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94
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 845 (50 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.
ICOLLIDE: An interactive and exact collision detection system for largescale environments
 In Proc. of ACM Interactive 3D Graphics Conference
, 1995
"... We present an exact and interactive collision detection system, ICOLLIDE, for largescale environments. Such environments are characterized by the number of objects undergoing rigid motion and the complexity of the models. The algorithm does not assume the objects ’ motions can be expressed as a c ..."
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Cited by 323 (25 self)
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We present an exact and interactive collision detection system, ICOLLIDE, for largescale environments. Such environments are characterized by the number of objects undergoing rigid motion and the complexity of the models. 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 interfaced with a variety of applications. The algorithm uses a twolevel approach based on pruning multipleobject 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 HP9000/750. 1
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 289 (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 213 (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...
Enhancing GJK: Computing Minimum and Penetration Distances between Convex Polyhedra
 Proceedings of International Conference on Robotics and Automation
, 1997
"... The problem of tracking the distance between two convex polyhedra is finding applications in many areas of robotics, including intersection detection, collision detection, and path planning. We present new results that confirm an almostconstant time complexity for an enhanced version of Gilbert, Jo ..."
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Cited by 136 (5 self)
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The problem of tracking the distance between two convex polyhedra is finding applications in many areas of robotics, including intersection detection, collision detection, and path planning. We present new results that confirm an almostconstant time complexity for an enhanced version of Gilbert, Johnson and Keerthi's algorithm, and also describe modifications to the algorithm to compute measures of penetration distance.
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 126 (3 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 ...
Nonconvex rigid bodies with stacking
 ACM Trans. Graph
"... 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 d ..."
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Cited by 118 (12 self)
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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.
A Random Sampling Scheme for Path Planning
 INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
, 1996
"... Several randomizod path planners have been proposed during the last few years. Their attractiveness stems from their applicability to virtually any type of robots, and their empirically observed success. In this paper we attempt to present a unifying view of these planners and to theoretically expla ..."
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Cited by 103 (23 self)
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Several randomizod path planners have been proposed during the last few years. Their attractiveness stems from their applicability to virtually any type of robots, and their empirically observed success. In this paper we attempt to present a unifying view of these planners and to theoretically explain their success. First, we introduce a general planning scheme that consists of randomly sampling the robot' s configuration space. We then describe two previously developed planners as instances of planners based on this scheme, but applying very different sampling strategies. These planners are probabilistically complete: if a path exists, they will find one with high probability, if we let them run long enough. Next, for one of the planners, we analyze the relation between the probability of failure and the running time. Under assumptions characterizing the "goodness" of the robot's free space, we show that the running time only grows as the absolute value of the logarithm of the probability of failure that we are willing to tolerate. We also show that it increases at a reasonable rate as the space goodness degrades. In the last section we suggest directions for future research.
Evaluation of Collision Detection Methods for Virtual Reality FlyThroughs
 In Canadian Conference on Computational Geometry
, 1995
"... We consider the problem of preprocessing a scene of polyhedral models in order to perform collision detection very efficiently for an object that moves amongst obstacles. This problem is of central importance in virtual reality applications, where it is necessary to check for collisions at realtime ..."
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Cited by 78 (7 self)
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We consider the problem of preprocessing a scene of polyhedral models in order to perform collision detection very efficiently for an object that moves amongst obstacles. This problem is of central importance in virtual reality applications, where it is necessary to check for collisions at realtime rates. We give an algorithm for collision detection that is based on the use of a mesh (tetrahedralization) of the free space that has (hopefully) low stabbing number. The algorithm has been implemented and tested, and we give experimental results comparing its performance against three other algorithms that we implemented, based on standard data structures. A preliminary version of this paper appeared in the proceedings of the 7 th Canad. Conf. Computat. Geometry, Qu'ebec, Aug 1013, 1995. y held@ams.sunysb.edu; Supported by NSF Grant DMS9312098. On sabbatical leave from Universitat Salzburg, Salzburg, Austria. z jklosow@ams.sunysb.edu; Supported by NSF grants ECSE8857642 and C...