Category: Deformables

Simulation of Complex Nonlinear Elastic Bodies using Lattice Deformers

Taylor Patterson, Nathan Mitchell, Eftychios Sifakis

Lattice deformers are a popular option for modeling the behavior of elastic bodies as they avoid the need for conforming mesh generation, and their regular structure offers significant opportunities for performance optimizations. Our work expands the scope of current lattice-based elastic deformers, adding support for a number of important simulation features. We accommodate complex nonlinear, optionally anisotropic materials while using an economical one-point quadrature scheme. Our formulation fully accommodates near-incompressibility by enforcing accurate nonlinear constraints, supports implicit integration for large time steps, and is not susceptible to locking or poor conditioning of the discrete equations. Additionally, we increase the accuracy of our solver by employing a novel high-order quadrature scheme on lattice cells overlapping with the model boundary, which are treated at sub-cell precision. Finally, we detail how this accurate boundary treatment can be implemented at a minimal computational premium over the cost of a voxel-accurate discretization. We demonstrate our method in the simulation of complex musculoskeletal human models.

Simulation of Complex Nonlinear Elastic Bodies using Lattice Deformers

An implicit Tensor-Mass solver on the GPU for soft bodies simulation

Xavier Faure, Florence Zara, Fabrice Jaillet, Jean-Michel Moreau

The realistic and interactive simulation of deformable objects has become a challenge in Computer Graphics. In this paper, we propose a GPU implementation of the resolution of the mechanical equations, using a semi-implicit as well as an implicit integration scheme. At the contrary of the classical FEM approach, forces are directly computed at each node of the discretized objects, using the evaluation of the strain energy density of the elements. This approach allows to mix several mechanical behaviors in the same object. Results show a notable speedup of 30, especially in the case of complex scenes. Running times shows that this efficient implementation may contribute to make this model more popular for soft bodies simulations.

An implicit Tensor-Mass solver on the GPU for soft bodies simulation

Geometric Numerical Integration of Inequality Constrained Nonsmooth Hamiltonian Systems

Danny Kaufman, Dinesh Pai

We consider the geometric numerical integration of Hamiltonian systems subject to both equality and “hard” inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. Additionally, however, we also consider invariant preservation over persistent, simultaneous, and/or frequent boundary interactions. Appropriately formulating geometric methods for these cases has long remained challenging due the inherent nonsmoothness and one-sided conditions that they impose. To resolve these issues we thus focus both on symplectic-momentum preserving behavior and the preservation of additional structures, unique to the inequality constrained setting. Toward these goals we introduce, for the first time, a fully nonsmooth, discrete Hamilton’s principle and obtain an associated framework for composing geometric numerical integration methods for inequality-equality–constrained systems. Applying this framework, we formulate a new family of geometric numerical integration methods that, by construction, preserve momentum and equality constraints and are observed to retain good long-term energy behavior. Along with these standard geometric properties, the derived methods also enforce multiple simultaneous inequality constraints, obtain smooth unilateral motion along constraint boundaries, and allow for both nonsmooth and smooth boundary approach and exit trajectories. Numerical experiments are presented to illustrate the behavior of these methods on difficult test examples where both smooth and nonsmooth active constraint modes persist with high frequency.

Geometric Numerical Integration of Inequality Constrained Nonsmooth Hamiltonian Systems

Speculative Parallel Asynchronous Contact Mechanics

Samantha Ainsley, Etienne Vouga, Eitan Grinspun, Rasmus Tamstorf

We extend the Asynchronous Contact Mechanics algorithm [Harmon et al. 2009] and improve its performance by two orders of magnitude, using only optimizations that do not compromise ACM’s three guarantees of safety, progress, and correctness. The key to this speedup is replacing ACM’s timid, forward-looking mechanism for detecting collisions—locating and rescheduling separating plane kinetic data structures—with an optimistic speculative method inspired by Mirtich’s rigid body Time Warp algorithm [2000]. Time warp allows us to perform collision detection over a window of time containing many of ACM’s asynchronous trajectory changes; in this way we cull away large intervals as being collision free. Moreover, by replacing force processing intermingled with KDS rescheduling by windows of pure processing followed by collision detection, we tranform an algorithm that is very difficult to parallelize into one that is embarrassingly parallel.

Speculative Parallel Asynchronous Contact Mechanics

Rig-Space Physics

Fabian Hahn, Sebastian Martin, Bernhard Thomaszewski, Robert Sumner, Stelian Coros, Markus Gross

We present a method that brings the benefits of physics-based simulations to traditional animation pipelines. We formulate the equations of motions in the subspace of deformations defined by an animator’s rig. Our framework fits seamlessly into the workflow typically employed by artists, as our output consists of animation curves that are identical in nature to the result of manual keyframing. Artists can therefore explore the full spectrum between handcrafted animation and unrestricted physical simulation. To enhance the artist’s control, we provide a method that transforms stiffness values defined on rig parameters to a non-homogeneous distribution of material parameters for the underlying FEM model. In addition, we use automatically extracted high-level rig parameters to intuitively edit the results of our simulations, and also to speed up computation. To demonstrate the effectiveness of our method, we create compelling results by adding rich physical motions to coarse input animations. In the absence of artist input, we create realistic passive motion directly in rig space.

Rig-Space Physics

Efficient Simulation of Example-Based Materials

Christian Schumacher, Bernhard Thomaszewski, Stelian Coros, Sebastian Martin, Robert Sumner, Markus Gross

We present a new method for efficiently simulating art-directable deformable materials. We use example poses to define subspaces of desirable deformations via linear interpolation. As a central aspect of our approach, we use an incompatible representation for input and interpolated poses that allows us to interpolate between elements individually. This enables us to bypass costly reconstruction steps and we thus achieve significant performance improvements compared to previous work. As a natural continuation, we furthermore present a formulation of example-based plasticity. Finally, we extend the directability of example-based materials and explore a number of powerful control mechanisms. We demonstrate these novel concepts on a number of solid and shell animations including artistic deformation behaviors, cartoon physics, and example-based pose space dynamics.

Efficient Simulation of Example-Based Materials

Interactive High-Resolution Boundary Surfaces for Deformable Bodies with Changing Topology

Jun Wu, Christian Dick, Rudiger Westermann

Recent work has demonstrated that composite finite-elements provide an effective means for physically based modeling of deformable bodies. In this paper we present a number of highly effective improvements of previous work to allow for a high-performance and high-quality simulation of boundary surfaces of deformable bodies with changing topology, for instance, due to cuts and incisions. Starting at a coarse resolution simulation grid, along a cut we perform an adaptive octree refinement of this grid down to a desired resolution and iteratively pull the fine level finite-element equations to the coarse level. In this way, the fine level dynamics can be approximated with a small number of degrees of freedom at the coarse level. By embedding the hierarchical adaptive composite finite-element scheme into a geometric multigrid solver, and by exploiting the fact that during cutting only a small number of cells are modified in each time step, high update rates can be achieved for high resolution surfaces at very good approximation quality.  To construct a high quality surface that is accurately aligned with a cut, we employ the dual-contouring approach on the fine resolution level, and we instantly bind the constructed triangle mesh to the coarse grid via geometric constrains.

Interactive High-Resolution Boundary Surfaces for Deformable Bodies with Changing Topology

SIGGRAPH Course: Data-Driven Simulation Methods in Computer Graphics: Cloth, Tissue, and Faces

Miguel Otaduy, Bernd Bickel, Derek Bradley, Huamin Wang

In recent years, the field of computer animation has witnessed the invention of multiple simulation methods that exploit pre-recorded data to improve the performance and/or realism of dynamic deformations. Various methods have been presented concurrently, and they present differences, but also similarities, that have not yet been analyzed or discussed. This course focuses on the application of data-driven methods to three areas of computer animation, namely dynamic deformation of faces, soft volumetric tissue, and cloth. The course describes the particular challenges tackled in a data-driven manner, classifies the various methods, and also shares insights for the application to other settings.

The explosion of data-driven animation methods and the success of their results make this course extremely timely. Up till now, the proposed methods have remained familiar only at the research context, and have not made their way through computer graphics industry. This course aims to fit two main purposes. First, present a common theory and understanding of data-driven methods for dynamic deformations that may inspire the development of novel solutions, and second, bridge the gap with industry, by making data-driven approaches accessible. The course targets an audience consisting of both researchers and programmers in computer animation.

Data-Driven Simulation Methods in Computer Graphics: Cloth, Tissue, and Faces

SIGGRAPH Course: FEM Simulation of 3D Deformable Solids: A practitioner's guide to theory, discretization and model reduction

Eftychios Sifakis and Jernej Barbic

A practical guide to finite-element-method (FEM) simulation of 3D deformable solids reviews essential offline FEM simulation techniques: complex nonlinear materials, invertible treatment of elasticity, and model-reduction techniques for real-time simulation.

Simulations of deformable solids are important in many applications in computer graphics, including film special effects, computer games, and virtual surgery. FEM has become a popular method in many applications. Both offline simulation and real-time techniques have matured in computer graphics literature.

This course is designed for attendees familiar with numerical simulation in computer graphics who would like to obtain a cohesive picture of the various FEM simulation methods available, their strengths and weaknesses, and their applicability in various simulation scenarios. The course is also a practical implementation guide for the visual-effects developer, offering a very lean yet adequate synopsis of the underlying mathematical theory. The first section introduces FEM deformable-object simulation and its fundamental concepts, such as deformation gradient, strain, stress, and elastic energy, discusses corotational FEM models, isotropic hyperelasticity, and numerical methods such as conjugate gradients and multigrid. The second section presents the state of the art in model reduction techniques for real-time FEM solid simulation. Topics include linear modal analysis, modal warping, subspace simulation, domain decomposition, and which techniques are suitable for which application.

FEM Simulation of 3D Deformable Solids: A practitioner’s guide to theory, discretization and model reduction

Deformable Objects Alive!

Stelian Coros, Sebastian Martin, Bernhard Thomaszewski, Christian Schumacher, Robert Sumner, Markus Gross

We present a method for controlling the motions of active deformable characters. As an underlying principle, we require that all motions be driven by internal deformations. We achieve this by dynamically adapting rest shapes in order to induce deformations that, together with environment interactions, result in purposeful and physically-plausible motions. Rest shape adaptation is a powerful concept and we show that by restricting shapes to suitable subspaces, it is possible to explicitly control the motion styles of deformable characters. Our formulation is general and can be combined with arbitrary elastic models and locomotion controllers. We demonstrate the efficiency of our method by animating curve, shell, and solid-based characters whose motion repertoires range from simple hopping to complex walking behaviors.

Deformable Objects Alive!