Physics-Based Animation

Gilles Daviet

We devise a local–global solver dedicated to the simulation of Discrete Elastic Rods (DER) with Coulomb friction that can fully leverage the massively parallel compute capabilities of moderns GPUs. We verify that our simulator can reproduce analytical results on recently published cantilever, bend–twist, and stick–slip experiments, while drastically decreasing iteration times for high-resolution hair simulations. Being able to handle contacting assemblies of several thousand elastic rods in real-time, our fast solver paves the ways for new workflows such as interactive physics-based editing of digital grooms.

Interactive Hair Simulation on the GPU using ADMM

Hang Yin, Mohammad Sina Nabizadeh, Baichun Wu, Stephanie Wang, Albert Chern

The vorticity-streamfunction formulation for incompressible inviscid fluids is the basis for many fluid simulation methods in computer graphics, including vortex methods, streamfunction solvers, spectral methods, and Monte Carlo methods. We point out that current setups in the vorticity-streamfunction formulation are insufficient at simulating fluids on general non-simply-connected domains. This issue is critical in practice, as obstacles, periodic boundaries, and nonzero genus can all make the fluid domain multiply connected. These scenarios introduce nontrivial cohomology components to the flow in the form of harmonic fields. The dynamics of these harmonic fields have been previously overlooked. In this paper, we derive the missing equations of motion for the fluid cohomology components. We elucidate the physical laws associated with the new equations, and show their importance in reproducing physically correct behaviors of fluid flows on domains with general topology.

Fluid Cohomology

Tianye Xie, Minchen Li, Yin Yang, Chenfanfu Jiang

We present a robust and efficient method for simulating Lagrangian solid-fluid coupling based on a new operator splitting strategy. We use variational formulations to approximate fluid properties and solid-fluid interactions, and introduce a unified two-way coupling formulation for SPH fluids and FEM solids using interior point barrier-based frictional contact. We split the resulting optimization problem into a fluid phase and a solid-coupling phase using a novel time-splitting approach with augmented contact proxies, and propose efficient custom linear solvers. Our technique accounts for fluids interaction with nonlinear hyperelastic objects of different geometries and codimensions, while maintaining an algorithmically guaranteed non-penetrating criterion. Comprehensive benchmarks and experiments demonstrate the efficacy of our method.

A Contact Proxy Splitting Method for Lagrangian Solid-Fluid Coupling

• A Contact Proxy Splitting Method for Lagrangian Solid-Fluid Coupling
• Second-order Stencil Descent for Interior-point Hyperelasticity
• A Sparse Distributed Gigascale Resolution Material Point Method
• PolyStokes: A Polynomial Model Reduction Method for Viscous Fluid Simulation
• Data-Free Learning of Reduced-Order Kinematics
• Generalizing Shallow Water Simulations with Dispersive Surface Waves
• Fluid Cohomology
• Complex Wrinkle Field Evolution
• Sag-free Initialization for Strand-based Hybrid Hair Simulation
• Interactive Hair Simulation on the GPU Using ADMM
• Beyond Chainmail: Computational Modeling of Discrete Interlocking Materials
• Fast Complementary Dynamics via Skinning Eigenmodes
• Motion From Shape Change
• Nonlinear Compliant Modes for Large-deformation Analysis of Flexible Structures
• Improved Water Sound Synthesis Using Coupled Bubbles
• Building a Virtual Weakly-compressible Wind Tunnel Testing Facility
• Fluid-solid Coupling in Kinetic Two-phase Flow Simulation
• In-Timestep Remeshing for Contacting Elastodynamics
• Fast GPU-based Two-way Continuous Collision Handling
• Shortest Path to Boundary for Self-Intersecting Meshes
• Sum-of-squares Collision Detection for Curved Shapes and Paths
• High-order Incremental Potential Contact for Elastodynamic Simulation on Curved Meshes
• Multi-Layer Thick Shells
• Constraint-Based Simulation of Passive Suction Cups
• Nonlinear Compliant Modes for Large-Deformation Analysis of Flexible Structures
• Anatomically Detailed Simulation of Human Torso

Fan Feng, Jinyuan Liu, Shiying Xiong, Shuqi Yang, Yaorui Zhang, Bo Zhu

We propose a new incompressible Navier–Stokes solver based on the impulse gauge transformation. The mathematical model of our approach draws from the impulse–velocity formulation of Navier–Stokes equations, which evolves the fluid impulse as an auxiliary variable of the system that can be projected to obtain the incompressible flow velocities at the end of each time step. We solve the impulse-form equations numerically on a Cartesian grid. At the heart of our simulation algorithm is a novel model to treat the impulse stretching and a harmonic boundary treatment to incorporate the surface tension effects accurately. We also build an impulse PIC/FLIP solver to support free-surface fluid simulation. Our impulse solver can naturally produce rich vortical flow details without artificial enhancements. We showcase this feature by using our solver to facilitate a wide range of fluid simulation tasks including smoke, liquid, and surface-tension flow. In addition, we discuss a convenient mechanism in our framework to control the scale and strength of the turbulent effects of fluid.

Impulse Fluid Simulation

Tianyu Wang, Jiong Chen, Dongping Li, Xiaowei Liu, Huamin Wang, Kun Zhou

Step-and-project is a popular way to simulate non-penetrated deformable bodies in physically-based animation. First integrating the system in time regardless of contacts and post resolving potential intersections practically strike a good balance between plausibility and efficiency. However, existing methods could be defective and unsafe when the time step is large, taking risks of failures or demands of repetitive collision testing and resolving that severely degrade performance. In this paper, we propose a novel two-way method for fast and reliable continuous collision handling. Our method launches the optimization at both ends of the intermediate time-integrated state and the previous intersection-free state, progressively generating a piecewise-linear path and finally reaching a feasible solution for the next time step. Technically, our method interleaves between a forward step and a backward step at a low cost, until the result is conditionally converged. Due to a set of unified volume-based contact constraints, our method can flexibly and reliably handle a variety of codimensional deformable bodies, including volumetric bodies, cloth, hair and sand. The experiments show that our method is safe, robust, physically faithful and numerically efficient, especially suitable for large deformations or large time steps.

Fast GPU-Based Two-Way Continuous Collision Handling

Chongyao Zhao, Jinkeng Lin, Tianyu Wang, Hujun Bao, Jin Huang

Piecewise linear inextensible Cosserat rods are usually represented by Cartesian coordinates of vertices and quaternions on the segments. Such representations use excessive degrees of freedom (DOFs), and need many additional constraints, which causes unnecessary numerical difficulties and computational burden for simulation. We propose a simple yet compact representation that exactly matches the intrinsic DOFs and naturally satisfies all such constraints. Specifically, viewing a rod as a chain of rigid segments, we encode its shape as the Cartesian coordinates of its root vertex, and use axis-angle representation for the material frame on each segment. Under our representation, the Hessian of the implicit timestepping has special non-zero patterns. Exploiting such specialties, we can solve the associated linear equations in nearly linear complexity. Furthermore, we carefully designed a preconditioner, which is proved to be always symmetric positive-definite and accelerates the PCG solver in one or two orders of magnitude compared with the widely used block-diagonal one. Compared with other technical choices including Super-Helices, a specially designed compact representation for inextensible Cosserat rods, our method achieves better performance and stability, and can simulate an inextensible Cosserat rod with hundreds of vertices and tens of collisions in real time under relatively large time steps.

Efficient and Stable Simulation of Inextensible Cosserat Rods by a Compact Representation

Simon Duenser, Bernhard Thomaszewski, Roi Poranne, Stelian Coros

Many flexible structures are characterized by a small number of compliant
modes, i.e., large deformation paths that can be traversed with little mechanical effort, whereas resistance to other deformations is much stiffer. Predicting the compliant modes for a given flexible structure, however, is challenging. While linear eigenmodes capture the small-deformation behavior, they quickly divert into states of unrealistically high energy for larger displacements. Moreover, they are inherently unable to predict nonlinear phenomena such as buckling, stiffening, multistability, and contact. To address this limitation, we propose Nonlinear Compliant Modes—a physically-principled extension of linear eigenmodes for large-deformation analysis. Instead of constraining the entire structure to deform along a given eigenmode, our method only prescribes the projection of the system’s state onto the linear mode while all other degrees of freedom follow through energy minimization. We evaluate the potential of our method on a diverse set of flexible structures, ranging from compliant mechanisms to topology-optimized joints and structured materials. As validated through experiments on physical prototypes, our method correctly predicts a broad range of nonlinear effects that linear eigenanalysis fails to capture.

Nonlinear Compliant Modes for Large-Deformation Analysis of Flexible
Structures

Nicolas Rosset, Guillaume Cordonnier, Regis Duvigneau, Adrien Bousseau

The design of car shapes requires a delicate balance between aesthetic and performance. While fluid simulation provides the means to evaluate the aerodynamic performance of a given shape, its computational cost hinders its usage during the early explorative phases of design, when aesthetic is decided upon. We present an interactive system to assist designers in creating aerodynamic car profiles. Our system relies on a neural surrogate model to predict fluid flow around car shapes, providing fluid visualization and shape optimization feedback to designers as soon as they sketch a car profile. Compared to prior work that focused on time-averaged fluid flows, we describe how to train our model on instantaneous, synchronized observations extracted from multiple pre-computed simulations, such that we can visualize and optimize for dynamic flow features, such as vortices. Furthermore, we architectured our model to support gradient-based shape optimization within a learned latent space of car profiles. In addition to regularizing the optimization process, this latent space and an associated encoder-decoder allows us to input and output car profiles in a bitmap form, without any explicit parameterization of the car boundary. Finally, we
designed our model to support pointwise queries of fluid properties around car shapes, allowing us to adapt computational cost to application needs. As an illustration, we only query our model along streamlines for flow visualization, we query it in the vicinity of the car for drag optimization, and we query it behind the car for vortex attenuation.

Interactive design of 2D car profiles with aerodynamic feedback

Tianxing Li, Rui Shi, Takashi Kanai

This paper presents a novel learning-based clothing deformation method to generate rich and reasonable detailed deformations for garments worn by bodies of various shapes in various animations. In contrast to existing learning-based methods, which require numerous trained models for different garment topologies or poses and are unable to easily realize rich details, we use a unified framework to produce high fidelity deformations efficiently and easily. To address the challenging issue of predicting deformations influenced by multi-source attributes, we propose three strategies from novel perspectives. Specifically, we first found that the fit between the garment and the body has an important impact on the degree of folds. We then designed an attribute parser to generate detail-aware encodings and infused them into the graph neural network, therefore enhancing the discrimination of details under diverse attributes. Furthermore, to achieve better convergence and avoid overly smooth deformations, we proposed output reconstruction to mitigate the complexity of the learning task. Experiment results show that our proposed deformation method achieves better performance over existing methods in terms of generalization ability and quality of details.

Detail-aware Deep Clothing Animations Infused with Multi-source Attributes