Abstract We present a technique for simulating detailed cloth dynamics on coarse meshes at interactive rates. Building on the wrinkle parameterization introduced by [CCK*21], we introduce a dynamics model for a cloth sheet represented as a superposition of a base surface and a wrinkle distribution parameterized by spatially varying amplitude and frequency. Our model incorporates two‐way coupling of the base surface and the wrinkle parameters, allowing the base deformation to drive emergence of wrinkles and permitting compression of the base surface in turn. To deform the mesh using the computed wrinkle parameters, we also introduce a simple phase reconstruction strategy that produces dynamically evolving, temporally coherent wrinkles on the simulated mesh.

Animating a virtual character based on a real performance of an actor is a challenging task that currently requires expensive motion capture setups and additional effort by expert animators, rendering it accessible only to large production houses. The goal of our work is to democratize this task by developing a frugal alternative termed “Transfer4D” that uses only commodity depth sensors and further reduces animators' effort by automating the rigging and animation transfer process. Our approach can transfer motion from an incomplete, single-view depth video to a semantically similar target mesh, unlike prior works that make a stricter assumption on the source to be noise-free and watertight. To handle sparse, incomplete videos from depth video inputs and variations between source and target objects, we propose to use skeletons as an intermediary representation between motion capture and transfer. We propose a novel unsupervised skeleton extraction pipeline from a single-view depth sequence that incorporates additional geometric information, resulting in superior performance in motion reconstruction and transfer in comparison to the contemporary methods and making our approach generic. We use non-rigid reconstruction to track motion from the depth sequence, and then we rig the source object using skinning decomposition. Finally, the rig is embedded into the target object for motion retargeting.

This paper studies the problem of inverse cloth simulation—to estimate shape and time-varying poses of the underlying body that generates physically plausible cloth motion, which matches to the point cloud measurements on the clothed humans. A key innovation is to represent the dynamics of the cloth geometry using a dynamical system that is controlled by the body states (shape and pose). This allows us to express the cloth motion as a resultant of external (skin friction and gravity) and internal (elasticity) forces. Inspired by the theory of optimal control, we optimize the body states such that the simulated cloth motion is matched to the point cloud measurements, and the analytic gradient of the simulator is back-propagated to update the body states. We propose a cloth relaxation scheme to initialize the cloth state, which ensures the physical validity. Our method produces physically plausible and temporally smooth cloth and body movements that are faithful to the measurements, and shows superior performance compared to the existing methods. As a byproduct, the stress and strain that are applied to the body and clothes can be recovered.

Abstract We present a method to minimize distortion and compute globally injective mappings from non‐injective initialization Many approaches for distortion minimization subject to injectivity constraints require an injective initialization and feasible intermediate states. However, it is often the case that injective initializers are not readily available, and many distortion energies of interest have barrier terms that stall global progress. The alternating direction method of multipliers (ADMM) has recently gained traction in graphics due to its efficiency and generality. In this work we explore how to endow ADMM with global injectivity while retaining the ability to traverse non‐injective iterates. We develop an iterated coupled‐solver approach that evolves two solution states in tandem. Our primary solver rapidly drives down energy to a nearly injective state using a dynamic set of efficiently enforceable inversion and overlap constraints. Then, a secondary solver corrects the state, herding the solution closer to feasibility. The resulting method not only compares well to previous work, but can also resolve overlap with free boundaries.

Local-global solvers such as ADMM for elastic simulation and geometry optimization struggle to resolve large rotations such as bending and twisting modes, and large distortions in the presence of barrier energies. We propose two improvements to address these challenges. First, we introduce a novel local-global splitting based on the polar decomposition that separates the geometric nonlinearity of rotations from the material nonlinearity of the deformation energy. The resulting ADMM-based algorithm is a combination of an L-BFGS solve in the global step and proximal updates of element stretches in the local step. We also introduce a novel method for dynamic reweighting that is used to adjust element weights at runtime for improved convergence. With both improved rotation handling and element weighting, our algorithm is considerably faster than state-of-the-art approaches for quasi-static simulations. It is also much faster at making early progress in parameterization problems, making it valuable as an initializer to jump-start second-order algorithms.

Triangle mesh-based simulations are able to produce satisfying animations of knitted and woven cloth; however, they lack the rich geometric detail of yarn-level simulations. Naive texturing approaches do not consider yarn-level physics, while full yarn-level simulations may become prohibitively expensive for large garments. We propose a method to animate yarn-level cloth geometry on top of an underlying deforming mesh in a mechanics-aware fashion. Using triangle strains to interpolate precomputed yarn geometry, we are able to reproduce effects such as knit loops tightening under stretching. In combination with precomputed mesh animation or real-time mesh simulation, our method is able to animate yarn-level cloth in real-time at large scales.

We propose a simple and efficient method for guiding an Eulerian smoke simulation to match the behavior of a specified velocity field, such as a low-resolution animation of the same scene, while preserving the rich, turbulent details arising in the simulated fluid. Our method works by simply combining the high-frequency component of the simulated fluid velocity with the low-frequency component of the input guiding field. We show how to eliminate the grid-aligned artifacts that appear in naive guiding approaches, and provide a frequency-domain analysis that motivates the use of ideal low-pass and high-pass filters to prevent artificial dissipation of small-scale details. We demonstrate our method on many scenes including those with static and moving obstacles, and show that it produces high-quality results with very little computational overhead.

We present a method for animating yarn-level cloth effects using a thin-shell solver. We accomplish this through numerical homogenization: we first use a large number of yarn-level simulations to build a model of the potential energy density of the cloth, and then use this energy density function to compute forces in a thin shell simulator. We model several yarn-based materials, including both woven and knitted fabrics. Our model faithfully reproduces expected effects like the stiffness of woven fabrics, and the highly deformable nature and anisotropy of knitted fabrics. Our approach does not require any real-world experiments nor measurements; because the method is based entirely on simulations, it can generate entirely new material models quickly, without the need for testing apparatuses or human intervention. We provide data-driven models of several woven and knitted fabrics, which can be used for efficient simulation with an off-the-shelf cloth solver.

We propose a method for accurately simulating dissipative forces in deformable bodies when using optimization-based integrators. We represent such forces using dissipation functions which may be nonlinear in both positions and velocities, enabling us to model a range of dissipative effects including Coulomb friction, Rayleigh damping, and power-law dissipation. We propose a general method for incorporating dissipative forces into optimization-based time integration schemes, which hitherto have been applied almost exclusively to systems with only conservative forces. To improve accuracy and minimize artificial damping, we provide an optimization-based version of the second-order accurate TR-BDF2 integrator. Finally, we present a method for modifying arbitrary dissipation functions to conserve linear and angular momentum, allowing us to eliminate the artificial angular momentum loss caused by Rayleigh damping.

Cloth dynamics plays an important role in the visual appearance of moving characters. Properly accounting for contact and friction is of utmost importance to avoid cloth-body and cloth-cloth penetration and to capture typical folding and stick-slip behavior due to dry friction. We present here the first method able to account for cloth contact with exact Coulomb friction, treating both cloth self-contacts and contacts occurring between the cloth and an underlying character. Our key contribution is to observe that for a nodal system like cloth, the frictional contact problem may be formulated based on velocities as primary variables, without having to compute the costly Delassus operator. Then, by reversing the roles classically played by the velocities and the contact impulses, conical complementarity solvers of the literature can be adapted to solve for compatible velocities at nodes. To handle the full complexity of cloth dynamics scenarios, we have extended this base algorithm in two ways: first, towards the accurate treatment of frictional contact at any location of the cloth, through an adaptive node refinement strategy; second, towards the handling of multiple constraints at each node, through the duplication of constrained nodes and the adding of pin constraints between duplicata. Our method allows us to handle the complex cloth-cloth and cloth-body interactions in full-size garments with an unprecedented level of realism compared to former methods, while maintaining reasonable computational timings.

Advection-projection methods for fluid animation are widely appreciated for their stability and efficiency. However, the projection step dissipates energy from the system, leading to artificial viscosity and suppression of small-scale details. We propose an alternative approach for detail-preserving fluid animation that is surprisingly simple and effective. We replace the energy-dissipating projection operator applied at the end of a simulation step by an energy-preserving reflection operator applied at mid-step. We show that doing so leads to two orders of magnitude reduction in energy loss, which in turn yields vastly improved detail-preservation. We evaluate our reflection solver on a set of 2D and 3D numerical experiments and show that it compares favorably to state-of-the-art methods. Finally, our method integrates seamlessly with existing projection-advection solvers and requires very little additional implementation.

Abstract One of the major challenges in physically based modelling is making simulations efficient. Adaptive models provide an essential solution to these efficiency goals. These models are able to self‐adapt in space and time, attempting to provide the best possible compromise between accuracy and speed. This survey reviews the adaptive solutions proposed so far in computer graphics. Models are classified according to the strategy they use for adaptation, from time‐stepping and freezing techniques to geometric adaptivity in the form of structured grids, meshes and particles. Applications range from fluids, through deformable bodies, to articulated solids.

Large multi-agent systems such as crowds involve inter-agent interactions that are typically anticipatory in nature, depending strongly on both the positions and the velocities of agents. We show how the nonlinear, anticipatory forces seen in multi-agent systems can be made compatible with recent work on energy-based formulations in physics-based animation, and propose a simple and effective optimization-based integration scheme for implicit integration of such systems. We apply this approach to crowd simulation by using a state-of-the-art model derived from a recent analysis of human crowd data, and adapting it to our framework. Our approach provides, for the first time, guaranteed collision-free motion while simultaneously maintaining high-quality collective behavior in a way that is insensitive to simulation parameters such as time step size and crowd density. These benefits are demonstrated through simulation results on various challenging scenarios and validation against real-world crowd data.

We apply the alternating direction method of multipliers (ADMM) optimization algorithm to implicit time integration of elastic bodies, and show that the resulting method closely relates to the recently proposed projective dynamics algorithm. However, as ADMM is a general purpose optimization algorithm applicable to a broad range of objective functions, it permits the use of nonlinear constitutive models and hard constraints while retaining the speed, parallelizability, and robustness of projective dynamics. We further extend the algorithm to improve the handling of dynamically changing constraints such as sliding and contact, while maintaining the benefits of a constant, prefactored system matrix. We demonstrate the benefits of our algorithm on several examples that include cloth, collisions, and volumetric deformable bodies with nonlinear elasticity and skin sliding effects.

We present a technique for displaying three-dimensional imagery of general scenes with nearly correct focus cues on multi-plane displays. These displays present an additive combination of images at a discrete set of optical distances, allowing the viewer to focus at different distances in the simulated scene. Our proposed technique extends the capabilities of multi-plane displays to general scenes with occlusions and non-Lambertian effects by using a model of defocus in the eye of the viewer. Requiring no explicit knowledge of the scene geometry, our technique uses an optimization algorithm to compute the images to be displayed on the presentation planes so that the retinal images when accommodating to different distances match the corresponding retinal images of the input scene as closely as possible. We demonstrate the utility of the technique using imagery acquired from both synthetic and real-world scenes, and analyze the system's characteristics including bounds on achievable resolution.

This paper describes a method for view-dependent cloth simulation using dynamically adaptive mesh refinement and coarsening. Given a prescribed camera motion, the method adjusts the criteria controlling refinement to account for visibility and apparent size in the camera's view. Objectionable dynamic artifacts are avoided by anticipative refinement and smoothed coarsening, while locking in extremely coarsened regions is inhibited by modifying the material model to compensate for unresolved sub-element buckling. This approach preserves the appearance of detailed cloth throughout the animation while avoiding the wasted effort of simulating details that would not be discernible to the viewer. The computational savings realized by this method increase as scene complexity grows. The approach produces a 2× speed-up for a single character and more than 4× for a small group as compared to view-independent adaptive simulations, and respectively 5× and 9× speed-ups as compared to non-adaptive simulations.

This paper presents a method for adaptive fracture propagation in thin sheets. A high-quality triangle mesh is dynamically restructured to adaptively maintain detail wherever it is required by the simulation. These requirements include refining where cracks are likely to either start or advance. Refinement ensures that the stress distribution around the crack tip is well resolved, which is vital for creating highly detailed, realistic crack paths. The dynamic meshing framework allows subsequent coarsening once areas are no longer likely to produce cracking. This coarsening allows efficient simulation by reducing the total number of active nodes and by preventing the formation of thin slivers around the crack path. A local reprojection scheme and a substepping fracture process help to ensure stability and prevent a loss of plasticity during remeshing. By including bending and stretching plasticity models, the method is able to simulate a large range of materials with very different fracture behaviors.

Local collision avoidance algorithms in crowd simulation often ignore agents beyond a neighborhood of a certain size. This cutoff can result in sharp changes in trajectory when large groups of agents enter or exit these neighborhoods. In this work, we exploit the insight that exact collision avoidance is not necessary between agents at such large distances, and propose a novel algorithm for extending existing collision avoidance algorithms to perform approximate, long-range collision avoidance. Our formulation performs long-range collision avoidance for distant agent groups to efficiently compute trajectories that are smoother than those obtained with state-of-the-art techniques and at faster rates. Comparison to real-world data demonstrates that crowds simulated with our algorithm exhibit an improved speed sensitivity to density similar to human crowds. Another issue often sidestepped in existing work is that discrete and continuum collision avoidance algorithms have different regions of applicability. For example, low-density crowds cannot be modeled as a continuum, while high-density crowds can be expensive to model using discrete methods. We formulate a hybrid technique for crowd simulation which can accurately and efficiently simulate crowds at any density with seamless transitions between continuum and discrete representations. Our approach blends results from continuum and discrete algorithms, based on local density and velocity variance. In addition to being robust across a variety of group scenarios, it is also highly efficient, running at interactive rates for thousands of agents on portable systems.

Local collision avoidance algorithms in crowd simulation often ignore agents beyond a neighborhood of a certain size. This cutoff can result in sharp changes in trajectory when large groups of agents enter or exit these neighborhoods. In this work, we exploit the insight that exact collision avoidance is not necessary between agents at such large distances, and propose a novel algorithm for extending existing collision avoidance algorithms to perform approximate, long-range collision avoidance. Our formulation performs long-range collision avoidance for distant agent groups to efficiently compute trajectories that are smoother than those obtained with state-of-the-art techniques and at faster rates.

Abstract We present a GPU‐based streaming algorithm to perform high‐resolution and accurate cloth simulation. We map all the components of cloth simulation pipeline, including time integration, collision detection, collision response, and velocity updating to GPU‐based kernels and data structures. Our algorithm perform intra‐object and inter‐object collisions, handles contacts and friction, and is able to accurately simulate folds and wrinkles. We describe the streaming pipeline and address many issues in terms of obtaining high throughput on many‐core GPUs. In practice, our algorithm can perform high‐fidelity simulation on a cloth mesh with 2M triangles using 3GB of GPU memory. We highlight the parallel performance of our algorithm on three different generations of GPUs. On a high‐end NVIDIA Tesla K20c, we observe up to two orders of magnitude performance improvement as compared to a single‐threaded CPU‐based algorithm, and about one order of magnitude improvement over a 16‐core CPU‐based parallel implementation.

The central argument against data-driven methods in computer graphics rests on the curse of dimensionality: it is intractable to precompute "everything" about a complex space. In this paper, we challenge that assumption by using several thousand CPU-hours to perform a massive exploration of the space of secondary clothing effects on a character animated through a large motion graph. Our system continually explores the phase space of cloth dynamics, incrementally constructing a secondary cloth motion graph that captures the dynamics of the system. We find that it is possible to sample the dynamical space to a low visual error tolerance and that secondary motion graphs containing tens of gigabytes of raw mesh data can be compressed down to only tens of megabytes. These results allow us to capture the effect of high-resolution, off-line cloth simulation for a rich space of character motion and deliver it efficiently as part of an interactive application.

We present a technique for simulating plastic deformation in sheets of thin materials, such as crumpled paper, dented metal, and wrinkled cloth. Our simulation uses a framework of adaptive mesh refinement to dynamically align mesh edges with folds and creases. This framework allows efficient modeling of sharp features and avoids bend locking that would be otherwise caused by stiff in-plane behavior. By using an explicit plastic embedding space we prevent remeshing from causing shape diffusion. We include several examples demonstrating that the resulting method realistically simulates the behavior of thin sheets as they fold and crumple.

Simulating fluids in large-scale scenes with appreciable quality using state-of-the-art methods can lead to high memory and compute requirements. Since memory requirements are proportional to the product of domain dimensions, simulation performance is limited by memory access, as solvers for elliptic problems are not compute-bound on modern systems. This is a significant concern for large-scale scenes. To reduce the memory footprint and memory/compute ratio, vortex singularity bases can be used. Though they form a compact bases for incompressible vector fields, robust and efficient modeling of nonrigid obstacles and free-surfaces can be challenging with these methods. We propose a hybrid domain decomposition approach that couples Eulerian velocity-based simulations with vortex singularity simulations. Our formulation reduces memory footprint by using smaller Eulerian domains with compact vortex bases, thereby improving the memory/compute ratio, and simulation performance by more than 1000x for single phase flows as well as significant improvements for free-surface scenes. Coupling these two heterogeneous methods also affords flexibility in using the most appropriate method for modeling different scene features, as well as allowing robust interaction of vortex methods with free-surfaces and nonrigid obstacles.

We present a technique for cloth simulation that dynamically refines and coarsens triangle meshes so that they automatically conform to the geometric and dynamic detail of the simulated cloth. Our technique produces anisotropic meshes that adapt to surface curvature and velocity gradients, allowing efficient modeling of wrinkles and waves. By anticipating buckling and wrinkle formation, our technique preserves fine-scale dynamic behavior. Our algorithm for adaptive anisotropic remeshing is simple to implement, takes up only a small fraction of the total simulation time, and provides substantial computational speedup without compromising the fidelity of the simulation. We also introduce a novel technique for strain limiting by posing it as a nonlinear optimization problem. This formulation works for arbitrary non-uniform and anisotropic meshes, and converges more rapidly than existing solvers based on Jacobi or Gauss-Seidel iterations.

We present a novel continuum-based model that enables efficient simulation of granular materials. Our approach fully solves the internal pressure and frictional stresses in a granular material, thereby allows visually noticeable behaviors of granular materials to be reproduced, including freely dispersing splashes without cohesion, and a global coupling between friction and pressure. The full treatment of internal forces in the material also enables two-way interaction with solid bodies. Our method achieves these results at only a very small fraction of computational costs of the comparable particle-based models for granular flows.

Large dense crowds show aggregate behavior with reduced individual freedom of movement. We present a novel, scalable approach for simulating such crowds, using a dual representation both as discrete agents and as a single continuous system. In the continuous setting, we introduce a novel variational constraint calledunilateral incompressibility, to model the large-scale behavior of the crowd, and accelerate inter-agent collision avoidance in dense scenarios. This approach makes it possible to simulate very large, dense crowds composed of up to a hundred thousand agents at near-interactive rates on desktop computers.

Accurate sound rendering can add significant realism to complement visual display in interactive applications, as well as facilitate acoustic predictions for many engineering applications, like accurate acoustic analysis for architectural design (Monks et al., 2000). Numerical simulation can provide this realism most naturally by modeling the underlying physics of wave propagation. However, wave simulation has traditionally posed a tough computational challenge. In this paper, we present a technique which relies on an adaptive rectangular decomposition of 3D scenes to enable efficient and accurate simulation of sound propagation in complex virtual environments. It exploits the known analytical solution of the wave equation in rectangular domains, and utilizes an efficient implementation of the discrete cosine transform on graphics processors (GPU) to achieve at least a 100-fold performance gain compared to a standard finite-difference time-domain (FDTD) implementation with comparable accuracy, while also being 10-fold more memory efficient. Consequently, we are able to perform accurate numerical acoustic simulation on large, complex scenes in the kilohertz range. To the best of our knowledge, it was not previously possible to perform such simulations on a desktop computer. Our work thus enables acoustic analysis on large scenes and auditory display for complex virtual environments on commodity hardware.

Abstract We present a technique for coupling simulated fluid phenomena that interact with real dynamic scenes captured as a binocular video sequence. We first process the binocular video sequence to obtain a complete 3D reconstruction of the scene, including velocity information. We use stereo for the visible parts of 3D geometry and surface completion to fill the missing regions. We then perform fluid simulation within a 3D domain that contains the object, enabling one‐way coupling from the video to the fluid. In order to maintain temporal consistency of the reconstructed scene and the animated fluid across frames, we develop a geometry tracking algorithm that combines optic flow and depth information with a novel technique for “velocity completion”. The velocity completion technique uses local rigidity constraints to hypothesize a motion field for the entire 3D shape, which is then used to propagate and filter the reconstructed shape over time. This approach not only generates smoothly varying geometry across time, but also simultaneously provides the necessary boundary conditions for one‐way coupling between the dynamic geometry and the simulated fluid. Finally, we employ a GPU based scheme for rendering the synthetic fluid in the real video, taking refraction and scene texture into account.

We present a novel technique for the animation of turbulent fluids by coupling a procedural turbulence model with a numerical fluid solver to introduce subgrid-scale flow detail. From the large-scale flow simulated by the solver, we model the production and behavior of turbulent energy using a physically motivated energy model. This energy distribution is used to synthesize an incompressible turbulent velocity field, whose features show plausible temporal behavior through a novel Lagrangian approach for advected noise. The synthesized turbulent flow has a dynamical effect on the large-scale flow, and produces visually plausible detailed features on both gaseous and free-surface liquid flows. Our method is an order of magnitude faster than full numerical simulation of equivalent resolution, and requires no manual direction.