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

We present a scheme for exact collision detection between complex models undergoing rigid motion and deformation. The scheme relies on a hierarchical model representation using axis-aligned bounding boxes (AABBs). In recent work, AABB trees have been shown to be slower than oriented bounding box (OBB) trees. In this paper, we describe a way to speed up overlap tests between AABBs, such that for collision detection of rigid models, the difference in performance between the two representations is greatly reduced. Furthermore, we show how to quickly update an AABB tree as a model is deformed. We thus find AABB trees to be the method of choice for collision detection of complex models undergoing deformation. In fact, because they are not much slower to test, are faster to build, and use less storage than OBB trees, AABB trees might be a reasonable choice for rigid models as well. Keywords: computer animation, collision detection, hierarchical data structures, deformable model...

The power crust is a construction which takes a sample of points from the surface of a three-dimensional object and produces a surface mesh and an approximate medial axis. The approach is to first approximate the medial axis transform (MAT) of the object. We then use an inverse transform to produce the surface representation from the MAT.

The medial axis transform (or MAT) is a representation of an object as an infinite union of balls. We consider approximating the MAT of a three-dimensional object, and its complement, with a finite union of balls. Using this approximate MAT we define a new piecewise-linear approximation to the object surface, which we call the power crust. We assume that we are given as input a suficiently dense sample of points from the object surface. We select a subset of the Voronoi balls of the sample, the polar balls, as the union of balls representation. We bound the geometric error of the union, and of the corresponding power crust, and show that both representations are topologically correct as well. Thus, our results provide a new algorithm for surface reconstruction from sample points. By construction, the power crust is always the boundary of a solid, so we avoid the hole-filling or manifold extraction steps used in previous algorithms. The union of balls representation and the power crust have corresponding piecewise-linear dual representations, which in some sense approximate the medial axis. We show a geometric relationship between these duals and the medial axis by proving that, as the sampling density goes to infinity, the set of poles, the centers of the polar balls, converge to the medial axis.

Similarity search is a very important operation in multimedia databases and other database applications involving complex objects, and involves finding objects in a data set S similar to a query object q, based on some similarity measure. In this article, we focus on methods for similarity search that make the general assumption that similarity is represented with a distance metric d. Existing methods for handling similarity search in this setting typically fall into one of two classes. The first directly indexes the objects based on distances (distance-based indexing), while the second is based on mapping to a vector space (mapping-based approach). The main part of this article is dedicated to a survey of distance-based indexing methods, but we also briefly outline how search occurs in mapping-based methods. We also present a general framework for performing search based on distances, and present algorithms for common types of queries that operate on an arbitrary “search hierarchy. ” These algorithms can be applied on each of the methods presented, provided a suitable search hierarchy is defined.

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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

Interactive environments for dynamically deforming objects play an important role in surgery simulation and entertainment technology. These environments require fast deformable models and very efficient collision handling techniques. While collision detection for rigid bodies is well-investigated, collision detection for deformable objects introduces additional challenging problems. This paper focusses on these aspects and summarizes recent research in the area of deformable collision detection. Various approaches based on bounding volume hierarchies, distance fields, and spatial partitioning are discussed. Further, image-space techniques and stochastic methods are considered. Applications in cloth modeling and surgical simulation are presented.

The traditional high-level algorithms for rigid body simulation work well for moderate numbers of bodies but scale poorly to systems of hundreds or more moving, interacting bodies. The problem is unnecessary synchronization implicit in these methods. Jefferson´s timewarp algorithm (Jefferson 85) is a technique for alleviating this problem in parallel discrete event simulation. Rigid body dynamics, though a continuous process, exhibits many aspects of a discrete one. With modification, the timewarp algorithm can be used in a uniprocessor rigid body simulator to give substantial performance improvements for simulations with large numbers of bodies. This paper describes the limitations of the traditional high-level simulation algorithms, introduces Jefferson´s algorithm, and extends and optimizes it for the rigid body case. It addresses issues particular to rigid body simulation, such as collision detection and contact group management, and describes how to incorporate these into the timewarp framework. Quantitative experimental results indicate that the timewarp algorithm offers significant performance improvements over traditional high-level rigid body simulation algorithms, when applied to systems with hundreds of bodies. It also helps pave the way to parallel implementations, as the paper discusses.

This paper presents a method, along with some optimizations, for computing whether or not two triangles intersect. The code, which is shown to be fast, can be used in, for example, collision detection algorithms. 1 Introduction Most collision detection algorithms, such as OBBTree [Gottschalk96], sphere hierarchies [Hubbard96] and BV-trees [Klosowski97], try to minimize the number of primitive-primitive intersections that have to be computed. Still, a fast and reliable method for computing the primitive-primitive intersection is desired. Since rendering hardware is often targeted for triangles, the primitives in collision detection algorithms are often triangles as well. This paper describes a method for determining if two triangles intersect. 2 Intersection Test Method Let us denote the two triangles # # and # # ; the vertices of # # and # # by # # # , # # # , # # # , and # # # , # # # , # # # respectively; and the planes in which the triangles lie # # and # # . Firs...