Category: Deformables

Ebb: A DSL for Physical Simulation on CPUs and GPUs

Gilbert Bernstein, Chinmayee Shah, Crystal Lemire, Zachery DeVito, Matthew Fisher, Philip Levis, Pat Hanrahan

Designing programming environments for physical simulation is challenging because simulations rely on diverse algorithms and geometric domains. These challenges are compounded when we try to run efficiently on heterogeneous parallel architectures. We present Ebb, a domain-specific language (DSL) for simulation, that runs efficiently on both CPUs and GPUs. Unlike previous DSLs, Ebb uses a three-layer architecture to separate (1) simulation code, (2) definition of data structures for geometric domains, and (3) runtimes supporting parallel architectures. Different geometric domains are implemented as libraries that use a common, unified, relational data model. By structuring the simulation framework in this way, programmers implementing simulations can focus on the physics and algorithms for each simulation without worrying about their implementation on parallel computers. Because the geometric domain libraries are all implemented using a common runtime based on relations, new geometric domains can be added as needed, without specifying the details of memory management, mapping to different parallel architectures, or having to expand the runtime’s interface. We evaluate Ebb by comparing it to several widely used simulations, demonstrating comparable performance to hand-written GPU code where available, and surpassing existing CPU performance optimizations by up to 9x when no GPU code exists.

Ebb: A DSL for Physical Simulation on CPUs and GPUs

Interactively Cutting and Constraining Vertices in Meshes Using Augmented Matrices

Yu-Hong Yeung, Jessica Crouch, Alex Pothen

We present a finite element solution method that is well-suited for interactive simulations of cutting meshes in the regime of linear elastic models. Our approach features fast updates to the solution of the stiffness system of equations to account for real-time changes in mesh connectivity and boundary conditions. Updates are accomplished by augmenting the stiffness matrix to keep it consistent with the changes to the underlying model, without re-factoring the matrix at each step of cutting. The initial stiffness matrix and its Cholesky factors are used to implicitly form and solve a Schur complement system using an iterative solver. As changes accumulate over many simulation time steps, the augmented solution method slows down due to the size of the augmented matrix. However, by periodically re-factoring the stiffness matrix in a concurrent background process, fresh Cholesky factors that incorporate recent model changes can replace the initial factors. This controls the size of the augmented matrices and provides a way to maintain a fast solution rate as the number of changes to a model grows. We exploit sparsity in the stiffness matrix, the right-hand-side vectors and the solution vectors to compute the solutions fast, and show that the time complexity of the update steps is bounded linearly by the size of the Cholesky factor of the initial matrix. Our complexity analysis and experimental results demonstrate that this approach scales well with problem size. Results for cutting and deformation of 3D linear elastic models are reported for meshes representing the brain, eye, and model problems with element counts up to 167, 000; these show the potential of this method for real-time interactivity. An application to limbal incisions for surgical correction of astigmatism, where linear elastic models and small deformations are sufficient, is included.

Interactively Cutting and Constraining Vertices in Meshes Using Augmented Matrices

Simit: A Language for Physical Simulation

Fredrik Kjolstad, Shoaib Kamil Jonathan Ragan-Kelley, David I.W. Levin,Shinjiro Sueda, Desai Chen, Etienne Vouga, Danny M. Kaufman, Gurtej Kanwar,Wojciech Matusik, and Saman Amarasinghe

Using existing programming tools, writing high-performance simulation code is labor intensive and requires sacrificing readability and portability. The alternative is to prototype simulations in a high-level language like Matlab, thereby sacrificing performance. The Matlab programming model naturally describes the behavior of an entire physical system using the language of linear algebra. However, simulations also manipulate individual geometric elements, which are best represented using linked data structures like meshes. Translating between the linked data structures and linear algebra comes at significant cost, both to the programmer and the machine. High-performance implementations avoid the cost by rephrasing the computation in terms of linked or index data structures, leaving the code complicated and monolithic, often increasing its size by an order of magnitude. In this paper, we present Simit, a new language for physical simulations that lets the programmer view the system both as a linked data structure in the form of a hypergraph, and as a set of global vectors, matrices and tensors depending on what is convenient at any given time. Simit provides a novel assembly construct that makes it conceptually easy and computationally efficient to move between the two abstractions. Using the information provided by the assembly construct, the compiler generates efficient in-place computation on the graph. We demonstrate that Simit is easy to use: a Simit program is typically shorter than a Matlab program; that it is high-performance: a Simit program running sequentially on a CPU performs comparably to hand-optimized simulations; and that it is portable: Simit programs can be compiled for GPUs with no change to the program, delivering 4-20x speedups over our optimized CPU code.

Simit: A Language for Physical Simulation

Dexterous Manipulation of Cloth

Yunfei Bai, Wenhao Yu, and C. Karen Liu

This paper introduces a new technique to synthesize dexterous manipulation of cloth. Given a simple description of the desired cloth motion, our algorithm computes appropriate joint torques for physically simulated hands, such that, via contact forces, the result of cloth simulation follows the desired motion. Instead of optimizing the hand control forces directly, we formulate an optimization problem that solves for the commanding forces from the hands to the cloth, which have more direct impact on the dynamic state of the hands and that of the cloth. The solution of the optimization provides commanding forces that achieve the desired cloth motion described by the user, while respecting the kinematic constraints of the hands. These commanding forces are then used to guide the joint torques of the hands. To balance between the effectiveness of control and computational costs, we formulate a model-predictive-control problem as a quadratic program at each time step. We demonstrate our technique on a set of cloth manipulation tasks in daily activities, including folding laundry, wringing a towel, and putting on a scarf.

Dexterous Manipulation of Cloth

Modeling and Estimation of Energy-Based Hyperelastic Objects

Eder Miguel, David Miraut, Miguel A. Otaduy

In this paper, we present a method to model hyperelasticity that is well suited for representing the nonlinearity of real-world objects, as well as for estimating it from deformation examples. Previous approaches suffer several limitations, such as lack of integrability of elastic forces, failure to enforce energy convexity, lack of robustness of parameter estimation, or difficulty to model cross-modal effects. Our method avoids these problems by relying on a general energy-based definition of elastic properties. The accuracy of the resulting elastic model is maximized by defining an additive model of separable energy terms, which allow progressive parameter estimation. In addition, our method supports efficient modeling of extreme nonlinearities thanks to energy-limiting constraints. We combine our energy-based model with an optimization method to estimate model parameters from force-deformation examples, and we show successful modeling of diverse deformable objects, including cloth, human finger skin, and internal human anatomy in a medical imaging application.

Modeling and Estimation of Energy-Based Hyperelastic Objects

Ductile Fracture for Clustered Shape Matching

Ben Jones, April Martin, Joshua A. Levine, Tamar Shinar, and Adam W. Bargteil

In this paper, we incorporate ductile fracture into the clustered shape matching simulation framework for deformable bodies, thus filling a gap in the shape matching literature. Our plasticity and fracture models are inspired by the finite element literature on deformable bodies, but are adapted to the clustered shape matching framework. The resulting approach is fast, versatile, and simple to implement.

Ductile Fracture for Clustered Shape Matching

Dyna: A Model of Dynamic Human Shape in Motion

Gerard Pons-Moll, Javier Romero, Naureen Mahmood, and Michael J. Black

To look human, digital full-body avatars need to have soft tissue deformations like those of real people. Current methods for physics simulation of soft tissue lack realism, are computationally expensive, or are hard to tune. Learning soft tissue motion from example, however, has been limited by the lack of dense, high-resolution, training data. We address this using a 4D capture system and a method for accurately registering 3D scans across time to a template mesh. Using over 40,000 scans of ten subjects, we compute how soft tissue motion causes mesh triangles to deform relative to a base 3D body model and learn a low-dimensional linear subspace approximating this soft-tissue deformation. Our model, called Dyna, relates the linear coefficients of this body surface deformation to the changing pose of the body. We learn a second-order auto-regressive model that predicts soft-tissue deformations based on previous deformations, the velocity and acceleration of the body, and the angular velocities and accelerations of the limbs. Dyna also models how deformations vary with a person’s body mass index (BMI), producing different deformations for people with different shapes. Dyna realistically represents the dynamics of soft tissue for previously unseen subjects and motions. Finally, we provide tools for animators to vary BMI to produce different effects, to selectively control the location and intensity of soft-tissue motions, and to apply the model to new, stylized characters.

Dyna: A Model of Dynamic Human Shape in Motion

Biomechanical Simulation and Control of Hands and Tendinous Systems

Prashant Sachdeva, Shinjiro Sueda, Susanne Bradley, Mikhail Fain, Dinesh K. Pai

The tendons of the hand and other biomechanical systems form a complex network of sheaths, pulleys, and branches. By modeling these anatomical structures, we obtain realistic simulations of coordination and dynamics that were previously not possible. First, we introduce Eulerian-on-Lagrangian discretization of tendon strands, with a new selective quasistatic formulation that eliminates unnecessary degrees of freedom in the longitudinal direction, while maintaining the dynamic behavior in transverse directions. This formulation also allows us to take larger time steps. Second, we introduce two control methods for biomechanical systems: first, a general-purpose learning-based approach requiring no previous system knowledge, and a second approach using data extracted from the simulator. We use various examples to compare the performance of these controllers.

Biomechanical Simulation and Control of Hands and Tendinous Systems

Subspace Dynamic Simulation Using Rotation-Strain Coordinates

Zherong Pan, Hujun Bao, Jin Huang

In this paper, we propose a full featured and efficient subspace simulation method in the rotation-strain (RS) space for elastic objects. Sharply different from previous methods using the rotation-strain space, except for the ability to handle non-linear elastic materials and external forces, our method correctly formulates the kinetic energy, centrifugal and Coriolis forces which significantly reduces the dynamic artifacts. We show many techniques used in the Euclidean space methods, such as modal derivatives, polynomial and cubature approximation, can be adapted to our RS simulator. Carefully designed experiments show that the equation of motion in RS space has less non-linearity than its Euclidean counterpart, and as a consequence, our method has great advantages of lower dimension and computational complexity than state-of-the-art methods in the Euclidean space.

Subspace Dynamic Simulation Using Rotation-Strain Coordinates

Smoothed Aggregation Multigrid for Cloth Simulation

Rasmus Tamstorf, Toby Jones, Stephen F. McCormick

Existing multigrid methods for cloth simulation are based on geometric multigrid. While good results have been reported, geometric methods are problematic for unstructured grids, widely varying material properties, and varying anisotropies, and they often have difficulty handling constraints arising from collisions. This paper applies the algebraic multigrid method known as smoothed aggregation to cloth simulation. This method is agnostic to the underlying tessellation, which can even vary over time, and it only requires the user to provide a fine-level mesh. To handle contact constraints efficiently, a prefiltered preconditioned conjugate gradient method is introduced. For highly efficient preconditioners, like the ones proposed here, prefiltering is essential, but, even for simple preconditioners, prefiltering provides significant benefits in the presence of many constraints. Numerical tests of the new approach on a range of examples confirm 6-8X speedups on a fully dressed character with 371k vertices, and even larger speedups on synthetic examples.

Smoothed Aggregation Multigrid for Cloth Simulation