Physics-Based Animation

Wei Li, Tongtong Wang, Zherong Pan, Xifeng Gao, Kui Wu, Mathieu Desbrun

Kinetic solvers for incompressible fluid simulation were designed to run efficiently on massively parallel architectures such as GPUs. While these lattice Boltzmann solvers have recently proven much faster and more accurate than the macroscopic Navier-Stokes-based solvers traditionally used in graphics, it systematically comes at the price of a very large memory requirement: a mesoscopic discretization of statistical mechanics requires over an order of magnitude more variables per grid node than most fluid solvers in graphics. In order to open up kinetic simulation to gaming and simulation software packages on commodity hardware, we propose a High-Order Moment-Encoded Lattice-Boltzmann-Method solver which we coined HOME-LBM, requiring only the storage of a few moments per grid node, with little to no loss of accuracy in the typical simulation scenarios encountered in graphics. We show that our lightweight and lightspeed fluid solver requires three times less memory and runs ten times faster than state-of-the-art kinetic solvers, for a nearly-identical visual output.

High-Order Moment-Encoded Kinetic Simulation of Turbulent Flows

Xuan Li, Yu Fang, Lei Lan, Huamin Wang, Yin Yang, Minchen Li, Chenfanfu Jiang

We propose an efficient cloth simulation method that combines the merits of two drastically different numerical procedures, namely the subspace integration and parallelizable iterative relaxation. We show those two methods can be organically coupled within the framework of projective dynamics (PD), where both low- and high-frequency cloth motions are effectively and efficiently computed. Our method works seamlessly with the state-of-the-art contact handling algorithm, the incremental potential contact (IPC), to offer the non-penetration guarantee of the resulting animation. Our core ingredient centers around the utilization of subspace for the expedited convergence of Jacobi-PD. This involves solving the reduced global system and smartly employing its precomputed factorization. In addition, we incorporate a time-splitting strategy to handle the frictional self-contacts. Specifically, during the PD solve, we employ a quadratic proxy to approximate the contact barrier. The prefactorized subspace system matrix is exploited in a reduced-space LBFGS. The LBFGS method starts with the reduced system matrix of the rest shape as the initial
Hessian approximation, incorporating contact information into the reduced system progressively, while the full-space Jacobi iteration captures high-frequency details. Furthermore, we address penetration issues through a penetration correction step. It minimizes an incremental potential without elasticity using Newton-PCG. Our method can be efficiently executed on modern GPUs. Experiments show significant performance improvements over existing GPU solvers for high-resolution cloth simulation.

Subspace-Preconditioned GPU Projective Dynamics with Contact for Cloth Simulation

Christian Hafner, Bernd Bickel

The Kirchhoff rod model describes the bending and twisting of slender elastic rods in three dimensions, and has been widely studied to enable the prediction of how a rod will deform, given its geometry and boundary conditions. In this work, we study a number of inverse problems with the goal of computing the geometry of a straight rod that will automatically deform to match a curved target shape after attaching its endpoints to a support structure. Our solution lets us finely control the static equilibrium state of a rod by varying the cross-sectional profiles along its length. We also show that the set of physically realizable equilibrium states admits a concise geometric description in terms of linear line complexes, which leads to very efficient computational design algorithms. Implemented in an interactive software tool, they allow us to convert three-dimensional hand-drawn spline curves to elastic rods, and give feedback about the feasibility and practicality of a design in real time. We demonstrate the efficacy of our method by designing and manufacturing several physical prototypes with applications to interior design and soft robotics.

The Design Space of Kirchhoff Rods

Lorenzo Diazzi, Daniele Panozzo, Amir Vaxman, Marco Attene

We present a numerically robust algorithm for computing the constrained Delaunay tetrahedrization (CDT) of a piecewise-linear complex, which has a 100% success rate on the 4408 valid models in the Thingi10k dataset. We build on the underlying theory of the well-known TetGen software, but use a floating-point implementation based on indirect geometric predicates to implicitly represent Steiner points: this new approach dramatically simplifies the implementation, removing the need for ad-hoc tolerances in geometric operations. Our approach leads to a robust and parameter-free implementation, with an empirically manageable number of added Steiner points. Furthermore, our algorithm addresses a major gap in TetGen’s theory which may lead to algorithmic failure on valid models, even when assuming perfect precision in the calculations. Our output tetrahedrization conforms with the input geometry without approximations. We can further round our output to floating-point coordinates for downstream applications, which almost always results in valid floating-point meshes unless the input triangulation is very close to being degenerate.

Constrained Delaunay Tetrahedrization: A Robust and Practical Approach

• Constrained Delaunay Tetrahedrization: A Robust and Practical Approach
• The Design Space of Kirchhoff Rods
• High-Order Moment-Encoded Kinetic Simulation of Turbulent Flows
• Subspace-Preconditioned GPU Projective Dynamics with Contact for Cloth Simulation
• Real-time Height-field Simulation of Sand and Water Mixtures
• A Physically-inspired Approach to the Simulation of Plant Wilting
• Power Plastics: A Hybrid Lagrangian/Eulerian Solver for Mesoscale Inelastic Flows
• Neural Stress Fields for Reduced-order Elastoplasticity and Fracture
• Kirchhoff-Love Shells with Arbitrary Hyperelastic Materials
• Second-Order Finite Elements for Deformable Surfaces
• Fluid Simulation on Neural Flow Maps
• Capturing Animation-Ready Isotropic Materials Using Systematic Poking
• DiffFR: Differentiable SPH-based Fluid-Rigid Coupling for Rigid Body Control
• 3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing
• A Parametric Kinetic Solver for Simulating Boundary-Dominated Turbulent Flow Phenomena
• Stable Discrete Bending by Analytic Eigensystem and Adaptive Orthotropic Geometric Stiffness
• Progressive Shell Quasistatics for Unstructured Meshes
• GARM-LS: A Gradient-Augmented Reference-Map Method for Level-Set Fluid Simulation
• Neural Metamaterial Networks for Nonlinear Material Design
• An Implicitly Stable Mixture Model for Dynamic Multi-fluid Simulations
• High Density Ratio Multi-fluid Simulation with Peridynamics
• Real-Time Reconstruction of Fluid Flow under Unknown Disturbance
• Authoring and Simulating Meandering Rivers
• Neural Collision Fields for Triangle Primitives
• Learning Contact Deformations with General Collider Descriptors
• ClothCombo: Modeling Inter-Cloth Interaction for Draping Multi-Layered Clothes
• LiCROM: Linear-Subspace Continuous Reduced Order Modeling with Neural Fields
• Subspace Mixed Finite Elements for Real-Time Heterogeneous Elastodynamics
• ViCMA: Visual Control of Multibody Animations
• Non-Newtonian ViRheometry via Similarity Analysis

Yu Fang, Minchen Li, Yadi Cao, Xuan Li, Joshuah Wolper, Yin Yang, Chenfanfu Jiang

We introduce a variational formulation for simulating sticky interactions between elastoplastic solids. Our method brings a wider range of material behaviors into the reach of the Incremental Potential Contact (IPC) solver recently developed by [1]. Extending IPC requires several contributions. We first augment IPC with the classical Raous-Cangemi-Cocou (RCC) adhesion model. This allows us to robustly simulate the sticky interactions between arbitrary codimensional-0, 1, and 2 geometries. To enable user-friendly practical adoptions of our method, we further introduce a physically parametrized, easily controllable normal adhesion formulation based on the unsigned distance, which is fully compatible with IPC’s barrier formulation. Furthermore, we propose a smoothly clamped tangential adhesion model that naturally models intricate behaviors including debonding. Lastly, we perform benchmark studies comparing our method with the classical models as well as real-world experimental results to demonstrate the efficacy of our method.

Augmented Incremental Potential Contact for Sticky Interactions

Seunghwan Lee, Yifeng Jiang, C. Karen Liu

Existing digital human models approximate the human skeletal system using rigid bodies connected by rotational joints. While the simplification is considered acceptable for legs and arms, it significantly lacks fidelity to model rich torso movements in common activities such as dancing, Yoga, and various sports. Research from biomechanics provides more detailed modeling for parts of the torso, but their models often operate in isolation and are not fast and robust enough to support computationally heavy applications and large-scale data generation for full-body digital humans. This paper proposes a new torso model that aims to achieve high fidelity both in perception and in functionality, while being computationally feasible for simulation and optimal control tasks. We build a detailed human torso model consisting of various anatomical components, including facets, ligaments, and intervertebral discs, by coupling efficient finite-element and rigid-body simulations. Given an existing motion capture sequence without dense markers placed on the torso, our new model is able to recover the underlying torso bone movements. Our method is remarkably robust that it can be used to automatically “retrofit” the entire Mixamo motion database of highly diverse human motions without user intervention. We also show that our model is computationally efficient for solving trajectory optimization of highly dynamic full-body movements, without relying on any reference motion. Physiological validity of the model is validated against established literature.

Anatomically Detailed Simulation of Human Torso

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

Alvin Shi, Theodore Kim

We analyze a wide class of penalty energies used for contact response through the lens of a reduced frame. Applying our analysis to both spring-based and barrier-based energies, we show that we can obtain closed-form, analytic eigensystems that can be used to guarantee positive semidefiniteness in implicit solvers. Our approach is both faster than direct numerical methods, and more robust than approximate methods such as Gauss-Newton. Over the course of our analysis, we investigate physical interpretations for two separate notions of length. Finally, we showcase the stability of our analysis on challenging strand, cloth, and volume scenarios with large timesteps on the order of 1/40 s.

A Unified Analysis of Penalty-Based Collision Energies

Haomiao Wu, Theodore Kim

Angle-based energies appear in numerous physics-based simulation models, including thin-shell bending and isotropic elastic strands. We present a generic analysis of these energies that allows us to analytically filter the negative eigenvalues of the second derivative (Hessian), which is critical for stable, implicit time integration. While these energies are usually formulated in terms of angles and positions, we propose an abstract edge stencil that succinctly parameterizes the edge deformation, and allows us to derive generic, closed-form analytical expressions for the energy eigensystems. The resultant eigenvectors have straightforward geometric interpretations.We demonstrate that our method is readily applicable to a variety of 2D and 3D angle-based elastic energies, including both cloth and strands, and is up to 7x faster than numerical eigendecomposition.

An Eigenanalysis of Angle-Based Deformation Energies