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69
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 228 (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 178 (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 Transactions on Visualization and Computer Graphics
, 1995
"... Solid objects in the real world do not pass through each other when they collide. Enforcing this property of "solidness" is important in many interactive graphics applications; for example, solidness makes virtual reality more believable, and solidness is essential for the correctness of vehicle sim ..."
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Cited by 173 (5 self)
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Solid objects in the real world do not pass through each other when they collide. Enforcing this property of "solidness" is important in many interactive graphics applications; for example, solidness makes virtual reality more believable, and solidness is essential for the correctness of vehicle simulators. These applications use a collisiondetection algorithm to enforce the solidness of objects. Unfortunately, previous collisiondetection algorithms do not adequately address the needs of interactive applications. To work in these applications, a collisiondetection algorithm must run at realtime rates, even when many objects can collide, and it must tolerate objects whose motion is specified "on the fly" by a user. This dissertation describes a new collisiondetection algorithm that meets these criteria through approximation and graceful degradation, elements of timecritical computing. The algorithm is not only fast but also interruptible, allowing an application to trade accuracy ...
Determining the Separation of Preprocessed Polyhedra  A Unified Approach
, 1990
"... We show how (now familiar) hierarchical representations of (convex) polyhedra can be used to answer various separation queries efficiently (in a number of cases, optimally). Our emphasis is i) the uniform treatment of polyhedra separation problems, ii) the use of hierarchical representations of prim ..."
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Cited by 105 (5 self)
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We show how (now familiar) hierarchical representations of (convex) polyhedra can be used to answer various separation queries efficiently (in a number of cases, optimally). Our emphasis is i) the uniform treatment of polyhedra separation problems, ii) the use of hierarchical representations of primitive objects to provide implicit representations of composite or transformed objects, and iii) applications to natural problems in graphics and robotics. Among the specific results is an O(log jP j 1 log jQj) algorithm for determining the sepa ration of polyhedra P and Q (which have been individually preprocessed in at most linear time).
Fast proximity queries with swept sphere volumes
, 1999
"... We present novel algorithms for fast proximity queries using swept sphere volumes. The set of proximity queries includes collision detection and both exact and approximate separation distance computation. We introduce a new family of bounding volumes that correspond to a core primitive shape grown ..."
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Cited by 94 (19 self)
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We present novel algorithms for fast proximity queries using swept sphere volumes. The set of proximity queries includes collision detection and both exact and approximate separation distance computation. We introduce a new family of bounding volumes that correspond to a core primitive shape grown outward by some offset. The set of core primitive shapes includes a point, line, and rectangle. This family of bounding volumes provides varying tightness of t to the underlying geometry. Furthermore, we describe efficient and accurate algorithms to perform different queries using these bounding volumes. We present a novel analysis of proximity queries that highlights the relationship between collision detection and distance computation. We also present traversal techniques for accelerating distance queries. These algorithms have been used to perform proximity queries for applications including virtual prototyping, dynamic simulation, and motion planning on complex models. As compared to earlier algorithms based on bounding volume hierarchies for separation distance and approximate distance computation, our algorithms have
OutputSensitive Results on Convex Hulls, Extreme Points, and Related Problems
, 1996
"... . We use known data structures for rayshooting and linearprogramming queries to derive new outputsensitive results on convex hulls, extreme points, and related problems. We show that the f face convex hull of an npoint set P in a fixed dimension d # 2 can be constructed in O(n log f + (nf) ..."
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Cited by 65 (13 self)
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. We use known data structures for rayshooting and linearprogramming queries to derive new outputsensitive results on convex hulls, extreme points, and related problems. We show that the f face convex hull of an npoint set P in a fixed dimension d # 2 can be constructed in O(n log f + (nf) 11/(#d/2#+1) log O(1) n) time; this is optimal if f = O(n 1/#d/2# / log K n) for some sufficiently large constant K . We also show that the h extreme points of P can be computed in O(n log O(1) h + (nh) 11/(#d/2#+1) log O(1) n) time. These results are then applied to produce an algorithm that computes the vertices of all the convex layers of P in O(n 2# ) time for any constant #<2/(#d/2# 2 + 1). Finally, we obtain improved time bounds for other problems including levels in arrangements and linear programming with few violated constraints. In all of our algorithms the input is assumed to be in general position. 1. Introduction Let P be a set of n points in ddimen...
A Randomized Parallel 3D Convex Hull Algorithm For Coarse Grained Multicomputers
 In Proc. ACM Symp. on Parallel Algorithms and Architectures
, 1995
"... We present a randomized parallel algorithm for constructing the 3D convex hull on a generic pprocessor coarse grained multicomputer with arbitrary interconection network and n=p local memory per processor, where n=p p 2+ffl (for some arbitrarily small ffl ? 0). For any given set of n points in ..."
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Cited by 50 (11 self)
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We present a randomized parallel algorithm for constructing the 3D convex hull on a generic pprocessor coarse grained multicomputer with arbitrary interconection network and n=p local memory per processor, where n=p p 2+ffl (for some arbitrarily small ffl ? 0). For any given set of n points in 3space, the algorithm computes the 3D convex hull, with high probaility, in O( n log n p ) local computation time and O(1) communication phases with at most O(n=p) data sent/received by each processor. That is, with high probability, the algorithm computes the 3D convex hull of an arbitrary point set in time O( n logn p + \Gamma n;p ), where \Gamma n;p denotes the time complexity of one communication phase. The assumption n p p 2+ffl implies a coarse grained, limited parallelism, model which is applicable to most commercially available multiprocessors. In the terminology of the BSP model, our algorithm requires, with high probability, O(1) supersteps, synchronization period L = \Th...
Computing the IntersectionDepth of Polyhedra
 Algorithmica
, 1993
"... Given two intersecting polyhedra P , Q and a direction d, find the smallest translation of Q along d that renders the interiors of P and Q disjoint. The same problem can also be posed without specifying the direction, in which case the minimum translation over all directions is sought. These are fun ..."
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Cited by 49 (2 self)
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Given two intersecting polyhedra P , Q and a direction d, find the smallest translation of Q along d that renders the interiors of P and Q disjoint. The same problem can also be posed without specifying the direction, in which case the minimum translation over all directions is sought. These are fundamental problems that arise in robotics and computer vision. We develop techniques for implicitly building and searching convolutions and apply them to derive efficient algorithms for these problems. 1 Introduction The computation of spatial relationships among geometric objects is a fundamental problem in such areas as robotics, computeraided design, VLSI layout, and computer graphics. In a dynamic environment where objects are mobile, intersection or proximity among objects has obvious applications. Consider, for instance, the problem of collision detection in robot motion planning. The Euclidean distance is a commonly used measure in these areas. Numerous efficient algorithms are known...
Intersection of Convex Objects in Two and Three Dimensions
, 1987
"... One of the basic geometric operations involves determining whether a pair of convex objects intersect. This problem is well understood in a model of computation in which the objects are given as input and their intersection is returned as output. For many applications, however, it may be assumed tha ..."
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Cited by 49 (3 self)
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One of the basic geometric operations involves determining whether a pair of convex objects intersect. This problem is well understood in a model of computation in which the objects are given as input and their intersection is returned as output. For many applications, however, it may be assumed that the objects already exist within the computer and that the only output desired is a single piece of data giving a common point if the objects intersect or reporting no intersection if they are disjoint. For this problem, none of the previous lower bounds are valid and algorithms are proposed requiring sublinear time for their solution in two and three dimensions.
Fast Distance Queries with Rectangular Swept Sphere Volumes
 Proc. of IEEE Int. Conference on Robotics and Automation
, 2000
"... : We present new distance computation algorithms using hierarchies of rectangular swept spheres. Each bounding volume of the tree is described as the Minkowski sum of a rectangle and a sphere, and fits tightly to the underlying geometry. We present accurate and efficient algorithms to build the hier ..."
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Cited by 48 (13 self)
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: We present new distance computation algorithms using hierarchies of rectangular swept spheres. Each bounding volume of the tree is described as the Minkowski sum of a rectangle and a sphere, and fits tightly to the underlying geometry. We present accurate and efficient algorithms to build the hierarchies and perform distance queries between the bounding volumes. We also present traversal techniques for accelerating distance queries using coherence and priority directed search. These algorithms have been used to perform proximity queries for applications including virtual prototyping, dynamic simulation, and motion planning on complex models. As compared to earlier algorithms based on bounding volume hierarchies for separation distance and approximate distance computation, our algorithms have achieved significant speedups on many benchmarks. 1