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322
OBBTree: A hierarchical structure for rapid interference detection
 PROC. ACM SIGGRAPH, 171–180
, 1996
"... We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal and curved models. It precomputes a hierarchical representation of models using tightfitting oriented bo ..."
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Cited by 847 (53 self)
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We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal and curved models. It precomputes a hierarchical representation of models using tightfitting oriented bounding box trees. At runtime, the algorithm traverses the tree and tests for overlaps between oriented bounding boxes based on a new separating axis theorem, which takes less than 200 operations in practice. It has been implemented and we compare its performance with other hierarchical data structures. In particular, it can accurately detect all the contacts between large complex geometries composed of hundreds of thousands of polygons at interactive rates, almost one order of magnitude faster than earlier methods.
Efficient collision detection using bounding volume hierarchies of kdops
 IEEE Transactions on Visualization and Computer Graphics
, 1998
"... 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 ..."
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Cited by 291 (4 self)
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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 realtime rates. Applications such as haptic forcefeedback can require over 1,000 collision queries per second. In this paper, we develop and analyze a method, based on boundingvolume hierarchies, for efficient collision detection for objects moving within highly complex environments. Our choice of bounding volume is to use a “discrete orientation polytope” (“kdop”), 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 (“BVtrees”) of bounding kdops. Further, we propose algorithms for maintaining an effective BVtree of kdops for moving objects, as they rotate, and for performing fast collision detection using BVtrees 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
Approximating Polyhedra with Spheres for TimeCritical Collision Detection
 ACM Transactions on Graphics
, 1996
"... This paper presents a method for approximating polyhedral objects to support a timecritical collisiondetection algorithm. The approximations are hierarchies of spheres, and they allow the timecritical algorithm to progressively refine the accuracy of its detection, stopping as needed to maintain ..."
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Cited by 211 (1 self)
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This paper presents a method for approximating polyhedral objects to support a timecritical collisiondetection algorithm. The approximations are hierarchies of spheres, and they allow the timecritical algorithm to progressively refine the accuracy of its detection, stopping as needed to maintain the realtime performance essential for interactive applications. The key to this approach is a preprocess that automatically builds tightly fitting hierarchies for rigid and articulated objects. The preprocess uses medialaxis surfaces, which are skeletal representations of objects. These skeletons guide an optimization technique that gives the hierarchies accuracy properties appropriate for collision detection. In a sample application, hierarchies built this way allow the timecritical collisiondetection algorithm to have acceptable accuracy, improving significantly on that possible with hierarchies built by previous techniques. The performance of the timecritical algorithm in this appli...
Collision Detection for Interactive Graphics Applications,”
 IEEE Trans. Vis. Comput. Graph.
, 1995
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Six DegreeofFreedom Haptic Rendering Using Voxel Sampling
 Proc. ACM Siggraph, ACM
, 1999
"... A simple, fast, and approximate voxelbased approach to 6DOF haptic rendering is presented. It can reliably sustain a 1000 Hz haptic refresh rate without resorting to asynchronous physics and haptic rendering loops. It enables the manipulation of a modestly complex rigid object within an arbitraril ..."
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Cited by 172 (1 self)
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A simple, fast, and approximate voxelbased approach to 6DOF haptic rendering is presented. It can reliably sustain a 1000 Hz haptic refresh rate without resorting to asynchronous physics and haptic rendering loops. It enables the manipulation of a modestly complex rigid object within an arbitrarily complex environment of static rigid objects. It renders a shortrange force field surrounding the static objects, which repels the manipulated object and strives to maintain a voxelscale minimum separation distance that is known to preclude exact surface interpenetration. Force discontinuities arising from the use of a simple penalty force model are mitigated by a dynamic simulation based on virtual coupling. A generalization of octree improves voxel memory efficiency. In a preliminary implementation, a commercially available 6DOF haptic prototype device is driven at a constant 1000 Hz haptic refresh rate from one dedicated haptic processor, with a separate processor for graphics. This system yields stable and convincing force feedback for a wide range of user controlled motion inside a large, complex virtual environment, with very few surface interpenetration events. This level of performance appears suited to applications such as certain maintenance and assembly task simulations that can tolerate voxelscale minimum separation distances.
3D Collision Detection: A Survey
 Computers and Graphics
, 2000
"... Many applications in Computer Graphics require fast and robust 3D collision detection algorithms. These algorithms can be grouped into four approaches: spacetime volume intersection, swept volume interference, multiple interference detection and trajectory parameterization. While some approaches ar ..."
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Cited by 128 (4 self)
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Many applications in Computer Graphics require fast and robust 3D collision detection algorithms. These algorithms can be grouped into four approaches: spacetime volume intersection, swept volume interference, multiple interference detection and trajectory parameterization. While some approaches are linked to a particular object representation scheme (e.g., spacetime 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 ...
A SingleQuery BiDirectional Probabilistic Roadmap Planner with Lazy Collision Checking
, 2001
"... This paper describes a nev probabilistic roadmap (PRM) path planner that is: (1) singlequery instead of precomputing a roadmap covering the entire free space, it uses the tvo input query configurations as seeds to explore as little space as possible; (2) hidirectional it explores the robotis free ..."
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Cited by 120 (4 self)
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This paper describes a nev probabilistic roadmap (PRM) path planner that is: (1) singlequery instead of precomputing a roadmap covering the entire free space, it uses the tvo input query configurations as seeds to explore as little space as possible; (2) hidirectional it explores the robotis free space by concur rently building a roadmap made of tvo trees rooted at the query configurations; (3) adaptive it makes longer steps in opened areas of the free space and shorter steps in cluttered areas; and (4) lazy in checking collision it delays collision tests along the edges of the roadmap until they are absolutely needed. Experimental results shov that this combination of techniques drastically reduces planning times, making it possible to handle difficult problems, including multirobot problems in geometrically complex environments.