Geometric Stiffness for Real-time Constrained Multibody Dynamics

Sheldon Andrews, Marek Teichmann, Paul Kry

This paper focuses on the stable and efficient simulation of articulated rigid body systems for real-time applications. Specifically, we focus on the use of geometric stiffness, which can dramatically increase simulation stability. We examine several numerical problems with the inclusion of geometric stiffness in the equations of motion, as proposed by previous work, and address these issues by introducing a novel method for efficiently building the linear system. This offers improved tractability and numerical efficiency. Furthermore, geometric stiffness tends to significantly dissipate kinetic energy. We propose an adaptive damping scheme, inspired by the geometric stiffness, that uses a stability criterion based on the numerical integrator to determine the amount of non-constitutive damping required to stabilize the simulation. With this approach, not only is the dynamical behavior better preserved, but the simulation remains stable for mass ratios of 1,000,000-to-1 at time steps up to 0.1 s. We present a number of challenging scenarios to demonstrate that our method improves efficiency, and that it increases stability by orders of magnitude compared to previous work.

Geometric Stiffness for Real-time Constrained Multibody Dynamics

Fluxed Animated Boundary Method

Alexey Stomakhin, Andrew Selle

We present a novel approach to guiding physically based particle simulations using boundary conditions. Unlike commonly used ad hoc particle techniques for adding and removing the material from a simulation, our approach is principled by utilizing the concept of volumetric flux. Artists are provided with a simple yet powerful primitive called a fluxed animated boundary (FAB), allowing them to specify a control shape and a material flow field. The system takes care of enforcing the corresponding boundary conditions and necessary particle reseeding. We show how FABs can be used artistically or physically. Finally, we demonstrate production examples that show the efficacy of our method.

Fluxed Animated Boundary Method

Quasi-Newton Methods for Real-time Simulation of Hyperelastic Materials

Tiantian Liu, Sofien Bouaziz, Ladislav Kavan

We present a new method for real-time physics-based simulation supporting many different types of hyperelastic materials. Previous methods such as Position Based or Projective Dynamics are fast, but support only limited selection of materials; even classical materials such as the Neo-Hookean elasticity are not supported. Recently, Xu et al. [2015] introduced new “splinebased materials” which can be easily controlled by artists to achieve desired animation effects. Simulation of these types of materials currently relies on Newton’s method, which is slow, even with only one iteration per timestep. In this paper, we show that Projective Dynamics can be interpreted as a quasi-Newton method. This insight enables very efficient simulation of a large class of hyperelastic materials, including the Neo-Hookean, spline-based materials, and others. The quasi-Newton interpretation also allows us to leverage ideas from numerical optimization. In particular, we show that our solver can be further accelerated using L-BFGS updates (Limitedmemory Broyden-Fletcher-Goldfarb-Shanno algorithm). Our final method is typically more than 10 times faster than one iteration of Newton’s method without compromising quality. In fact, our result is often more accurate than the result obtained with one iteration of Newton’s method. Our method is also easier to implement, implying reduced software development costs.

Quasi-Newton Methods for Real-time Simulation of Hyperelastic Materials

Symposium on Computer Animation 2017

Anisotropic Elastoplasticity for Cloth, Knit and Hair Frictional Contact

Chenfanfu Jiang, Theodore Gast, Joseph Teran

The typical elastic surface or curve simulation method takes a Lagrangian approach and consists of three components: time integration, collision detection and collision response. The Lagrangian view is beneficial because it naturally allows for tracking of the codimensional manifold, however collision must then be detected and resolved separately. Eulerian methods are promising alternatives because collision processing is automatic and while this is effective for volumetric objects, advection of a codimensional manifold is too inaccurate in practice. We propose a novel hybrid Lagrangian/Eulerian approach that preserves the best aspects of both views. Similar to the Drucker-Prager and Mohr-Coulomb models for granular materials, we define our collision response with a novel elastoplastic constitutive model. To achieve this, we design an anisotropic hyperelastic constitutive model that separately characterizes the response to manifold strain as well as shearing and compression in the directions orthogonal to the manifold. We discretize the model with the Material Point Method and a novel codimensional Lagrangian/Eulerian update of the deformation gradient. Collision intensive scenarios with millions of degrees of freedom require only a few minutes per frame and examples with up to one million degrees of freedom run in less than thirty seconds per frame.

Anisotropic Elastoplasticity for Cloth, Knit and Hair Frictional Contact

Dynamics-Aware Numerical Coarsening for Fabrication Design

Desai Chen, David I. W. Levin, Wojciech Matusik, Danny M. Kaufman

The realistic simulation of highly-dynamic elastic objects is important for a broad range of applications in computer graphics, engineering and computational fabrication. However, whether simulating flipping toys, jumping robots, prosthetics or quickly moving creatures, performing such simulations in the presence of contact, impact and friction is both time consuming and inaccurate. In this paper we present Dynamics-Aware Coarsening (DAC) and the Boundary Balanced Impact (BBI) model which allow for the accurate simulation of dynamic, elastic objects undergoing both large scale deformation and frictional contact, at rates up to 79 times faster than state-of-the-art methods. DAC and BBI produce simulations that are accurate and fast enough to be used (for the first time) for the computational design of 3D-printable compliant dynamic mechanisms. Thus we demonstrate the efficacy of DAC and BBI by designing and fabricating mechanisms which flip, throw and jump over and onto obstacles as requested.

Dynamics-Aware Numerical Coarsening for Fabrication Design

Authoring Landscapes by Combining Ecosystem and Terrain Erosion Simulation

Guillaume Cordonnier, Eric Galin, James Gain, Bedrich Benes, Eric Guérin, Adrien Peytavie, Marie-Paule Cani

We introduce a novel framework for interactive landscape authoring that supports bi-directional feedback between erosion and vegetation simulation. Vegetation and terrain erosion have strong mutual impact and their interplay influences the overall realism of virtual scenes. Despite their importance, these complex interactions have been neglected in computer graphics. Our framework overcomes this by simulating the effect of a variety of geomorphological agents and the mutual interaction between different material and vegetation layers, including rock, sand, humus, grass, shrubs, and trees. Users are able to exploit these interactions with an authoring interface that consistently shapes the terrain and populates it with details. Our method, validated through side-by-side comparison with real terrains, can be used not only to generate realistic static landscapes, but also to follow the temporal evolution of a landscape over a few centuries.

Authoring Landscapes by Combining Ecosystem and Terrain Erosion Simulation

Data-Driven Physics for Human Soft Tissue Animation

Meekyoung Kim, Gerard Pons-Moll, Sergi Pujades, Sungbae Bang, Jinwwok Kim, Michael Black, Sung-Hee Lee

Data driven models of human poses and soft-tissue deformations can produce very realistic results, but they only model the visible surface of the human body and cannot create skin deformation due to interactions with the environment. Physical simulations can generalize to external forces, but their parameters are difficult to control. In this paper, we present a layered volumetric human body model learned from data. Our model is composed of a data-driven inner layer and a physics-based external layer. The inner layer is driven with a volumetric statistical body model (VSMPL). The soft tissue layer consists of a tetrahedral mesh that is driven using the finite element method (FEM). Model parameters, namely the segmentation of the body into layers and the soft tissue elasticity, are learned directly from 4D registrations of humans exhibiting soft tissue deformations. The learned two layer model is a realistic full-body avatar that generalizes to novel motions and external forces. Experiments show that the resulting avatars produce realistic results on held out sequences and react to external forces. Moreover, the model supports the retargeting of physical properties from one avatar when they share the same topology.

Data-Driven Physics for Human Soft Tissue Animation

Regularized Kelvinlets: Sculpting Brushes based on Fundamental Solutions of Elasticity

Fernando de Goes, Doug L. James

We introduce a new technique for real-time physically based volume sculpting of virtual elastic materials. Our formulation is based on the elastic response to localized force distributions associated with common modeling primitives such as grab, scale, twist, and pinch. The resulting brush-like displacements correspond to the regularization of fundamental solutions of linear elasticity in infinite 2D and 3D media. These deformations thus provide the realism and plausibility of volumetric elasticity, and the interactivity of closed-form analytical solutions. To finely control our elastic deformations, we also construct compound brushes with arbitrarily fast spatial decay. Furthermore, pointwise constraints can be imposed on the displacement field and its derivatives via a single linear solve. We demonstrate the versatility and efficiency of our method with multiple examples of volume sculpting and image editing.

Regularized Kelvinlets: Sculpting Brushes based on Fundamental Solutions of Elasticity

Bounce Maps: An Improved Restitution Model for Real-Time Rigid-Body Impact

Jui-Hsien Wang, Rajsekhar Setaluri, Dinesh K Pai, Doug L James

We present a novel method to enrich standard rigid-body impact models with a spatially varying coefficient of restitution map, or Bounce Map. Even state-of-the art methods in computer graphics assume that for a single rigid body, post- and pre-impact dynamics are related with a single global, constant, namely the coefficient of restitution. We first demonstrate that this assumption is highly inaccurate, even for simple objects. We then present a technique to efficiently and automatically generate a function which maps locations on the object’s surface along with impact normals, to a scalar coefficient of restitution value. Furthermore, we propose a method for two-body restitution analysis, and, based on numerical experiments, estimate a practical model for combining one-body Bounce Map values to approximate the two-body coefficient of restitution. We show that our method not only improves accuracy, but also enables visually richer rigid-body simulations

Bounce Maps: An Improved Restitution Model for Real-Time Rigid-Body Impact