Physics-Based Animation

Yun (Raymond) Fei, Qi Guo, Rundong Wu, Li Huang, Ming Gao

The material point method recently demonstrated its efficacy at simulating many materials and the coupling between them on a massive scale. However, in scenarios containing debris, MPM manifests more dissipation and numerical viscosity than traditional Lagrangian methods. We have two observations from carefully revisiting existing integration methods used in MPM. First, nearby particles would end up with smoothed velocities without recovering momentum for each particle during the particle-grid-particle transfers. Second, most existing integrators assume continuity in the entire domain and advect particles by directly interpolating the positions from deformed nodal positions, which would trap the particles and make them harder to separate. We propose an integration scheme that corrects particle positions at each time step. We demonstrate our method’s effectiveness with several large-scale simulations involving brittle materials. Our approach effectively reduces diffusion and unphysical viscosity compared to traditional integrators.

Revisiting Integration in the Material Point Method: A Scheme for Easier Separation and Less Dissipation

George Sperl, Rahul Narain, Chris Wojtan

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.

Mechanics-Aware Deformation of Yarn Pattern Geometry

Vismay Modi, Lawson Fulton, Shinjiro Sueda, Alec Jacobson, David I.W. Levin

EMU is an efficient and scalable model to simulate bulk musculoskeletal motion with heterogenous materials. First, EMU requires no model reductions, or geometric coarsening, thereby producing results visually accurate when compared to an FEM simulation. Second, EMU is efficient and scales much better than state-of-the-art FEM with the number of elements in the mesh, and is more easily parallelizable. Third, EMU can handle heterogeneously stiff meshes with an arbitrary constitutive model, thus allowing it to simulate soft muscles, stiff tendons and even stiffer bones all within one unified system. These three key characteristics of EMU enable us to efficiently orchestrate muscle activated skeletal movements. We demonstrate the efficacy of our approach via a number of examples with tendons, muscles, bones and joints.

EMU: Efficient Muscle Simulation in Deformation Space

Kuixin Zhu, Xiaowei He, Sheng Li, Hongan Wang, Guoping Wang

Granular media is the second-most-manipulated substance on Earth, second only to water. However, simulation of granularmedia is still challenging due to the complexity of granular materials and the large number of discrete solid particles. As we know, drygranular materials could form a hybrid state between a fluid and a solid, therefore we propose a two-layer model and divide thesimulation domain into a dilute layer, where granules can move freely as a fluid, and a dense layer, where granules act more like asolid. Motivated by the shallow water equations, we derive a set of shallow sand equations for modeling dry granular flows bydepth-integrating three-dimensional governing equations along its vertical direction. Unlike previous methods for simulating a 2Dgranular media, our model does not restrict the depth of the granular media to be shallow anymore. To allow efficient fluid-solidinteractions, we also present a ray casting algorithm for one-way solid-fluid coupling. Finally, we introduce a particle-tracking method toimprove the visual representation. Our method can be efficiently implemented based on a height field and is fully compatible withmodern GPUs, therefore allows us to simulate large-scale dry granular flows in real time.

Shallow Sand Equations: Real-Time Height Field Simulation of Dry Granular Flows

Bohan Wang, Jernej Barbič

Real-time deformable object simulation is important in interactive applications such as games and virtual reality. One common approach to achieve speed is to employ model reduction, a technique whereby the equations of motion of a deformable object are projected to a suitable low-dimensional space. Improving the real-time performance of model-reduced systems has been the subject of much research. While modern GPUs play an important role in real-time simulation and parallel computing, existing model reduction systems typically utilize CPUs and seldom employ GPUs. We give a method to efficiently employ GPUs for vertex position computation in model-reduced simulations. Our CUDA-based algorithm gives a substantial speedup compared to a CPU implementation, thanks to our system architecture that employs a memory layout friendly to GPU memory, reduces the communication between the CPU and GPU, and enables the CPU and GPU to work in parallel.

CUDA Deformers for Model Reduction

Bohan Wang, Mianlun Zheng, Jernej Barbič

Physically based simulation is often combined with geometric mesh animation to add realistic soft-body dynamics to virtual characters. This is commonly done using constraint-based simulation whereby a soft-tissue simulation is constrained to geometric animation of a subpart (or otherwise proxy representation) of the character. We observe that standard constraint-based simulation suffers from an important flaw that limits the expressiveness of soft-body dynamics. Namely, under correct physics, the frequency and amplitude of soft-tissue dynamics arising from constraints (“inertial amplitude”) are coupled, and cannot be adjusted independently merely by adjusting the material properties of the model. This means that the space of physically based simulations is inherently limited and cannot capture all effects typically expected by computer animators. For example, animators need the ability to adjust the frequency, inertial amplitude, gravity sag and damping properties of the virtual character, independently from each other, as these are the primary visual characteristics of the soft-tissue dynamics. We demonstrate that independence can be achieved by transforming the equations of motion into a non-inertial reference coordinate frame, then scaling the resulting inertial forces, and then converting the equations of motion back to the inertial frame. Such scaling of inertia makes it possible for the animator to set the character’s inertial amplitude independently from frequency. We also provide exact controls for the amount of character’s gravity sag, and the damping properties. In our examples, we use linear blend skinning and pose-space deformation for geometric mesh animation, and the Finite Element Method for soft-body constrained simulation; but our idea of scaling inertial forces is general and applicable to other animation and simulation methods. We demonstrate our technique on several character examples.

Adjustable Constrained Soft-Tissue Dynamics

Tetsuya Takahashi, Christopher Batty

We propose Monolith, a monolithic pressure-viscosity-contact solver for more accurately, robustly, and efficiently simulating non-trivial two-way interactions of rigid bodies with inviscid, viscous, or non-Newtonian liquids. Our solver simultaneously handles incompressibility and (optionally) implicit viscosity integration for liquids, contact resolution for rigid bodies, and mutual interactions between liquids and rigid bodies by carefully formulating these as a single unified minimization problem. This monolithic approach reduces or eliminates an array of problematic artifacts, including liquid volume loss, solid interpenetrations, simulation instabilities, artificial “melting” of viscous liquid, and incorrect slip at liquid-solid interfaces. In the absence of solid-solid friction, our minimization problem is a Quadratic Program (QP) with a symmetric positive definite (SPD) matrix and can be treated with a single Linear Complementarity Problem (LCP) solve. When friction is present, we decouple the unified minimization problem into two subproblems so that it can be effectively handled via staggered projections with alternating LCP solves.We also propose a complementary approach for non-Newtonian fluids which can be seamlessly integrated and addressed during the staggered projections. We demonstrate the critical importance of a contact-aware, unified treatment of fluid-solid coupling and the effectiveness of our proposed Monolith solver in a wide range of practical scenarios.

Monolith: A Monolithic Pressure-Viscosity-Contact Solver for Strong Two-Way Rigid-Rigid Rigid-Fluid Coupling

Yunxin Sun, Tamar Shinar, Craig Schroeder

Time steps for explicit MPM simulation in computer graphics are often selected by trial and error due to the challenges in automatically selecting stable time step sizes. Our time integration scheme uses time step restrictions that take into account forces, collisions, and even grid-to-particle transfers calculated near the end of the time step. We propose a novel set of time step restrictions that allow a time step to be selected that is stable, efficient to compute, and not too far from optimal. We derive the general solution for the sound speed in nonlinear isotropic hyperelastic materials, which we use to enforce the classical CFL time step restriction. We identify a single-particle instability in explicit MPM integration and propose a corresponding time step restriction in the fluid case. We also propose a reflection-based boundary condition for domain walls that supports separation and accurate Coulomb friction while preventing particles from penetrating the domain walls.

Effective Time Step Restrictions for explicit MPM simulation

Pengbin Tang, Jonas Zehnder, Stelian Coros, Bernhard Thomaszewski

We present a computational method for designing compliant mechanical systems that exhibit large-amplitude oscillations. The technical core of our approach is an optimization-driven design tool that combines sensitivity analysis for optimization with the Harmonic Balance Method for simulation. By establishing dynamic force equilibrium in the frequency domain, our formulation avoids the major limitations of existing alternatives: it handles nonlinear forces, side-steps any transient process, and automatically produces periodic solutions. We introduce design objectives for amplitude optimization and trajectory matching that enable intuitive high-level authoring of large-amplitude motions. Our method can be applied to many types of mechanical systems, which we demonstrate through a set of examples involving compliant mechanisms, flexible rod networks, elastic thin shell models, and multi-material solids. We further validate our approach by manufacturing and evaluating several physical prototypes.

A Harmonic Balance Approach for Designing Compliant Mechanical Systems with Nonlinear Periodic Motions

Andreas Longva, Fabian Löschner, Tassilo Kugelstadt, José Antonio Fernández-Fernández, Jan Bender

As demands for high-fidelity physics-based animations increase, the need for accurate methods for simulating deformable solids grows. While higher-order finite elements are commonplace in engineering due to their superior approximation properties for many problems, they have gained little traction in the computer graphics community. This may partially be explained by the need for finite element meshes to approximate the highly complex geometry of models used in graphics applications. Due to the additional per-element computational expense of higher-order elements, larger elements are needed, and the error incurred due to the geometry mismatch eradicates the benefits of higher-order discretizations. One solution to this problem is the embedding of the geometry into a coarser finite element mesh. However, to date there is no adequate, practical computational framework that permits the accurate embedding into higher-order elements. We develop a novel, robust quadrature generation method that generates theoretically guaranteed high-quality sub-cell integration rules of arbitrary polynomial accuracy. The number of quadrature points generated is bounded only by the desired degree of the polynomial, independent of the embedded geometry. Additionally, we build on recent work in the Finite Cell Method (FCM) community so as to tackle the severe ill-conditioning caused by partially filled elements by adapting an Additive-Schwarz-based preconditioner so that it is suitable for use with state-of-the-art non-linear material models from the graphics literature. Together these two contributions constitute a general-purpose framework for embedded simulation with higher-order finite elements. We finally demonstrate the benefits of our framework in several scenarios, in which second-order hexahedra and tetrahedra clearly outperform their first-order counterparts.

Higher-Order Finite Elements for Embedded Simulation