Month: September 2019

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

David Hahn, Pol Banzet, James M. Bern, Stelian Coros

This paper presents a method for optimizing visco-elastic material parameters of a finite element simulation to best approximate the dynamic motion of real-world soft objects. We compute the gradient with respect to the material parameters of a least-squares error objective function using either direct sensitivity analysis or an adjoint state method. We then optimize the material parameters such that the simulated motion matches real-world observations as closely as possible. In this way, we can directly build a useful simulation model that captures the visco-elastic behaviour of the specimen of interest. We demonstrate the effectiveness of our method on various examples such as numerical coarsening, custom-designed objective functions,and of course real-world flexible elastic objects made of foam or 3D printed lattice structures, including a demo application in soft robotics

Real2Sim: Visco-elastic parameter estimation from dynamic motion

Juyong Zhang, Yue Peng, Wenqing Ouyang, Bailin Deng

The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications, including physical simulation, geometry processing, and image processing. However, ADMM can take a long time to converge to a solution of high accuracy. Moreover, many computer graphics tasks involve non-convex optimization, and there is often no convergence guarantee for ADMM on such problems since it was originally designed for convex optimization. In this paper, we propose a method to speed up ADMM using Anderson acceleration, an established technique for accelerating fixed-point iterations. We show that in the general case, ADMM is a fixed-point iteration of the second primal variable and the dual variable, and Anderson acceleration can be directly applied. Additionally, when the problem has a separable target function and satisfies certain conditions, ADMM becomes a fixed-point iteration of only one variable, which further reduces the computational overhead of Anderson acceleration. Moreover, we analyze a particular non-convex problem structure that is common in computer graphics, and prove the convergence of ADMM on such problems under mild assumptions. We apply our acceleration technique on a variety of optimization problems in computer graphics, with notable improvement on their convergence speed.

Accelerating ADMM for Simulation and Optimization

Jiong Chen, Max Budninskiy, Houman Owhadi, Hujun Bao, Jin Huang, Mathieu Desbrun

In this paper, we introduce a hierarchical construction of material-adapted refinable basis functions and associated wavelets to offer efficient coarse-graining of linear elastic objects. While spectral methods rely on global basis functions to restrict the number of degrees of freedom, our basis functions are locally supported; yet, unlike typical polynomial basis functions, they are adapted to the material inhomogeneity of the elastic object to better capture its physical properties and behavior. In particular, they share spectral approximation properties with eigenfunctions, offering a good compromise between computational complexity and accuracy. Their construction involves only linear algebra and follows a fine-to-coarse approach, leading to a block-diagonalization of the stiffness matrix where each block corresponds to an intermediate scale space of the elastic object. Once this hierarchy has been precomputed, we can simulate an object at runtime on very coarse resolution grids and still capture the correct physical behavior, with orders of magnitude speedup compared to a fine simulation. We show on a variety of heterogeneous materials that our approach outperforms all previous coarse-graining methods for elasticity.

Material-adapted Refinable Basis Functions for Elasticity Simulation

Sehee Min, Jungdam Won, Seunghwan Lee, Jungnam Park, Jehee Lee

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

Christopher Brandt, Leonardo Scandolo, Elmar Eisemann, Klaus Hildebrandt

We introduce the Reduced Immersed Method (RIM) for the real-time simu-lation of two-way coupled incompressible fluids and elastic solids and theinteraction of multiple deformables with (self-)collisions. Our framework isbased on a novel discretization of theimmersed boundary equations of motion,which model fluid and deformables as a single incompressible medium andtheir interaction as a unified system on a fixed domain combining Eulerianand Lagrangian terms. One advantage for real-time simulations resultingfrom this modeling is that two-way coupling phenomena can be faithfullysimulated while avoiding costly calculations such as tracking the deform-ing fluid-solid interfaces and the associated fluid boundary conditions. Ourdiscretization enables the combination of a PIC/FLIP fluid solver with areduced-order Lagrangian elasticity solver. Crucial for the performance ofRIM is the efficient transfer of information between the elasticity and thefluid solver and the synchronization of the Lagrangian and Eulerian set-tings. We introduce the concept oftwin subspacesthat enables an efficientreduced-order modeling of the transfer. Our experiments demonstrate thatRIM handles complex meshes and highly resolved fluids for large time stepsat high framerates on off-the-shelf hardware, even in the presence of highvelocities and rapid user interaction. Furthermore, it extends reduced-orderelasticity solvers such as Hyper-Reduced Projective Dynamics with naturalcollision handling.

The Reduced Immersed Method for Real-Time Fluid-Elastic Solid Interaction and Contact Simulation

Marie-Lena Eckert, Kiwon Um, Nils Thuerey

In this paper, we present ScalarFlow, a first large-scale data set of reconstructions of real-world smoke plumes. In addition, we propose a framework for accurate physics-based reconstructions from a small number of video streams. Central components of our framework are a novel estimation of unseen inflow regions and an efficient optimization scheme constrained by a simulation to capture real-world fluids. Our data set includes a large number of complex natural buoyancy-driven flows. The flows transition to turbulence and contain observable scalar transport processes. As such, the ScalarFlow data set is tailored towards computer graphics, vision, and learning applications. The published data set will contain volumetric reconstructions of velocity and density as well as the corresponding input image sequences with calibration data, code, and instructions how to reproduce the commodity hardware capture setup. We further demonstrate one of the many potential applications: a first perceptual evaluation study, which reveals that the complexity of the reconstructed flows would require large simulation resolutions for regular solvers in order to recreate at least parts of the natural complexity contained in the captured data.

ScalarFlow: A Large-Scale Volumetric Data Set of Real-world Scalar Transport Flows for Computer Animation and Machine Learning

Byungsoo Kim, Vinicius C. Azevedo, Markus Gross, Barbara Solenthaler

Artistically controlling fluids has always been a challenging task. Optimization techniques rely on approximating simulation states towards target velocity or density field configurations, which are often handcrafted by artists to indirectly control smoke dynamics. Patch synthesis techniques transfer image textures or simulation features to a target flow field. However, these are either limited to adding structural patterns or augmenting coarse flows with turbulent structures, and hence cannot capture the full spectrum of different styles and semantically complex structures. In this paper, we propose the first Transport-based Neural Style Transfer (TNST) algorithm for volumetric smoke data. Our method is able to transfer features from natural images to smoke simulations, enabling general content-aware manipulations ranging from simple patterns to intricate motifs. The proposed algorithm is physically inspired, since it computes the density transport from a source input smoke to a desired target configuration. Our transport-based approach allows direct control over the divergence of the stylization velocity field by optimizing incompressible and irrotational potentials that transport smoke towards stylization. Temporal consistency is ensured by transporting and aligning subsequent stylized velocities, and 3D reconstructions are computed by seamlessly merging stylizations from different camera viewpoints.

Transport-Based Neural Style Transfer for Smoke Simulations