We consider the simulation of nonconvex rigid bodies focusing on interactions such as collision, contact, friction (kinetic, static, rolling and spinning) and stacking. We advocate representing the geometry with both a triangulated surface and a signed distance function defined on a grid, and this dual representation is shown to have many advantages. We propose a novel approach to time integration merging it with the collision and contact processing algorithms in a fashion that obviates the need for ad hoc threshold velocities. We show that this approach matches the theoretical solution for blocks sliding and stopping on inclined planes with friction. We also present a new shock propagation algorithm that allows for efficient use of the propagation (as opposed to the simultaneous) method for treating contact. These new techniques are demonstrated on a variety of problems ranging from simple test cases to stacking problems with as many as 1000 nonconvex rigid bodies with friction as shown in Figure 1.

We introduce a novel "sensation preserving" simplification algorithm for faster collision queries between two polyhedral objects in haptic rendering. Given a polyhedral model, we construct a multiresolution hierarchy using "filtered edge collapse", subject to constraints imposed by collision detection. The resulting hierarchy is then used to compute fast contact response for haptic display. The computation model is inspired by human tactual perception of contact information. We have successfully applied and demonstrated the algorithm on a time-critical collision query framework for haptically displaying complex object-object interaction. Compared to existing exact contact query algorithms, we observe noticeable performance improvement in update rates with little degradation in the haptic perception of contacts.

Abstract — Static collision checking amounts to testing a given configuration of objects for overlaps. In contrast, the goal of dynamic checking is to determine whether all configurations along a continuous path are collision-free. While there exist effective methods for static collision detection, dynamic checking still lacks methods that are both reliable and efficient. A common approach is to sample paths at some fixed, prespecified resolution and statically test each sampled configuration. But this approach is not guaranteed to detect collision whenever one occurs, and trying to increase its reliability by refining the sampling resolution along the entire path results in slow checking. This paper introduces a new method for testing path segments in c-space or collections of such segments, that is both reliable and efficient. This method locally adjusts the sampling resolution by comparing lower bounds on distances between objects in relative motion with upper bounds on lengths of curves traced by points of these moving objects. Several additional techniques and heuristics increase the checker’s efficiency in scenarios with many moving objects (e.g., articulated arms and/or multiple robots) and high geometric complexity. The new method is general, but particularly well suited for use in probabilistic roadmap (PRM) planners, where it is critical to determine as quickly as possible whether given path segments collide, or not. Extensive tests, in particular on randomly generated path segments and on multi-segment paths produced by PRM planners, show that the new method compares favorably with a fixed-resolution approach at “suitable ” resolution, with the enormous advantage that it never fails to detect collision.

We present "contact levels of detail" (CLOD), a novel concept for multiresolution collision detection. Given a polyhedral model, our algorithm automatically builds a "dual hierarchy", both a multiresolution representation of the original model and its bounding volume hierarchy for accelerating collision queries. We have proposed various error metrics, including object-space errors, velocity dependent gap, screen-space errors and their combinations. At runtime,

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We present a fast algorithm for continuous collision detection between a moving avatar and its surrounding virtual environment. We model the avatar as an articulated body using line-skeletons with constant o#sets and the virtual environment as a collection of polygonized objects. Given the position and orientation of the avatar at discrete time steps, we use an arbitrary in-between motion to interpolate the path for each link between discrete instances. We bound the swept-space of each link using a swept volume (SV) and compute a bounding volume hierarchy to cull away links that are not in close proximity to the objects in the virtual environment. We generate the SV's of the remaining links and use them to check for possible interferences and estimate the time of collision between the surface of the SV and the objects in the virtual environment. Furthermore, we use graphics hardware to perform collision queries on the dynamically generated swept surfaces. Our overall algorithm requires no precomputation and is applicable to general articulated bodies. We have implemented the algorithm on a 2.4 GHz Pentium IV PC with NVIDIA GeForce FX 5800 graphics card and applied it to an avatar with 16 links, moving in a virtual environment composed of hundreds of thousands of polygons. Our prototype system is able to detect all contacts between the moving avatar and the environment in 10 30 milliseconds.

Abstract — Proximity query is an integral part of any motion planning algorithm and takes up the majority of planning time. Due to performance issues, most existing planners perform queries at fixed sampled configurations, sometimes resulting in missed collisions. Moreover, randomly determining collision-free configurations makes it difficult to obtain samples close to, or on, the surface of C-obstacles in the configuration space. In this paper, we present an efficient and practical local planning method in contact space which uses “continuous collision detection ” (CCD). We show how, using the precise contact information provided by a CCD algorithm, a randomized planner can be enhanced by efficiently sampling the contact space, as well as by constraining the sampling when the roadmap is expanded. We have included our contact-space planning methods in a freely available stateof-the-art planning library- the Stanford MPK library. We have been able to observe that in complex scenarios involving cluttered and narrow passages, which are typically difficult for randomized planners, the enhanced planner offers up to 70 times performance improvement when our contact-space sampling and constrained sampling methods are enabled.

In this paper, the collision prediction between polyhedra under screw motions and a static scene using a new K dimensional tree data structure (Multiresolution Kdtree, MKtree) is introduced. In a complex scene containing a high number of individual objects, the MKtree represents a hierarchical subdivision of the scene objects that guarantees a small space overlap between node regions. The proposed MKtree data structure succeeds in performing simultaneously space and scene subdivision. MKtrees are useful for broad phase collision and proximity detection tests and for time-critical rendering in large environments requiring external memory storage. The paper proposes an efficient broad phase collision prediction algorithm. Examples in ship design applications are presented and discussed..

Figure 1: (a) shoulder twist deformed by linear blend skinning produces the candy-wrapper artifact, (b) bounding spheres for linear blend skinning refitted by [Kavan and Zara 2005a], (c) the same posture deformed by spherical blend skinning [Kavan and Zara 2005b], (d) bounding spheres for spherical blend skinning refitted using the algorithm introduced in this paper. Efficient refitting of bounding spheres is a crucial component of our fast collision detection algorithm. Recently, two algorithms improving the real-time simulation of articulated models in virtual environments have been published: 1) fast collision detection for linear blend skinning and 2) spherical blend skinning. Both linear and spherical blending solve the skinning problem of a skeletally controlled 3D model (e.g., an avatar), but only spherical blending avoids artifacts such as the candywrapper. However, to date, fast collision detection has been limited to linear blending. This paper describes how to perform collision detection for models skinned with the more sophisticated spherical method. As a result, both high-quality skinning and fast and exact collision detection can be achieved – there is no longer any need for a trade-off. The generalization from linear to spherical blending involves the construction of rotation bounds, derived using a quaternion representation. The resulting algorithm is simple to implement and fast enough for real-time virtual reality applications.

in the presence of friction. Most previous approaches in computer graphics rely on a linear complementarity formulation for handling contact in a stable way, and approximate Coulombs’s friction law for making the problem tractable. In contrast, following the seminal work by Alart and Curnier in contact mechanics, we simultaneously model contact and exact Coulomb friction as a zero finding problem of a nonsmooth function. A semi-implicit time-stepping scheme is then employed to discretize the dynamicsofrodsconstrainedbyfrictionalcontact:thisleadstoasetoflinearequationssubjecttoanequalityconstraintinvolvinganon-differentiable function.Tosolvethisone-stepproblemweintroduceasimpleandpractical nonsmooth Newton algorithm, which proves to be reasonably efficient and robust for systems that are not over-constrained. We show that our method is able to finely capture the subtle effects that occur when thin elastic rods with various geometries enter into contact, such as stick-slip instabilities in free configurations, entangling curls, resting contacts in braid-like structures, or the formation of tight knots under large constraints. Our method can be viewed as a first step towards the accurate modeling of dynamic fibrousmaterials.