We present an exact and interactive collision detection system, I-COLLIDE, for large-scale environments. Such environments are characterized by the number of objects undergoing rigid motion and the complexity of the mod-els. The algorithm does not assume the objects ’ motions can be expressed as a closed form function of time. The collision detection system is general and can be easily in-terfaced with a variety of applications. The algorithm uses a two-level approach based on pruning multiple-object pairs using bounding boxes and performing exact collision detection between selected pairs of polyhedral models. We demonstrate the performance of the system in walkthrough and simulation environments consisting of a large number of moving objects. In particular, the system takes less than l/20 of a second to determine all the collisions and contacts in an environment consisting of more than a 1000 moving polytopes, each consisting of more than 50 faces on an HP-9000/750. 1

Abstract—Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment. In addition to determining accurately the contacts that occur between pairs of objects, one needs also to do so at real-time rates. Applications such as haptic force-feedback can require over 1,000 collision queries per second. In this paper, we develop and analyze a method, based on bounding-volume hierarchies, for efficient collision detection for objects moving within highly complex environments. Our choice of bounding volume is to use a “discrete orientation polytope” (“k-dop”), a convex polytope whose facets are determined by halfspaces whose outward normals come from a small fixed set of k orientations. We compare a variety of methods for constructing hierarchies (“BV-trees”) of bounding k-dops. Further, we propose algorithms for maintaining an effective BV-tree of k-dops for moving objects, as they rotate, and for performing fast collision detection using BV-trees of the moving objects and of the environment. Our algorithms have been implemented and tested. We provide experimental evidence showing that our approach yields substantially faster collision detection than previous methods. Index Terms—Collision detection, intersection searching, bounding volume hierarchies, discrete orientation polytopes, bounding boxes, virtual reality, virtual environments. 1

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The need to perform fast and accurate proximity queries arises frequently in physically-based modeling, simulation, animation, real-time interaction within a virtual environment, and game dynamics. The set of proximity queries include intersection detection, tolerance verification, exact and approximate minimum distance computation, and (disjoint) contact determination. Specialized data structures and algorithms have often been designed to perform each type of query separately. We present a unified approach to perform any of these queries seamlessly for general, rigid polyhedral objects with boundary representations which are orientable 2-manifolds. The proposed method involves a hierarchical data structure built upon a surface decomposition of the models. Furthermore, the incremental query algorithm takes advantage of coherence between successive frames. It has been applied to complex benchmarks and compares very favorably with earlier algorithms and systems.

Many applications in Computer Graphics require fast and robust 3D collision detection algorithms. These algorithms can be grouped into four approaches: space-time volume intersection, swept volume interference, multiple interference detection and trajectory parameterization. While some approaches are linked to a particular object representation scheme (e.g., space-time volume intersection is particularly suited to a CSG representation), others do not. The multiple interference detection approach has been the most widely used under a variety of sampling strategies, reducing the collision detection problem to multiple calls to static interference tests. In most cases, these tests boil down to detecting intersections between simple geometric entities, such as spheres, boxes aligned with the coordinate axes, or polygons and segments. The computational cost of a collision detection algorithm depends not only on the complexity of the basic interference test used, but also on the ...

solid models

In a geometric context, a collision or proximity query reports information about the relative configuration or placement of two objects. Some of the common examples of such queries include checking whether two objects overlap in space, or whether their boundaries intersect, or computing the minimum Euclidean separation distance between their boundaries. Hundreds of papers have been published on di#erent aspects of these queries in computational geometry and related areas such as robotics, computer graphics, virtual environments, and computer-aided design. These queries arise in di#erent applications including robot motion planning, dynamic simulation, haptic rendering, virtual prototyping, interactive walkthroughs, computer gaming, and molecular modeling. For example, a large-scale virtual environment, e.g., a walkthrough, creates a model of the environment with virtual objects. Such an environment is used to give the user a sense of presence in a synthetic world and it s

In this paper we present a framework for minimum distance computations that allows efficient solution of minimum distance queries on a variety of surface representations, including sculptured surfaces. The framework depends on geometric reasoning rather than numerical methods and can be implemented straightforwardly. We demonstrate performance that compares favorably to other polygonal methods and is faster than reported results for other methods on sculptured surfaces. 1 Introduction We introduce a framework for minimum distance calculations that applies well to both polygonal and parametric model representations (Figure 1). The resulting methods scale well with problem size, have time-critical properties, and are interactive for large polygonal models and sculptured surfaces. In robotics, minimum distance queries have been used in path planning [2], path modification [25], and collision avoidance [15]. In computer graphics, minimum distance computations have played roles in physical...

This paper discusses a new approach to dynamic simulation called impulse-based simulation. We have focused on the twin goals of physical accuracy and computational efficiency. Our simulator can accurately model complex dynamic systems in real time. The organization of this paper is as follows. Section 2 gives an overview of the impulse-based method for dynamic simulation, highlighting its differences from and advantages over more traditional constraint-based methods. Section 3 describes collision check scheduling, and how this standard bottleneck in dynamic simulation can be streamlined. Section 4 discusses our method of resolving collisions between bodies. We treat collisions in a fully general manner, accounting for friction as well as non-perfectly elastic behavior. Correctly computing collision impulses is critical for achieving physically accurate simulations. Finally, section 5 describes some of the simulations wehave performed with our simulator, illustrating the speed and accuracy of the approach, and mentions some future work