Physics-Based Animation

Huancheng Lin, Floyd M. Chitalu, Taku Komura

Isotropic As-Rigid-As-Possible (ARAP) energy has been popular for shape editing, mesh parametrisation and soft-body simulation for almost two decades. However, a formulation using Cauchy-Green (CG) invariants has always been unclear, due to a rotation-polluted trace term that cannot be directly expressed using these invariants. We show how this incongruent trace term can be understood via an implicit relationship to the CG invariants. Our analysis reveals this relationship to be a polynomial where the roots equate to the trace term, and where the derivatives also give rise to closed-form expressions of the Hessian to guarantee positive semi-definiteness for a fast and concise Newton-type implicit time integration. A consequence of this analysis is a novel approach to determine rotations and singular values of deformation-gradient tensors without explicit/numerical factorization which is significant, resulting in up-to 3.5× speedup and benefits energy function evaluation for reducing solver time. We validate our energy formulation by experiments and comparison, demonstrating that our resulting eigendecomposition using the CG invariants is equivalent to existing ARAP formulations. We thus reveal isotropic ARAP energy to be a member of the “Cauchy-Green club”, meaning that it can indeed be defined using CG invariants and therefore that the closed-form expressions of the resulting Hessian are shared with other energies written in their terms.

Isotropic ARAP energy using Cauchy-Green invariants

Julian Panetta, Haleh Mohammadian, Emiliano Luci, Vahid Babaei

Objects with different shapes can dissolve in significantly different ways inside a solution. Predicting different shapes’ dissolution dynamics is an important problem especially in pharmaceutics. More important and challenging, however, is controlling the dissolution via shape, \ie, designing shapes that lead to a desired release behavior of materials in a solvent over a specific time. Here, we tackle this challenge by introducing a computational inverse design pipeline. We begin by introducing a simple, physically-inspired differentiable forward model of dissolution. % that is both efficient and amenable to differentiation. We then formulate our inverse design as a PDE-constrained topology optimization that has access to analytical derivatives obtained via sensitivity analysis. Furthermore, we incorporate fabricability terms in the optimization objective that enable physically realizing our designs. We thoroughly analyze our approach on a diverse set of examples via both simulation and fabrication.

Shape from Release: Inverse Design and Fabrication of Controlled Release Structures

Mianlun Zheng*, Bohan Wang*, Jingtao Huang, Jernej Barbič (*joint first authors)

Precision modeling of the hand internal musculoskeletal anatomy has been largely limited to individual poses, and has not been connected into continuous volumetric motion of the hand anatomy actuating across the hand’s entire range of motion. This is for a good reason, as hand anatomy and its motion are extremely complex and cannot be predicted merely from the anatomy in a single pose. We give a method to simulate the volumetric shape of hand’s musculoskeletal organs to any pose in the hand’s range of motion, producing external hand shapes and internal organ shapes that match ground truth optical scans and medical images (MRI) in multiple scanned poses. We achieve this by combining MRI images in multiple hand poses with FEM multibody nonlinear elastoplastic simulation. Our system models bones, muscles, tendons, joint ligaments and fat as separate volumetric organs that mechanically interact through contact and attachments, and whose shape matches medical images (MRI) in the MRI-scanned hand poses. The match to MRI is achieved by incorporating pose-space deformation and plastic strains into the simulation. We show how to do this in a non-intrusive manner that still retains all the simulation benefits, namely the ability to prescribe realistic material properties, generalize to arbitrary poses, preserve volume and obey contacts and attachments. We use our method to produce volumetric renders of the internal anatomy of the human hand in motion, and to compute and render highly realistic hand surface shapes. We evaluate our method by comparing it to optical scans, and demonstrate that we qualitatively and quantitatively substantially decrease the error compared to previous work. We test our method on five complex hand sequences, generated either using keyframe animation or performance animation using modern hand tracking techniques.

Simulation of Hand Anatomy Using Medical Imaging

Jinyuan Liu, Mengdi Wang, Fan Feng, Annie Tang, Qiqin Le, Bo Zhu  

We propose a novel solid-fluid coupling method to capture the subtle hydrophobic and hydrophilic interactions between liquid, solid, and air at their multi-phase junctions. The key component of our approach is a Lagrangian model that tackles the coupling, evolution, and equilibrium of dynamic contact lines evolving on the interface between surface-tension fluid and deformable objects. This contact-line model captures an ensemble of small-scale geometric and physical processes, including dynamic waterfront tracking, local momentum transfer and force balance, and interfacial tension calculation. On top of this contact-line model, we further developed a mesh-based level set method to evolve the three-phase T-junction on a deformable solid surface. Our dynamic contact-line model, in conjunction with its monolithic coupling system, unifies the simulation of various hydrophobic and hydrophilic solid-fluid-interaction phenomena and enables a broad range of challenging small-scale elastocapillary phenomena that were previously difficult or impractical to solve, such as the elastocapillary origami and self-assembly, dynamic contact angles of drops, capillary adhesion, as well as wetting and splashing on vibrating surfaces.

Hydrophobic and Hydrophilic Solid-Fluid Interaction

Damien Rioux-Lavoie*, Ryusuke Sugimoto*, Tümay Özdemir, Naoharu H. Shimada, Christopher Batty, Derek Nowrouzezahrai, Toshiya Hachisuka (*joint first authors)

We present a novel Monte Carlo-based fluid simulation approach capable of pointwise and stochastic estimation of fluid motion. Drawing on the Feynman-Kac representation of the vorticity transport equation, we propose a recursive Monte Carlo estimator of the Biot-Savart law and extend it with a stream function formulation that allows us to treat free-slip boundary conditions using a Walk-on-Spheres algorithm. Inspired by the Monte Carlo literature in rendering, we design and compare variance reduction schemes suited to a fluid simulation context for the first time, show its applicability to complex boundary settings, and detail a simple and practical implementation with temporal grid caching. We validate the correctness of our approach via quantitative and qualitative evaluations – across a range of settings and domain geometries – and thoroughly explore its parameters’ design space. Finally, we provide an in-depth discussion of several axes of future work building on this new numerical simulation modality.

A Monte Carlo Method for Fluid Simulation

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