Matthias Müller, Nuttapong Chentanez, Miles Macklin, Stefan Jeschke
The two main constraints used in rigid body simulations are contacts and joints. Both constrain the motion of a small number of bodies in close proximity. However, it is often the case that a series of constraints restrict the motion of objects over longer distances such as the contacts in a large pile or the joints in a chain of rigid bodies. When only short range constraints are considered, a large number of solver iterations is typically needed for long range effects to emerge because information has to be propagated through individual joints and contacts. Our basic idea to signicantly speed up this process is to analyze the contact or joint graphs and automatically derive long range constraints such as upper and lower distance bounds between bodies that can potentially be far apart both spatially and topologically. The long range constraints are either generated or updated at every time step in case of contacts or whenever their topology changes within a joint graph. The signicant increase of the convergence rate due to the use of long range constraints allows us to simulate scenarios that cannot be handled by traditional solvers with a number of solver iterations that allow real time simulation.
Long Range Constraints for Rigid Body Simulations
René Weller, Nicole Debowski and Gabriel Zachmann
We define a novel geometric predicate and a class of objects that enables us to prove a linear bound on the number of intersecting polygon pairs for colliding 3D objects in that class. Our predicate is relevant both in theory and in practice: it is easy to check and it needs to consider only the geometric properties of the individual objects – it does not depend on the configuration of a given pair of objects. In addition, it characterizes a practically relevant class of objects: we checked our predicate on a large database of real-world 3D objects and the results show that it holds for all but the most pathological ones. Our proof is constructive in that it is the basis for a novel collision detection algorithm that realizes this linear complexity also in practice. Additionally, we present a parallelization of this algorithm with a worst-case running time that is independent of the number of polygons. Our algorithm is very well suited not only for rigid but also for deformable and even topology-changing objects, because it does not require any complex data structures or pre-processing. We have implemented our algorithm on the GPU and the results show that it is able to find in real-time all colliding polygons for pairs of deformable objects consisting of more than 200k triangles, including self-collisions.
kDet: Parallel Constant Time Collision Detection for Polygonal Objects
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
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
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.  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
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
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
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
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