructed by interpolating the discrete velocity samples from the staggered grid are not truly divergence-free, resulting in unphysical local volume changes that manifests as particle spreading and clustering. We present a new velocity interpolation method that produces analytically divergence-free velocity fields in 2D using a stream function. The resulting fields are guaranteed to be divergence-free by a simple calculus identity: the curl of any vector field yields a divergence-free vector field. Furthermore, our method works on cut cell grids to produce fields that strictly obey solid boundary conditions. Therefore, no artificial gaps are created between fluid particles and solids, and fluid particles do not trespass into solid regions.
Retageting a human-environment interaction motion to a different environment remains as an important research topic in computer animation. This paper introduces a novel method that can retarget an interaction motion to highly dissimilar environment, where not every contact in the source environment can be preserved. The key idea of the method is to prioritize the contact and preserve more important contact while sacrificing other contacts if necessary. Specifically, we propose a method to detect a manipulation contact and preserve the contact in the target furniture environment by allowing for a large deviation from the input pose.
The visualization of human articular movements associated with internal deformation is critical for many fields including biomechanics. In this work, we present a novel algorithm to describe realistic articular movement in a human model, which effectivelly combines free-form deformation and simple constrained deformation. The algorithm provides the articular movement with contractions/extensions in muscles followed by the deformations of embedded tissues, such as blood vessels, lymphatics, and nerves, treating the bones as a rigid body. An arm bending simulation of a human model using the algorithm was performed. The proposed algorithm has the potential for development as a hybrid method that combines multi-physical simulations and geometric modeling.
Hybrid-based character animation utilizing the motion capture data and a simplified physics model allows synthesizing the motion data without losing its naturalness of the original motion. However, using both the physical model and the motion data requires professional insights, experiences, and extra efforts such as preprocessing or off-line optimization. To handle the issue, we propose a new type of motion synthesis framework. The proposed framework combines multiple information sources that generate the reference motion based on the motion capture data and physical constraints based on the physical model. To verify the proposed framework, we define a mass-spring model to represent each skeletal joint of a human character model along with a small amount of motion capture data, a human walking motion.