Physics-Based Animation

We present a novel and general framework for the design and control of underwater soft-bodied animals. The whole body of an animal consisting of soft tissues is modeled by tetrahedral and triangular FEM meshes. The contraction of muscles embedded in the soft tissues actuates the body and limbs to move. We present a novel muscle excitation model that mimics the anatomy of muscular hydrostats and their muscle excitation patterns. Our deep reinforcement learning algorithm equipped with the muscle excitation model successfully learned the control policy of soft-bodied animals, which can be physically simulated in real-time, controlled interactively, and resilient to external perturbations. We demonstrate the effectiveness of our approach with various simulated animals including octopuses, lampreys, starfishes, stingrays, and cuttlefishes. They learn diverse behaviors such as swimming, grasping, and escaping from a bottle. We also implemented a simple user interface system that allows the user to easily create their creatures.

SoftCon: Simulation and Control of Soft-Bodied Animals with Biomimetic Actuators

Christian Hafner, Christian Schumacher, Espen Knoop, Thomas Auzinger, Bernd Bickel, Moritz Bächer

We propose a novel generic shape optimization method for CAD models based on the eXtended Finite Element Method (XFEM). Our method works directly on the intersection between the model and a regular simulation grid, without the need to mesh or remesh, thus removing a bottleneck of classical shape optimization strategies. This is made possible by a novel hierarchical integration scheme that accurately integrates finite element quantities with sub-element precision. For optimization, we efficiently compute analytical shape derivatives of the entire framework, from model intersection to integration rule generation and XFEM simulation. Moreover, we describe a differentiable projection of shape parameters onto a constraint manifold spanned by user-specified shape preservation, consistency, and manufacturability constraints. We demonstrate the utility of our approach by optimizing mass distribution, strength-to-weight ratio, and inverse elastic shape design objectives directly on parameterized 3D CAD models.

X-CAD: Optimizing CAD Models with Extended Finite Elements

Albert Peiret, Sheldon Andrews, József Kövecses, Paul G. Kry, Marek Teichmann

Substructuring permits parallelization of physics simulation on multi-core CPUs. We present a new substructuring approach for solving stiff multibody systems containing both bilateral and unilateral constraints. Our approach is based on non-overlapping domain decomposition with the Schur complement method, which we extend to systems involving contact formulated as a mixed bounds linear complementarity problem. At each time step, we alternate between solving the subsystem and interface constraint impulses, which leads to the identification of the active constraints. By using the active constraints to compute the effective mass of subsystems within the interface solve, we obtain an exact solution. We demonstrate that our simulations have preferable behavior compared to standard iterative solvers and substructuring techniques based on the exchange of forces at interface bodies. We observe considerable speedups for structured simulations where a user-defined partitioning can be applied, and moderate speedups for unstructured simulations, such as piles of bodies. In the latter case, we propose an automatic partitioning strategy based on the degree of bodies in the constraint graph. Because our method makes use of direct solvers, we are able to achieve interactive and real-time frame rates for a number of challenging scenarios involving large mass ratios, redundant constraints, and ill-conditioned systems.

Schur Complement-based Substructuring of Stiff Multibody Systems with Contact

Tassilo Kugelstadt, Andreas Longva, Nils Thuerey, Jan Bender

We propose a novel implicit density projection approach for hybrid Eulerian/Lagrangian methods like FLIP and APIC to enforce volume conservation of incompressible liquids. Our approach is able to robustly recover from highly degenerate configurations and incorporates volume-conserving boundary handling. A problem of the standard divergence-free pressure solver is that it only has a differential view on density changes. Numerical volume errors, which occur due to large time steps and the limited accuracy of pressure projections, are invisible to the solver and cannot be corrected. Moreover, these errors accumulate over time and can lead to drastic volume changes, especially in long-running simulations or interactive scenarios. Therefore, we introduce a novel method that enforces constant density throughout the fluid. The density itself is tracked via the particles of the hybrid Eulerian/Lagrangian simulation algorithm. To achieve constant density, we use the continuous mass conservation law to derive a pressure Poisson equation which also takes density deviations into account. It can be discretized with standard approaches and easily implemented into existing code by extending the regular pressure solver. Our method enables us to relax the strict time step and solver accuracy requirements of a regular solver, leading to significantly higher performance. Moreover, our approach is able to push fluid particles out of solid obstacles without losing volume and generates more uniform particle distributions, which makes frequent particle resampling unnecessary. We compare the proposed method to standard FLIP and APIC and to previous volume correction approaches in several simulations and demonstrate significant improvements in terms of incompressibility, visual realism and computational performance.

Implicit Density Projection for Volume Conserving Liquids

Jan Bender, Tassilo Kugelstadt, Marcel Weiler, Dan Koschier

In this paper, we present a novel method for the robust handling of static and dynamic rigid boundaries in Smoothed Particle Hydrodynamics (SPH) simulations. We build upon the ideas of the density maps approach which has been introduced recently by Koschier and Bender. They precompute the density contributions of solid boundaries and store them on a spatial grid which can be efficiently queried during runtime. This alleviates the problems of commonly used boundary particles, like bumpy surfaces and inaccurate pressure forces near boundaries. Our method is based on a similar concept but we precompute the volume contribution of the boundary geometry and store it on a grid. This maintains all benefits of density maps but offers a variety of advantages which are demonstrated in several experiments. Firstly, in contrast to the density maps method we can compute derivatives in the standard SPH manner by differentiating the kernel function. This results in smooth pressure forces, even for lower map resolutions, such that precomputation times and memory requirements are reduced by more than two orders of magnitude compared to density maps. Furthermore, this directly fits into the SPH concept so that volume maps can be seamlessly combined with existing SPH methods. Finally, the kernel function is not baked into the map such that the same volume map can be used with different kernels. This is especially useful when we want to incorporate common surface tension or viscosity methods that use different kernels than the fluid simulation.

Volume Maps: An Implicit Boundary Representation for SPH

Michael Tao, Christopher Batty, Eugene Fiume, David IW Levin

Although geometry arising “in the wild” most often comes in the form of a surface representation, a plethora of geometrical and physical applications require the construction of volumetric embeddings either of the geometry itself or the domain surrounding it. Cartesian cut-cell-based mesh generation provides an attractive solution in which volumetric elements are constructed from the intersection of the input surface geometry with a uniform or adaptive hexahedral grid. This choice, especially common in computational fluid dynamics, has the potential to efficiently generate accurate, surface-conforming cells; unfortunately, current solutions are often slow, fragile, or cannot handle many common topological situations. We therefore propose a novel, robust cut-cell construction technique for triangle surface meshes that explicitly computes the precise geometry of the intersection cells, even on meshes that are open or non-manifold. Its fundamental geometric primitive is the intersection of an arbitrary segment with an axis-aligned plane. Beginning from the set of intersection points between triangle mesh edges and grid planes, our bottom-up approach robustly determines cut-edges, cut-faces, and finally cut-cells, in a manner designed to guarantee topological correctness. We demonstrate its effectiveness and speed on a wide range of input meshes and grid resolutions, and make the code available as open source.

Mandoline: Robust Cut-Cell Generation for Arbitrary Triangle Meshes

Stefan Reinhardt, Tim Krake, Bernhard Eberhardt, Daniel Weiskopf

We present a novel technique to correct errors introduced by the discretization of a fluid body when animating it with smoothed particle hydrodynamics (SPH). Our approach is based on the Shepard correction, which reduces the interpolation errors from irregularly spaced data. With Shepard correction, the smoothing kernel function is normalized using the weighted sum of the kernel function values in the neighborhood. To compute the correction factor, densities of neighboring particles are needed, which themselves are computed with the uncorrected kernel. This results in an inconsistent formulation and an error-prone correction of the kernel. As a consequence, the density computation may be inaccurate, thus the pressure forces are erroneous and may  cause instabilities in the simulation process.We present a consistent formulation by using the corrected densities to compute the exact kernel correction factor and, thereby, increase the accuracy of the simulation. Employing our method, a smooth density  distribution is achieved, i.e., the noise in the density field is reduced by orders of magnitude. To show that our method is independent of the SPH variant, we evaluate our technique on weakly compressible SPH and on divergence-free SPH. Incorporating the corrected density into the correction process, the problem cannot be stated explicitly anymore. We propose an efficient and easy-to-implement algorithm to solve the implicit problem by applying the power method. Additionally, we demonstrate how our model can be applied to improve the density distribution on rigid bodies when using a well-known rigid-fluid coupling approach.

Consistent Shepard Interpolation for SPH-Based Fluid Animation

Mengyuan Ding, Xuchen Han, Stephanie Wang, Theodore Gast, Joseph Teran

We present a Material Point Method for visual simulation of baking breads, cookies, pancakes and similar materials that consist of dough or batter (mixtures of water flour, eggs, fat, sugar and leavening agents). We develop a novel thermomechanical model using mixture theory to resolve interactions between individual water, gas and dough species. Heat transfer with thermal expansion is used to model thermal variations in material properties. Water- based mass transfer is resolved through the porous mixture, gas represents carbon dioxide produced by leavening agents in the baking process and dough is modeled as a viscoelastoplastic solid to represent its varied and complex rheological properties. Water content in the mixture reduces during the baking process according to Fick’s Law which contributes to drying and cracking of crust at the material boundary. Carbon dioxide gas produced by leavening agents during baking creates internal pressure that causes rising. The viscoelastoplastic model for the dough is temperature dependent and is used to model melting and solidification. We discretize the governing equations using a novel Material Point Method designed to track the solid phase of the mixture.

A Thermomechanical Material Point Method for Baking and Cooking

Yuanming Hu, Tzu-Mao Li, Luke Anderson, Jonathan Ragan-Kelley, Fredo Durand

3D visual computing data are often spatially sparse. To exploit such sparsity, people have developed hierarchical sparse data structures, such as multi-level sparse voxel grids, particles, and 3D hash tables. However, developing and using these high-performance sparse data structures is challenging, due to their intrinsic complexity and overhead. We propose Taichi, a new data-oriented programming language for efficiently authoring, accessing, and maintaining such data structures. The language offers a high-level, data structure-agnostic interface for writing computation code. The user independently specifies the data structure. We provide several elementary components with different sparsity properties that can be arbitrarily composed to create a wide range of multi-level sparse data structures. This decoupling of data structures from computation makes it easy to experiment with different data structures without changing computation code, and allows users to write computation as if they are working with a dense array. Our compiler then uses the semantics of the data structure and index analysis to automatically optimize for locality, remove redundant operations for coherent accesses, maintain sparsity and memory allocations, and generate efficient parallel and vectorized instructions for CPUs and GPUs. Our approach yields competitive performance on common computational kernels such as stencil applications, neighbor lookups, and particle scattering. We demonstrate our language by implementing simulation, rendering, and vision tasks including a material point method simulation, finite element analysis, a multigrid Poisson solver for pressure projection, volumetric path tracing, and 3D convolution on sparse grids. Our computation-data structure decoupling allows us to quickly experiment with different data arrangements, and to develop high-performance data structures tailored for specific computational tasks. With 1/10th as many lines of code, we achieve 4.55× higher performance on average, compared to hand-optimized reference implementations.

Taichi: A Language for High-Performance Computation on Spatially Sparse Data Structures

Tuanfeng Y. Wang, Tianjia Shao, Kai Fu, Niloy Mitra

Authoring dynamic garment shapes for character animation on body motion is one of the fundamental steps in the CG industry. Established workflows are either time and labor consuming (i.e., manual editing on dense frames with controllers), or lack keyframe-level control (i.e., physically-based simulation). Not surprisingly, garment authoring remains a bottleneck in many production pipelines. Instead, we present a deep-learning-based approach for semi-automatic authoring of garment animation, wherein the user provides the desired garment shape in a selection of keyframes, while our system infers a latent representation for its motion-independent intrinsic parameters (e.g., gravity, cloth materials, etc.). Given new character motions, the latent representation allows to automatically generate a plausible garment animation at interactive rates. Having factored out character motion, the learned intrinsic garment space enables smooth transition between keyframes on a new motion sequence. Technically, we learn an intrinsic garment space with an motion-driven autoencoder network, where the encoder maps the garment shapes to the intrinsic space under the condition of body motions, while the decoder acts as a differentiable simulator to generate garment shapes according to changes in character body motion and intrinsic parameters. We evaluate our approach qualitatively and quantitatively on common garment types. Experiments demonstrate our system can significantly improve current garment authoring workflows via an interactive user interface. Compared with the standard CG pipeline, our system significantly reduces the ratio of required keyframes from 20% to 1 − 2%.

Learning an Intrinsic Garment Space for Interactive Authoring of Garment Animation