Physics-Based Animation

Jing Li, Tiantian Liu, Ladislav Kavan

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

Fast Simulation of Deformable Characters with Articulated Skeletons in Projective Dynamics

Daniel Holden, Bang Chi Duong, Sayantan Datta, Derek Nowrouzezahrai

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 sub-space 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.

Subspace Neural Physics: Fast Data-Driven Interactive Simulation

Peter Kadlecek, Ladislav Kavan

The human face is an anatomical system exhibiting heterogenous and anisotropic mechanical behavior. This leads to complex deformations even in a neutral facial expression due to external forces such as gravity. We start by building a volumetric model from magnetic resonance images of a neutral facial expression. To obtain data on facial deformations we capture and register 3D scans of the face with different gravity directions and with various facial expressions. Our main contribution consists in solving an inverse physics problem where we learn mechanical properties of the face from our training data (3D scans). Specifically, we learn heterogenous stiffness and prestrain (which introduces anisotropy). The generalization capability of our resulting physics-based model is tested on 3D scans. We demonstrate that our model generates predictions of facial deformations more accurately than recent related physics-based techniques.

Building Accurate Physics-Based Face Models From Data

Yu Ju (Edwin) Chen, David I.W. Levin, Danny Kaufman, Uri Ascher, Dinesh K. Pai

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 homogeneous and heterogeneous material distributions.

EigenFit for Consistent Elastodynamic Simulation Across Mesh Resolution

Jumyung Chang, Fang Da, Eitan Grinspun, Christopher Batty

We present a unified method to simulate deformable elastic bodies consisting of mixed-dimensional components represented with potentially non-manifold simplicial meshes. Building on well-known simplicial rod, shell, and solid models for elastic continua, we categorize and define a comprehensive palette expressing all possible constraints and elastic energies for stiff and flexible connections between the 1D, 2D, and 3D components of a single conforming simplicial mesh. This palette consists of three categories: point connections, in which simplices meet at a single vertex around which they may twist and bend; curve connections in which simplices share an edge around which they may rotate (bend) relative to one another; and surface connections, in which a shell is embedded on or into a solid. To define elastic behaviors across non-manifold point connections, we adapt and apply parallel transport concepts from elastic rods. To address discontinuous forces that would otherwise arise when large accumulated relative rotations wrap around in the space of angles, we develop an incremental angle-update strategy. Our method provides a conceptually simple, flexible, and highly expressive framework for designing complex elastic objects, by modeling the geometry with a single simplicial mesh and decorating its elements with appropriate physical models (rod, shell, solid) and connection types (point, curve, surface). We demonstrate a diverse set of possible interactions achievable with our method, through technical and application examples, including scenes featuring complex aquatic creatures, children’s toys, and umbrellas.

A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects

Minjae Lee, David Hyde, Kevin Li, Ronald Fedkiw

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 straightforward 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.

A Robust Volume Conserving Method for Character-Water Interaction

Marco Romeo, Carlos Monteagudo, Daniel Sánchez‐Quirós

Recent research on muscle and fascia simulation for visual effects relies on numerical methods such as the finite element method or finite volume method. These approaches produce realistic results, but require high computational time and are complex to set up. On the other hand, position‐based dynamics offers a fast and controllable solution to simulate surfaces and volumes, but there is no literature on how to implement constraints that could be used to realistically simulate muscles and fascia for digital creatures with this method. In this paper, we extend the current state‐of‐the‐art in Position‐Based Dynamics to efficiently compute realistic skeletal muscle and superficial fascia simulation. In particular, we embed muscle fibres in the solver by adding an anisotropic component to the distance constraints between mesh points and apply overpressure to realistically model muscle volume changes under contraction. In addition, we also define a modified distance constraint for the fascia that allows compression and enables the user to scale the constraint’s original distance to gain elastic potential at rest. Finally, we propose a modification of the extended position‐based dynamics algorithm to properly compute different sets of constraints and describe other details for proper simulation of character’s muscle and fascia dynamics.

Muscle and Fascia Simulation with Extended Position Based Dynamics

Mridul Aanjaneya, Chengguizi Han, Ryan Goldade, Christopher Batty

We present an efficient geometric Multigrid solver for simulating viscous liquids based on the variational approach of [Batty and Bridson 2008]. Although the governing equations for viscosity are elliptic, the strong coupling between different velocity components in the discrete stencils mandates the use of more exotic smoothing techniques to achieve textbook Multigrid efficiency. Our key contribution is the design of a novel box smoother involving small and sparse systems (at most 9×9 in 2D and 15×15 in 3D), which yields excellent convergence rates and performance improvements of 3.5x – 13.8x over a naïve Multigrid approach. We employ a hybrid approach by using a direct solver only inside the box smoother and keeping the remaining pipeline assembly-free, allowing our solver to efficiently accommodate more than 194 million degrees of freedom, while occupying a memory footprint of less than 16 GB. To reduce the computational overhead of using the box smoother, we precompute the Cholesky factorization of the subdomain system matrix for all interior degrees of freedom. We describe how the variational formulation, which requires volume weights computed at the centers of cells, edges, and faces, can be naturally accommodated in the Multigrid hierarchy to properly enforce boundary conditions. Our proposed Multigrid solver serves as an excellent preconditioner for Conjugate Gradients, outperforming existing state-of-the-art alternatives. We demonstrate the efficacy of our method on several high resolution examples of viscous liquid motion including two-way coupled interactions with rigid bodies.

An Efficient Geometric Multigrid Solver for Viscous Liquids

Maximilian Werhahn, You Xie, Mengyu Chu, Nils Thuerey

We propose a novel method to up-sample volumetric functions with generative neural networks using several orthogonal passes. Our method decomposes generative problems on Cartesian field functions into multiple smaller sub-problems that can be learned more efficiently. Specifically, we utilize two separate generative adversarial networks: the first one up-scales slices which are parallel to the XY- plane, whereas the second one refines the whole volume along the Z- axis working on slices in the YZ- plane. In this way, we obtain full coverage for the 3D target function and can leverage spatio-temporal supervision with a set of discriminators. Additionally, we demonstrate that our method can be combined with curriculum learning and progressive growing approaches. We arrive at a first method that can up-sample volumes by a factor of eight along each dimension, i.e., increasing the number of degrees of freedom by 512. Large volumetric up-scaling factors such as this one have previously not been attainable as the required number of weights in the neural networks renders adversarial training runs prohibitively difficult. We demonstrate the generality of our trained networks with a series of comparisons to previous work, a variety of complex 3D results, and an analysis of the resulting performance.

A Multi-Pass GAN for Fluid Flow Super-Resolution

• Fast Simulation of Deformable Characters with Articulated Skeletons in Projective Dynamics
• VIPER: Volume Invariant Position-based Elastic Rods
• A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects
• Small Steps in Physics Simulation
• Building Accurate Physics-based Face Models from Data
• A Robust Volume Conserving Method for Character-Water Interaction
• An Efficient Geometric Multigrid Solver for Viscous Liquids
• A Second-Order Advection-Reflection Solver
• A Hybrid Material Point Method for Frictional Contact with Diverse Materials
• Simulation and Visualization of Ductile Fracture with the Material Point Method
• EigenFit for Consistent Elastodynamic Simulation Across Mesh Resolution
• Subspace Neural Physics: Fast Data-Driven Interactive Simulation
• A Multi-Pass GAN for Fluid Flow Super-Resolution
• Fluid Simulation with Adaptive Staggered Power Particles on GPUs (TVCG)
• Flexible Use of Temporal and Spatial Reasoning for Fast and Scalable CPU Broad Phase Collision Detection using KD-Trees (CGF)