Physics-Based Animation

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

Arnaud Schoentgen, Pierre Poulin, Emmanuelle Darles, Philippe Meseure

It is notoriously difficult for artists to control liquids while generating plausible animations. We introduce a new liquid control tool that allows users to load, transform, and apply precomputed liquid simulation templates in a scene in order to control a particle-based simulation. Each template instance generates control forces that drive the global simulated liquid to locally reproduce the templated liquid behavior. Our system is augmented with a variable proportion of temporary particles to help efficiently reproduce the templated liquid density, with fewer requirements on the surrounding environment. The resulting control strategy adds only a small computational overhead, leading to quick visual feedback for resolutions allowing interactive simulation. We demonstrate the robustness and ease of use of our method on various examples in 2D and 3D.

Particle-based Liquid Control using Animation Templates

Yi-Lu Chen, Jonathan Meier, Barbara Solenthaler, Vinicius C. Azevedo

Simulating liquid phenomena utilizing Eulerian frameworks is challenging, since highly energetic flows often induce severe topological changes, creating thin and complex liquid surfaces. Thus, capturing structures that are small relative to the grid size become intractable, since continually increasing the resolution will scale sub-optimally due to the pressure projection step. Previous methods successfully relied on using higher resolution grids for tracking the liquid surface implicitly; however this technique comes with drawbacks. The mismatch of pressure samples and surface degrees of freedom will cause artifacts such as hanging blobs and permanent kinks at the liquid-air interface. In this paper, we propose an extended cut-cell method for handling liquid structures that are smaller than a grid cell. At the core of our method is a novel iso-surface Poisson Solver, which converges with second-order accuracy for pressure values while maintaining attractive discretization properties such as symmetric positive definiteness. Additionally, we extend the iso-surface assumption to be also compatible with surface tension forces. Our results show that the proposed method provides a novel framework for handling arbitrarily small splashes that can also correctly interact with objects embodied by complex geometries.

An Extended Cut-cell method for Sub-Grid Liquids Tracking with Surface Tension

Fabian Löschner, Andreas Longva, Stefan Jeske, Tassilo Kugelstadt, Jan Bender

Visually appealing and vivid simulations of deformable solids represent an important aspect of physically based computer animation. For the temporal discretization, it is customary in computer animation to use first-order accurate integration methods, such as Backward Euler, due to their simplicity and robustness. Although there is notable research on second-order methods, their use is not widespread. Many of these well-known methods have significant drawbacks such as severe numerical damping or scene-dependent time step restrictions to ensure stability. In this paper, we discuss the most relevant requirements on such methods in computer animation and motivate the interest beyond first-order accuracy. Keeping these requirements in mind, we investigate several promising methods from the families of diagonally implicit Runge-Kutta (DIRK) and Rosenbrock methods which currently do not appear to have considerable popularity in this field. We show that the usage of such methods improves the visual quality of physical animations. In addition, we demonstrate that they allow distinctly more control over damping at lower computational cost than classical methods. As part of our theoretical contribution, we review aspects of simulations that are often considered more intricate with higher-order methods, such as contact handling. To this end, we derive an implicit linearized contact model based on a predictor-corrector approach that leads to consistent behavior with higher-order integrators as predictors. Our contact model is well suited for the simulation of stiff, nonlinear materials with the integration methods presented in this paper and more common methods such as Backward Euler alike.

Higher-Order Time Integration for Deformable Solids

Matthias Müller, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tae-Yong Kim

We present a rigid body simulation method that can resolve small temporal and spatial details by using a quasi explicit integration scheme that is unconditionally stable. Traditional rigid body simulators linearize constraints because they operate on the velocity level or solve the equations of motion implicitly thereby freezing the constraint directions for multiple iterations. Our method always works with the most recent constraint directions. This allows us to trace high speed motion of objects colliding against curved geometry, to reduce the number of constraints, to increase the robustness of the simulation, and to simplify the formulation of the solver. In this paper we provide all the details to implement a fully fledged rigid body solver that handles contacts, a variety of joint types and the interaction with soft object

Detailed Rigid Body Simulation with Extended Position Based Dynamics