Physics-Based Animation

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

David A.B. Hyde, Steven W. Gagniere, Alan Marquez-Razon, Joseph Teran

We present an updated Lagrangian discretization of surface tension forcesfor the simulation of liquids with moderate to extreme surface tension effects.The potential energy associated with surface tension is proportional to the surface area of the liquid. We design discrete forces as gradients of this energy with respect to the motion of the fluid over a time step. We show that this naturally allows for inversion of the Hessian of the potential energy required with the use of Newton’s method to solve the systems of nonlinear equations associated with implicit time stepping. The rotational invariance of the surface tension energy makes it non-convex and we define a definiteness fix procedure as in [Teran et al. 2005]. We design a novel level-set-based boundary quadrature technique to discretize the surface area calculation in our energy based formulation. Our approach works most naturally with Particle-In-Cell [Harlow 1964] techniques and we demonstrate our approach with a weakly incompressible model for liquid discretized with the Material Point Method [Sulsky et al.1994]. We show that our approach is essential for allowing efficient implicit numerical integration in the limit of high surface tension materials like liquid metals.

An Implicit Updated Lagrangian Formulation for Liquids with Large Surface Energy

Zahra Forootaninia, Rahul Narain

We propose a simple and efficient method for guiding an Eulerian smoke simulation to match the behavior of a specified velocity field, such as a low-resolution animation of the same scene, while preserving the rich, turbulent details arising in the simulated fluid. Our method works by simply combining the high-frequency component of the simulated fluid velocity with the low-frequency component of the input guiding field. In contrast to previous work, we show that it is essential to use ideal low-pass and high-pass filters in the frequency domain, in order to avoid artifacts resulting from loss of small-scale details over time.We demonstrate our method on many scenes including those with static and moving obstacles, and show that it produces high-quality results with very little computational overhead.

Frequency-Domain Smoke Guiding

Xiao-Song Chen, Chen-Feng Li, Geng-Chen Cao, Yun-Tao Jiang and Shi-Min Hu

In physically based-based animation, pure particle methods are popular due to their simple data structure, easy implementation, and convenient parallelization. As a pure particle-based method and using Galerkin discretization, the Moving Least Square Reproducing Kernel Method (MLSRK) was developed in engineering computation as a general numerical tool for solving PDEs. The basic idea of Moving Least Square (MLS) has also been used in computer graphics to estimate d formation gradient for deformable solids. Based on these previous studies, we propose a multiphase MLSRK framework that animates complex and coupled fluids and solids in a unified manner. Specifically, we use the Cauchy momentum equation and phase field model to uniformly capture the momentum balance and phase evolution/interaction in a multiphase system, and systematically formulate the MLSRK discretization to support general multiphase constitutive models. A series of animation examples are presented to demonstrate the performance of our new multiphase MLSRK framework,including hyperelastic, elastoplastic, viscous, fracturing and multiphase coupling behaviours etc.

A Moving Least Square Reproducing Kernel Particle Method for Unified Multiphase Continuum Simulation

Moritz Geilinger, David Hahn, Jonas Zehnder, Moritz Bächer, Bernhard Thomaszewski, Stelian Coros

We present a differentiable dynamics solver that is able to handle fric-tional contact for rigid and deformable objects within a unified framework.Through a principled mollification of normal and tangential contact forces,our method circumvents the main difficulties inherent to the non-smooth nature of frictional contact. We combine this new contact model with fully-implicit time integration to obtain a robust and efficient dynamics solver that is analytically differentiable. In conjunction with adjoint sensitivity analysis, our formulation enables gradient-based optimization with adaptive trade-offs between simulation accuracy and smoothness of objective function landscapes. We thoroughly analyse our approach on a set of simulation examples involving rigid bodies, visco-elastic materials, and coupled multi-body systems. We furthermore showcase applications of our differentiable simulator to parameter estimation for deformable objects, motion planning for robotic manipulation, trajectory optimization for compliant walking robots, as well as efficient self-supervised learning of control policies

ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact

Yuwei Xiao, Szeyu Chan, Siqi Wang, Bo Zhu, Xubo Yang

Enabling adaptivity on a uniform Cartesian grid is challenging due to its highly structured grid cells and axis-aligned grid lines. In this paper, we propose a new grid structure – the adaptive staggered-tilted (AST) grid –to conduct adaptive fluid simulations on a regular discretization. The key mechanics underpinning our new grid structure is to allow the emergence of a new set of tilted grid cells from the nodal positions on a background uniform grid. The original axis-aligned cells, in conjunction with the populated axis-tilted cells, jointly function as the geometric primitives to enable adaptivity on a regular spatial discretization. By controlling the states of the tilted cells both temporally and spatially, we can dynamically evolve the adaptive discretizations on an Eulerian domain. Our grid structure preserves almost all the computational merits of a uniform Cartesian grid, including he cache-coherent data layout, the easiness for parallelization, and the existence of high-performance numerical solvers. Further, our grid structure can be integrated into other adaptive grid structures, such as an Octree or a sparsely populated grid, to accommodate the T-junction-free hierarchy. We demonstrate the efficacy of our AST grid by showing examples of large-scale incompressible flow simulation in domains with irregular boundaries

An Adaptive Staggered-Tilted Grid for Incompressible Flow Simulation

Ning Jin, Yilin Zhu, Zhenglin Geng, Ronald Fedkiw

With the aim of creating virtual cloth deformations more similar to real world clothing, we propose a new computational framework that recasts three dimensional cloth deformation as an RGB image in a two dimensional pat-tern space. Then a three dimensional animation of cloth is equivalent to a sequence of two dimensional RGB images,which in turn are driven/choreographed via animation parameters such as joint angles. This allows us to leverage popular CNNs to learn cloth deformations in image space.The two dimensional cloth pixels are extended into the real world via standard body skinning techniques, after which the RGB values are interpreted as texture offsets and dis-placement maps. Notably, we illustrate that our approach does not require accurate unclothed body shapes or robust skinning techniques. Additionally, we discuss how standard image based techniques such as image partitioning for higher resolution, GANs for merging partitioned image regions back together, etc., can readily be incorporated into our framework.

A Pixel-Based Framework for Data-Driven Clothing

Raquel Vidaurre, Igor Santesteban, Elena Garces, Dan Casas

We present a learning-based approach for virtual try-on applications based on a fully convolutional graph neural network. In contrast to existing data-driven models, which are trained for a specific garment or mesh topology, our fully convolutional model can cope with a large family of garments, represented as parametric predefined 2D panels with arbitrary mesh topology, including long dresses, shirts, and tight tops. Under the hood, our novel geometric deep learning approach learns to drape 3D garments by decoupling the three different sources of deformations that condition the fit of clothing: garment type, target body shape, and material. Specifically, we first learn a regressor that predicts the 3D drape of the input parametric garment when worn by a mean body shape. Then, after a mesh topology optimization step where we generate a sufficient level of detail for the input garment type, we further deform the mesh to reproduce deformations caused by the target body shape. Finally, we predict fine-scale details such as wrinkles that depend mostly on the garment material. We qualitatively and quantitatively demonstrate that our fully convolutional approach outperforms existing methods in terms of generalization capabilities and memory requirements, and therefore it opens the door to more general learning-based models for virtual try-on applications.

Fully Convolutional Graph Neural Networks for Parametric Virtual Try-On

Dieter Morgenroth, Stefan Reinhardt, Daniel Weiskopf, Bernhard Eberhardt

We present a method to simulate fluid flow on evolving surfaces, e.g., an oil film on a water surface. Given an animated surface (e.g., extracted from a particle-based fluid simulation) in three-dimensional space, we add a second simulation on this base animation. In general, we solve a partial differential equation (PDE) on a level set surface obtained from the animated input surface. The properties of the input surface are transferred to a sparse volume data structure that is then used for the simulation. We introduce one-way coupling strategies from input properties to our simulation and we add conservation of mass and momentum to existing methods that solve a PDE in a narrow-band using the Closest Point Method. In this way, we efficiently compute high-resolution 2D simulations on coarse input surfaces. Our approach helps visual effects creators easily integrate a workflow to simulate material flow on evolving surfaces into their existing production pipeline

Efficient 2D Simulation on Moving 3D Surfaces