We introduce the Bounded Deformation Tree, or BD-Tree, which can perform collision detection with reduced deformable models at costs comparable to collision detection with rigid objects. Reduced deformable models represent complex deformations as linear superpositions of arbitrary displacement fields, and are used in a variety of applications of interactive computer graphics. The BD-Tree is a bounding sphere hierarchy for output-sensitive collision detection with such models. Its bounding spheres can be updated after deformation in any order, and at a cost independent of the geometric complexity of the model; in fact the cost can be as low as one multiplication and addition per tested sphere, and at most linear in the number of reduced deformation coordinates. We show that the BDTree is also extremely simple to implement, and performs well in practice for a variety of real-time and complex off-line deformable simulation examples.

Collision detection is a vital task in almost all forms of computer animation and physical simulation. It is also one of the most computationally expensive, and therefore a frequent impediment to efficient implementation of real-time graphics applications. We describe how graphics hardware can be used as a geometric co-processor to carry out the bulk of the computation involved with collision detection. Hardware frame buffer operations are used to implement a ray-casting algorithm which detects static interference between solid polyhedral objects. The algorithm is linear in both the number of objects and number of polygons in the models. It also requires no preprocessing or special data structures.

Fast and accurate collision detection between geometric bodies is essential in application areas like virtual reality, animation, simulation, games and robotics. In this work, we address the collision detection problem in applications where deformable bodies are used, which change their overall shape every time step of the simulation. We propose and evaluate suitable bounding volume trees for deforming bodies that can be pre-built and then updated very efficiently during simulation. Several heuristics for updating the trees due to deformations are compared to each other. By combining a top-down and a bottom-up update strategy into a hybrid tree update method, promising results were achieved. Experiments show that our approach is four to five times faster than a previously leading method.

This paper describes a new efficient collision checker to test single straight-line segments in c-space, sequences of such segments, or more complex paths. This checker is particularly suited for probabilistic roadmap (PRM) planners applied to manipulator arms and multi-robot systems. Such planners spend most of their time checking local paths between randomly sampled configurations for collision. While commonly used approaches test intermediate configurations on a segment at a prespecified resolution, the checker presented in this paper is exact, i.e., it cannot fail to find an existing collision, even when some robot links and obstacles are very thin. Its efficiency relies on its core algorithm, which dynamically adjusts the required resolution by relating the distances between objects in the workspace to the maximum lengths of the paths traced out by points on these objects. The checker's efficiency is further increased by several additional techniques presented in this paper, which adequately approximate distances between objects and lengths of travelled paths in workspace, and order collision tests to reveal collisions as early as possible. The new checker has been extensively tested, first on segments randomly generated in c-space, next as part of an existing PRM planner, and finally as part of a path smoother/optimizer. These experiments show that the checker is faster than a resolution-based approach (with suitable resolution), with the enormous advantage that it never returns an incorrect answer. The checker also admits a number of straightforward extensions. For example, it can monitor a minimum workspace distance between each robot link and other objects (e.g., obstacles, links of other robots).

The prediction of collisions amongst N rigid objects may be reduced to a series of computations of the time to first contact for all pairs of objects. Simple enclosing bounds and hierarchical partitions of the space-time domain are often used to avoid testing object-pairs that clearly will not collide. When the remaining pairs involve only polyhedra under straight-line translation, the exact computation of the collision time and of the contacts requires only solving for intersections between linear geometries. When a pair is subject to a more general relative motion, such a direct collision prediction calculation may be intractable. The popular brute force collision detection strategy of executing the motion for a series of small time steps and of checking for static interferences after each step is often computationally prohibitive. We propose instead a less expensive collision prediction strategy, where we approximate the relative motion between pairs of objects by a sequence of screw motion segments, each defined by the relative position and orientation of the two objects at the beginning and at the end of the segment. We reduce the computation of the exact collision time and of the corresponding face/vertex and edge/edge collision points to the numeric extraction of the roots of simple univariate analytic functions. Furthermore, we propose a series of simple rejection tests, which exploit the particularity of the screw motion to immediately decide that some objects do not collide or to speed-up the prediction of collisions by about 30%, avoiding on average 3/4 of the root-finding queries even when the object actually collide.

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.

Figure 1: Tree with falling leaves: In this scene, leaves fall from the tree and undergo non-rigid motion. They collide with other leaves and branches. The environment consists of more than 40K triangles and 150 leaves. Our algorithm, FAR, can compute all the collisions in about 35 msec per time step. We present a reliable culling algorithm that enables fast and accurate collision detection between triangulated models in a complex environment. Our algorithm performs fast visibility queries on the GPUs for eliminating a subset of primitives that are not in close proximity. To overcome the accuracy problems caused by the limited viewport resolution, we compute the Minkowski sum of each primitive with a sphere and perform reliable 2.5D overlap tests between the primitives. We are able to achieve more effective collision culling as compared to prior object-space culling algorithms. We integrate our culling algorithm with CULLIDE [8] and use it to perform reliable GPU-based collision queries at interactive rates on all types of models, including non-manifold geometry, deformable models, and breaking objects.

Monte Carlo simulation (MCS) is a common methodology to compute pathways and thermodynamic prop-erties of proteins. A simulation run is a series of random steps in conformation space, each perturbing some degrees of freedom of the molecule. A step is accepted with a probability that depends on the change in value of an energy function. Typical energy functions sum many terms. The most costly ones to compute are contributed by atom pairs closer than some cutoff distance. This paper introduces a new method that speeds up MCS by exploiting the facts that proteins are long kinematic chains and that few degrees of freedom are changed at each step. A novel data structure, called the ChainTree, captures both the kinematics and the shape of a protein at successive levels of detail. It is used to efficiently detect self-collision (steric clash between atoms) and/or find all atom pairs contributing to the energy. It also makes it possible to identify partial energy sums left unchanged by a perturbation, thus allowing the energy value to be incrementally updated. Computational tests on four proteins of sizes ranging from 68 to 755 amino acids show that MCS with the ChainTree method is significantly faster (as much as 10 times faster for the largest protein) than with the widely used grid method. They also indicate that speed-up increases with larger proteins.

Several simulations for parallel collision detection have been suggested during the last years. The algorithms usually greatly depend on the parallel infrastructure and this dependency causes in many times non-scalability performance. The dependency also harms the portability of the simulation. This paper suggests a scalable and portable parallel algorithm for collision detection simulation that fits both clusters and MPI machines.

Randomized motion planners are greatly a#ected by the e#ciency and robustness of algorithms for collision checking of robot configurations. A number of powerful collision detection algorithms are currently available to the research community although their relative capabilities and performance cannot be easily compared due to the many factors involved.