Category: Collisions

Interpenetration Free Simulation of Thin Shell Rigid Bodies

R. Elliot English, Michael Lentine, Ron Fedkiw

We propose a new algorithm for rigid body simulation that guarantees each body is in an interpenetration free state, both increasing the accuracy and robustness of the simulation as well as alleviating the need for ad hoc methods to separate bodies for subsequent simulation and rendering. We cleanly separate collision and contact resolution such that objects move and collide in the first step, with resting contact handled in the second step. The first step of our algorithm guarantees that each time step produces geometry that does not intersect or overlap by using an approximation to the continuous collision detection (and response) problem and thus is amenable to thin shells and degenerately flat objects moving at high speeds. In addition we introduce a novel failsafe which allows us to resolve all interpenetration without iterating to convergence. Since the first step guarantees a non-interfering state for the geometry, in the second step we propose a contact model for handling thin shells in proximity considering only the instantaneous locations at the ends of the time step.

Interpenetration Free Simulation of Thin Shell Rigid Bodies

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

Energy-Based Self-Collision Culling for Arbitrary Mesh Deformations

Changxi Zheng, Doug James

In this paper, we accelerate self-collision detection (SCD) for a deforming triangle mesh by exploiting the idea that a mesh cannot self collide unless it deforms enough. Unlike prior work on subspace self-collision culling which is restricted to low-rank deformation subspaces, our energy-based approach supports arbitrary mesh deformations while still being fast. Given a bounding volume hierarchy (BVH) for a triangle mesh, we precompute Energy-based Self-Collision Culling (ESCC) certificates on bounding-volume-related sub-meshes which indicate the amount of deformation energy required for it to self collide. After updating energy values at runtime, many bounding-volume self-collision queries can be culled using the ESCC certificates. We propose an affine-frame Laplacian-based energy definition which sports a highly optimized certificate preprocess, and fast runtime energy evaluation. The latter is performed hierarchically to amortize Laplacian energy and affine-frame estimation computations. ESCC supports both discrete and continuous SCD with detailed and nonsmooth geometry. We demonstrate significant culling on various examples, with SCD speed-ups up to 26X.

Energy-Based Self-Collision Culling for Arbitrary Mesh Deformation

Adaptive Image-Based Intersection Volume

Bin Wang, Francois Faure, Dinesh Pai

A method for image-based contact detection and modeling, with guaranteed precision on the intersection volume, is presented. Unlike previous image-based methods, our method optimizes a non-uniform ray sampling resolution and allows precise control of the volume error. By cumulatively projecting all mesh edges into a generalized 2D texture, we construct a novel data structure, the Error Bound Polynomial Image (EBPI), which allows efficient computation of the maximum volume error as a function of ray density. Based on a precision criterion, EBPI pixels are subdivided or clustered. The rays are then cast in the projection direction according to the non-uniform resolution. The EBPI data, combined with ray-surface intersection points and normals, is also used to detect transient edges at surface intersections. This allows us to model intersection volumes at arbitrary resolution, while avoiding the geometric computation of mesh intersections. Moreover, the ray casting acceleration data structures can be reused for the generation of high quality images.

Adaptive Image-Based Intersection Volume

Reflections on Simultaneous Impact

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

Resolving simultaneous impacts is an open and significant problem in collision response modeling. Existing algorithms in this domain fail to fulfill at least one of five physical desiderata. To address this we present a simple generalized impact model motivated by both the successes and pitfalls of two popular approaches: pair-wise propagation and linear complementarity models. Our algorithm is the first to satisfy all identified desiderata, including simultaneously guaranteeing symmetry preservation, kinetic energy conservation, and allowing break-away. Furthermore, we address the associated problem of inelastic collapse, proposing a complementary generalized restitution model that eliminates this source of nontermination. We then consider the application of our models to the synchronous time-integration of large-scale assemblies of impacting rigid bodies. To enable such simulations we formulate a consistent frictional impact model that continues to satisfy the desiderata. Finally, we validate our proposed algorithm by correctly capturing the observed characteristics of physical experiments including the phenomenon of extended patterns in vertically oscillated granular materials.

Reflections on Simultaneous Impact

Interactive Editing of Deformable Simulations

Jernej Barbic, Funshing Sin, Eitan Grinspun

We present an interactive animation editor for complex deformable object animations. Given an existing animation, the artist directly manipulates the deformable body at any time frame, and the surrounding animation immediately adjusts in response. The automatic adjustments are designed to respect physics, preserve detail in both the input motion and geometry, respect prescribed bilateral contact constraints, and controllably and smoothly decay in spacetime. While the utility of interactive editing for rigid body and articulated figure animations is widely recognized, a corresponding approach to deformable bodies has not been technically feasible before. We achieve interactive rates by combining spacetime model reduction, rotation-strain coordinate warping, linearized elasticity, and direct manipulation. This direct editing tool can serve the final stages of animation production, which often call for detailed, direct adjustments that are otherwise tedious to realize by re-simulation or frame-by-frame editing.

Interactive Editing of Deformable Simulations

PolyDepth: Real-Time Penetration Depth Computation using Iterative Contact-Space Projection

Changsoo Je, Min Tang, Youngeun Lee, Minkyoung Lee, Young J. Kim

We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find an initial collision-free configuration using several methods such as centroid difference, maximally clear configuration, motion coherence, random configuration, and sampling-based search. We project this configuration on to a local contact space using a variant of continuous collision detection algorithm and construct a linear convex cone around the projected configuration. We then formulate a new projection of the in-collision configuration onto the convex cone as a Linear Complementarity Problem (LCP), which we solve using a type of Gauss-Seidel iterative algorithm. We repeat this procedure until a locally optimal PD is obtained. Our algorithm can process complicated models consisting of tens of thousands triangles at interactive rates.

PolyDepth: Real-Time Penetration Depth Computation using Iterative Contact-Space Projection

Efficient Geometrically Exact Continuous Collision Detection

Tyson Brochu, Essex Edwards, Robert Bridson

Continuous collision detection (CCD) between deforming triangle mesh elements in 3D is a critical tool for many applications. The standard method involving a cubic polynomial solver is vulnerable to rounding error, requiring the use of ad hoc tolerances, and nevertheless is particularly fragile in (near-)planar cases. Even with per-simulation tuning, it may still cause problems by missing collisions or erroneously flagging non-collisions. We present a geometrically exact alternative guaranteed to produce the correct Boolean result (significant collision or not) as if calculated with exact arithmetic, even in degenerate scenarios. Our critical insight is that only the parity of the number of collisions is needed for robust simulation, and this parity can be calculated with simpler non-constructive predicates. In essence we analyze the roots of the nonlinear system of equations defining CCD through careful consideration of the boundary of the parameter domain. The use of new conservative culling and interval filters allows typical simulations to run as fast as with the non-robust version, but without need for tuning or worries about failure cases even in geometrically degenerate scenarios. We demonstrate the effectiveness of geometrically exact detection with a novel adaptive cloth simulation, the first to guarantee to remain intersection-free despite frequent curvature-driven remeshing.

Efficient Geometrically Exact Continuous Collision Detection

Continuous Penalty Forces

Min Tang, Dinesh Manocha, Miguel Otaduy, Ruofeng Tong

We present a simple algorithm to compute continuous penalty forces to determine collision response between rigid and deformable models bounded by triangle meshes. Our algorithm provides a well-behaved solution in contrast to the traditional stability and robustness problems of penalty methods, induced by force discontinuities. We trace contact features along their deforming trajectories and accumulate penalty forces along the penetration time intervals between the overlapping feature pairs. Moreover, we present a closed-form expression to compute the continuous and smooth collision response. Our method has very small additional overhead compared to previous penalty methods, while significantly improves the stability and robustness. We highlight its benefits on several benchmarks.

Continuous Penalty Forces

STAR: Interactive Simulation of Rigid Body Dynamics in Computer Graphics

Jan Bender, Kenny Erleben, Jeff Trinkle, Erwin Coumans

Interactive rigid body simulation is an important part of many modern computer tools. No authoring tool nor a game engine can do without. The high performance computer tools open up new possibilities for changing how designers, engineers, modelers and animators work with their design problems.

This paper is a self contained state-of-the-art report on the physics, the models, the numerical methods and the algorithms used in interactive rigid body simulation all of which has evolved and matured over the past 20 years. The paper covers applications and the usage of interactive rigid body simulation.

Besides the mathematical and theoretical details that this paper communicates in a pedagogical manner the paper surveys common practice and reflects on applications of interactive rigid body simulation. The grand merger of interactive and off-line simulation methods is imminent, multi-core is everyman’s property. These observations pose future challenges for research which we reflect on. In perspective several avenues for possible future work is touched upon such as more descriptive models and contact point generation problems. This paper is not only a stake in the sand on what has been done, it also seeks to give newcomers practical hands on advices and reflections that can give experienced researchers afterthought for the future.

Interactive Simulation of Rigid Body Dynamics in Computer Graphics