Physics-Based Animation

Silvia Sellán, Jack Luong, Leticia Mattos Da Silva, Aravind Ramakrishnan, Yuchuan Yang, Alec Jacobson

Drawing a direct analogy with the well-studied vibration or elastic modes, we introduce an object’s fracture modes, which constitute its preferred or most natural ways of breaking. We formulate a sparsified eigenvalue problem, which we solve iteratively to obtain the n lowest-energy modes. These can be precomputed for a given shape to obtain a prefracture pattern that can substitute the state of the art for realtime applications at no runtime cost but significantly greater realism. Furthermore, any realtime impact can be projected onto our modes to obtain impact-dependent fracture patterns without the need for any online crack propagation simulation. We not only introduce this theoretically novel concept, but also show its fundamental and practical advantages in a diverse set of examples and contexts.

Breaking Good: Fracture Modes for Realtime Destruction

Ying Wang, Jasper Verheul, Sang-Hoon Yeo, Nima Khademi Kalantari, Shinjiro Sueda

We propose a simple and practical approach for incorporating the effects of muscle inertia, which has been ignored by previous musculoskeletal simulators in both graphics and biomechanics. We approximate the inertia of the muscle by assuming that muscle mass is distributed along the centerline of the muscle. We express the motion of the musculotendons in terms of the motion of the skeletal joints using a chain of Jacobians, so that at the top level, only the reduced degrees of freedom of the skeleton are used to completely drive both bones and musculotendons. Our approach can handle all commonly used musculotendon path types, including those with multiple path points and wrapping surfaces. For muscle paths involving wrapping surfaces, we use neural networks to model the Jacobians, trained using existing wrapping surface libraries, which allows us to effectively handle the Jacobian discontinuities that occur when musculotendon paths collide with wrapping surfaces. We demonstrate support for higher-order time integrators, complex joints, inverse dynamics, Hill-type muscle models, and differentiability. In the limit, as the muscle mass is reduced to zero, our approach gracefully degrades to traditional simulators without support for muscle inertia. Finally, it is possible to mix and match inertial and non-inertial musculotendons, depending on the application.

Differentiable Simulation of Inertial Musculotendons

• Differentiable Simulation of Inertial Musculotendons
• Simulation of Hand Anatomy Using Medical Imaging
• Shape from Release: Inverse Design and Fabrication of Controlled Release Structures
• Isotropic ARAP energy using Cauchy-Green invariants
• Breaking Good: Fracture Modes for Realtime Destruction
• Fast Stabilization of Inducible Magnet Simulation
• Progressive Simulation for Cloth Quasistatics
• Motion Guided Deep Dynamic 3D Garments
• Neural Cloth Simulation
• Learning-Based Bending Stiffness Parameter Estimation by a Drape Tester
• Dressing Avatars: Deep Photorealistic Appearance for Physically Simulated Clothing
• Fluidic Topology Optimization with an Anisotropic Mixture Model
• A Monte Carlo Method for Fluid Simulation
• Hidden Degrees of Freedom in Implicit Vortex Filaments
• Fast Octree Neighborhood Search for SPH Simulations
• Curl-Flow: Boundary-Respecting Pointwise Incompressible Velocity Interpolation for Grid-Based Fluids
• Position-Based Surface Tension Flow
• ElastoMonolith: A Monolithic Optimization-based Liquid Solver for Contact-Aware Elastic-Solid Coupling
• Hydrophobic and Hydrophilic Solid-Fluid Interaction
• Mixed Variational Finite Elements for Implicit Simulation of Deformables
• Versatile Control of Fluid-Directed Solid Objects Using Multi-Task Reinforcement Learning
• Physical Interaction: Reconstructing Hand-object Interactions with Physics
• Efficient Neural Style Transfer for Volumetric Simulations
• Capturing and Animation of Body and Clothing from Monocular Video

Pengbin Tang, Stelian Coros, Bernhard Thomaszewski

Strain limiting is a widely used approach for simulating biphasic materials such as woven textiles and biological tissue that exhibit a soft elastic regime followed by a hard deformation limit. However, existing methods are either based on slowly converging local iterations, or offer no guarantees on convergence. In this work, we propose a new approach to strain limiting based on second order cone programming (SOCP). Our work is based on the key insight that upper bounds on per-triangle deformations lead to convex quadratic inequality constraints. Though nonlinear, these constraints can be reformulated as inclusion conditions on convex sets, leading to a second order cone programming problem—a convex optimization problem that a) is guaranteed to have a unique solution and b) allows us to leverage efficient conic programming solvers. We first cast strain limiting with anisotropic bounds on stretching as a quadratically constrained quadratic program (QCQP), then show how this QCQP can be mapped to a second order cone programming problem. We further propose a constraint reflection scheme and empirically show that it exhibits superior energy-preservation properties compared to conventional end-of-step projection methods. Finally, we demonstrate our prototype implementation on a set of examples and illustrate how different deformation limits can be used to model a wide range of material behaviors.

A Second Order Cone Programming Approach for Simulating Biphasic Materials

Ryusuke Sugimoto, Christopher Batty, Toshiya Hachisuka

We propose a novel surface-only method for simulating dynamic deformables without the need for volumetric meshing or volumetric integral evaluations. While based upon a boundary element method (BEM) for linear elastodynamics, our method goes beyond simple adoption of BEM by addressing several of its key limitations. We alleviate large displacement artifacts due to linear elasticity by extending BEM with a moving reference frame and surface-only fictitious forces, so that it only needs to handle deformations. To reduce memory and computational costs, we present a simple and practical method to compress the series of dense matrices required to simulate propagation of elastic waves over time. Furthermore, we explore a constraint enforcement mechanism and demonstrate the applicability of our method to general computer animation problems, such as frictional contact.

Surface-Only Dynamic Deformables using a Boundary Element Method

Antoine Chan-Lock, Jesús Pérez, Miguel A. Otaduy

We propose a novel formulation of elastic materials based on high-order interpolants, which fits accurately complex elastic behaviors, but remains conservative. The proposed high-order interpolants can be regarded as a high-dimensional extension of radial basis functions, and they allow the interpolation of derivatives of elastic energy, in particular stress and stiffness. Given the proposed parameterization of elasticity models, we devise an algorithm to find optimal model parameters based on training data. We have tested our methodology for the homogenization of 2D microstructures, and we show that it succeeds to match complex behaviors with high accuracy.

High-Order Elasticity Interpolants for Microstructure Simulation

D. Dorda, D. Peter, D. Borer, N.B. Huber, I. Sailer, M. Gross, B. Solenthaler, B. Thomaszewski

Algorithms at the intersection of computer graphics and medicine have recently gained renewed attention. A particular interest are methods for virtual surgery planning (VSP), where treatment parameters must be carefully chosen to achieve a desired treatment outcome. FEM simulators can verify the treatment parameters by comparing a predicted outcome to the desired one. However, estimating the optimal parameters amounts to solving a challenging inverse problem. In current clinical practice it is solved manually by surgeons, who rely on their experience and intuition to iteratively refine the parameters, verifying them with simulated predictions. We prototype a differentiable FEM simulator and explore how it can enhance and simplify treatment planning, which is ulti- mately necessary to integrate simulation-based VSP tools into a clinical workflow. Specifically, we define a parametric treatment model based on surgeon input, and with analytically derived simulation gradients we optimise it against an objective defined on the visible facial 3D surface. By using sensitivity analysis, we can rapidly explore the solution-space through first-order approximations, which allow the surgeon to interactively visualise the effect of parameter variations on a given treatment plan. The objective function allows landmarks to be freely chosen, accommodating the multiple methodologies in clinical planning. We show that even with a very sparse set of guiding landmarks, our simulator robustly converges to a feasible post-treatment shape.

Differentiable Simulation for Outcome-Driven Orthognathic Surgery Planning

Juan J. Casafranca, Miguel A. Otaduy

The simulation of complex deformation problems often requires enrichment techniques that introduce local high-resolution detail on a generally coarse discretization. The use cases include spatial or temporal refinement of the discretization, the simulation of composite materials with phenomena occurring at different scales, or even codimensional simulation. We present an efficient simulation enrichment method for both local refinement of the discretization and codimensional effects. We dub our method Voronoi filters, as it combines two key computational elements. One is the use of kinematic filters to constrain coarse and fine deformations, and thus provide enrichment functions that are complementary to the coarse deformation. The other one is the use of a centroidal Voronoi discretization for the design of the enrichment functions, which adds high-resolution detail in a compact manner while preserving the rigid modes of coarse deformation. We demonstrate our method on simulation examples of composite materials, hybrid triangle-based and yarn-level simulation of cloth, or enrichment of flesh simulation with high-resolution detail

Voronoi Filters for Simulation Enrichment

Zhang, Paul, Dmitriy Smirnov, Justin Solomon

Much of computer-generated animation is created by manipulating meshes with rigs. While this approach works well for animating articulated objects like animals, it has limited flexibility for animating less structured free-form objects. We introduce Wassersplines, a novel trajectory inference method for animating unstructured densities based on recent advances in continuous normalizing flows and optimal transport. The key idea is to train a neurally-parameterized velocity field that represents the motion between keyframes. Trajectories are then computed by advecting keyframes through the velocity field. We solve an additional Wasserstein barycenter interpolation problem to guarantee strict adherence to keyframes. Our tool can stylize trajectories through a variety of PDE-based regularizers to create different visual effects. We demonstrate our tool on various keyframe interpolation problems to produce temporally-coherent animations without meshing or rigging

Wassersplines for Neural Vector Field–Controlled Animation

Song Bai, Craig Schroeder

In this paper we analyze the stability of the explicit material point method (MPM). We focus on PIC, APIC, and CPIC transfers using quadratic and cubic splines in two and three dimensions. We perform a fully three-dimensional Von Neumann stability analysis to study the behavior within the bulk of a material. This reveals the relationship between the sound speed, CFL number, and actual time step restriction and its dependence on discretization options. We note that boundaries are generally less stable than the interior, with stable time steps generally decreasing until the limit when particles become isolated. We then analyze the stability of a single particle to derive a novel time step restriction that stabilizes simulations at their boundaries. Finally, we show that for explicit MPM with APIC or CPIC transfers, there are pathological cases where growth is observed at arbitrarily small time steps sizes. While these cases do not necessarily pose a problem for practical usage, they do suggest that a guarantee of stability may be theoretically impossible and that necessary but not sufficient time step restrictions may be a necessary and
practical compromise.

Stability Analysis of Explicit MPM