Category: Collisions

Rigid Body Contact Problems using Proximal Operators

Kenny Erleben

Iterative methods are popular for solving contact force problems in rigid body dynamics. They are loved for their robustness and surrounded by mystery as to whether they converge or not. We provide a mathematical foundation for iterative (PROX) schemes based on proximal operators. This is a class of iterative Jacobi and blocked Gauss–Seidel variants that theoretically proven always converge and provides a flexible plug and play framework for exploring different friction laws. We provide a portfolio of experience for choosing r-Factor strategies for such schemes and we analyze the distribution of convergence behaviors. Our results indicate the Gauss-Seidel variant is superior in terms of delivering predictable convergence behaviour and hence should be preferred over Jacobi variants. Our results also suggest that Global r -Factor strategies are better for structured stacking scenarios and can achieve absolute convergence in more cases.

Rigid Body Contact Problems using Proximal Operators

Improving the GJK algorithm for faster and more reliable distance queries between convex objects

Mattia Montanari, Nik Petrinic, and Ettore Barbieri

This article presents a new version of the Gilbert-Johnson-Keerthi (GJK) algorithm that circumvents the shortcomings introduced by degenerate geometries. The original Johnson algorithm and Backup procedure are replaced by a distance subalgorithm that is faster and accurate to machine precision, thus guiding the GJK algorithm toward a shorter search path in less computing time. Numerical tests demonstrate that this effectively is a more robust procedure. In particular, when the objects are found in contact, the newly proposed subalgorithm runs from 15% to 30% times faster than the original one. The improved performance has a significant impact on various applications, such as real-time simulations and collision avoidance systems. Altogether, the main contributions made to the GJK algorithm are faster convergence rate and reduced computational time. These improvements may be easily added into existing implementations; furthermore, engineering applications that require solutions of distance queries to machine precision can now be tackled using the GJK algorithm.

Improving the GJK algorithm for faster and more reliable distance queries between convex objects

All’s Well That Ends Well: Guaranteed Resolution of Simultaneous Rigid Body Impact

Etienne Vouga, Breannan Smith, Danny M. Kaufman, Rasmus Tamstorf, Eitan Grinspun

Iterative algorithms are frequently used to resolve simultaneous impacts between rigid bodies in physical simulations. However, these algorithms lack formal guarantees of termination, which is sometimes viewed as potentially dangerous, so failsafes are used in practical codes to prevent infinite loops. We show such steps are unnecessary. In particular, we study the broad class of such algorithms that are conservative and satisfy a minimal set of physical correctness properties, and which encompasses recent methods like Generalized Reflections as well as pairwise schemes. We fully characterize finite termination of these algorithms. The only possible failure cases can be detected, and we describe a procedure for modifying the algorithms to provably ensure termination. We also describe modifications necessary to guarantee termination in the presence of numerical error due to the use of floating-point arithmetic. Finally, we discuss the challenges dissipation introduce for finite termination, and describe how dissipation models can be incorporated while retaining the termination guarantee.

All’s Well That Ends Well: Guaranteed Resolution of Simultaneous Rigid Body Impact

kDet: Parallel Constant Time Collision Detection for Polygonal Objects

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

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

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

Efficient and Reliable Self-Collision Culling using Unprojected Normal Cones

Tongtong Wang, Zhihua Liu, Min Tang, Roufeng Tong, and Dinesh Manocha

We present an efficient and accurate algorithm for self-collision detection in deformable models. Our approach can perform discrete and continuous collision queries on triangulated meshes. We present a simple and linear time algorithm to perform the normal cone test using the unprojected 3D vertices, which reduces to a sequence point-plane classification tests. Moreover, we present a hierarchical traversal scheme that can significantly reduce the number of normal cone tests and the memory overhead using front-based normal cone culling. The overall algorithm can reliably detect all (self) collisions in models composed of hundred of thousands of triangles. We observe considerable performance improvement over prior CCD algorithms.

Efficient and Reliable Self-Collision Culling using Unprojected Normal Cones

Accurate Contact Modeling for Multi-rate Single-point Haptic Rendering of Static and Deformable Environments

Thomas Knott, Torsten Kuhlen

Common approaches for the haptic rendering of complex scenarios employ multi-rate simulation schemes. Here, the collision queries or the simulation of a complex deformable object are often performed asynchronously on a lower frequency, while some kind of intermediate contact representation is used to simulate interactions on the haptic rate. However, this can produce artifacts in the haptic rendering when the contact situation quickly changes and the intermediate representation is not able to reflect the changes due to the lower update rate. We address this problem utilizing a novel contact model. It facilitates the creation of contact representations that are accurate for a large range of motions and multiple simulation time-steps.We handle problematic convex contact regions using a local convex decomposition and special constraints for convex areas.We combine our accurate contact model with an implicit temporal integration scheme to create an intermediate mechanical contact representation, which reflects the dynamic behavior of the simulated objects. Moreover, we propose a new iterative solving scheme for the involved constrained dynamics problems.We increase the robustness of our method using techniques from trust region-based optimization. Our approach can be combined with standard methods for the modeling of deformable objects or constraint-based approaches for the modeling of, for instance, friction or joints. We demonstrate its benefits with respect to the simulation accuracy and the quality of the rendered haptic forces in multiple scenarios.

Accurate Contact Modeling for Multi-rate Single-point Haptic Rendering of Static and Deformable Environments

SMASH: Physics-guided Reconstruction of Collisions from Videos

Aron Monszpart, Nils Thuerey, Niloy J. Mitra

Collision sequences are commonly used in games and entertainment to add drama and excitement. Authoring even two body collisions in the real world can be difficult, as one has to get timing and the object trajectories to be correctly synchronized. After tedious trial-and-error iterations, when objects can actually be made to collide, then they are difficult to capture in 3D. In contrast, synthetically generating plausible collisions is difficult as it requires adjusting different collision parameters (e.g., object mass ratio, coefficient of restitution, etc.) and appropriate initial parameters. We present SMASH to directly read off appropriate collision parameters directly from raw input video recordings. Technically we enable this by utilizing laws of rigid body collision to regularize the problem of lifting 2D trajectories to a physically valid 3D reconstruction of the collision. The reconstructed sequences can then be modified and combined to easily author novel and plausible collisions. We evaluate our system on a range of synthetic scenes and demonstrate the effectiveness of our method by accurately reconstructing several complex real world collision events.

SMASH: Physics-guided Reconstruction of Collisions from Videos