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188
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 718 (45 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 250 (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 193 (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 Deformable Objects
, 2004
"... 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 wellinvestigated, c ..."
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Cited by 93 (17 self)
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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 wellinvestigated, 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, imagespace techniques and stochastic methods are considered. Applications in cloth modeling and surgical simulation are presented.
BDTree: OutputSensitive Collision Detection for Reduced Deformable Models
 ACM Transactions on Graphics (SIGGRAPH
, 2004
"... We introduce the Bounded Deformation Tree, or BDTree, which can perform collision detection with reduced deformable models at costs comparable to collision detection with rigid objects. Reduced deformable models represent complex deformations as linear superpositions of arbitrary displacement field ..."
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Cited by 87 (11 self)
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We introduce the Bounded Deformation Tree, or BDTree, which can perform collision detection with reduced deformable models at costs comparable to collision detection with rigid objects. Reduced deformable models represent complex deformations as linear superpositions of arbitrary displacement fields, and are used in a variety of applications of interactive computer graphics. The BDTree is a bounding sphere hierarchy for outputsensitive collision detection with such models. Its bounding spheres can be updated after deformation in any order, and at a cost independent of the geometric complexity of the model; in fact the cost can be as low as one multiplication and addition per tested sphere, and at most linear in the number of reduced deformation coordinates. We show that the BDTree is also extremely simple to implement, and performs well in practice for a variety of realtime and complex offline deformable simulation examples.
Efficiently Approximating the MinimumVolume Bounding Box of a Point Set in Three Dimensions
 In Proc. 10th ACMSIAM Sympos. Discrete Algorithms
, 2001
"... We present an efficient O(n + 1/ε^4.5)time algorithm for computing a (1 + 1/ε)approximation of the minimumvolume bounding box of n points in R³. We also present a simpler algorithm (for the same purpose) whose running time is O(n log n+n/ε³). ..."
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Cited by 79 (12 self)
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We present an efficient O(n + 1/&epsilon;^4.5)time algorithm for computing a (1 + 1/&epsilon;)approximation of the minimumvolume bounding box of n points in R&sup3;. We also present a simpler algorithm (for the same purpose) whose running time is O(n log n+n/&epsilon;&sup3;). We give some experimental results with implementations of various variants of the second algorithm. The implementation of the algorithm described in this paper is available online [Har00].
Deformable free space tilings for kinetic collision detection
 International Journal of Robotics Research
, 2000
"... We present kinetic data structures for detecting collisions between a set of polygons that are not only moving continuously but whose shapes can also change continuously with time. We construct a planar subdivision of the common exterior of the polygons, called a pseudotriangulation, that certifies ..."
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Cited by 77 (13 self)
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We present kinetic data structures for detecting collisions between a set of polygons that are not only moving continuously but whose shapes can also change continuously with time. We construct a planar subdivision of the common exterior of the polygons, called a pseudotriangulation, that certifies their disjointness. We show different schemes for maintaining pseudotriangulations as a kinetic data structure, and we analyze their performance. Specifically, we first describe an algorithm for maintaining a pseudotriangulation of a point set, and show that the pseudotriangulation changes only quadratically many times if points move along algebraic arcs of constant degree. We then describe an algorithm for maintaining a pseudotriangulation of a set of convex polygons. Finally, we extend our algorithm to maintaining a pseudotriangulation of a set of simple polygons.
Rapid Collision Detection by Dynamically Aligned DOPTrees
 In Proc. of IEEE Virtual Reality Annual International Symposium; VRAIS ’98
, 1998
"... Based on a general hierarchical data structure, we present a fast algorithm for exact collision detection of arbitrary polygonal rigid objects. Objects consisting of hundreds of thousands of polygons can be checked for collision at interactive rates. ..."
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Cited by 69 (20 self)
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Based on a general hierarchical data structure, we present a fast algorithm for exact collision detection of arbitrary polygonal rigid objects. Objects consisting of hundreds of thousands of polygons can be checked for collision at interactive rates.
On Delaying Collision Checking in PRM Planning  Application To MultiRobot Coordination
 INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
, 2002
"... This paper describes the foundations and algorithms of a new probabilistic roadmap (PRM) planner that is: singlequery  instead of precomputing a roadmap covering the entire free space, it uses the two input query configurations to explore as little space as possible; bidirectional  it explo ..."
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Cited by 68 (16 self)
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This paper describes the foundations and algorithms of a new probabilistic roadmap (PRM) planner that is: singlequery  instead of precomputing a roadmap covering the entire free space, it uses the two input query configurations to explore as little space as possible; bidirectional  it explores the robot's free space by building a roadmap made of two trees rooted at the query configurations; and lazy in checking collisions  it delays collision tests along the edges of the roadmap until they are absolutely needed. Several observations motivated this strategy: (1) PRM planners spend a large fraction of their time testing connections for collision; (2) most connections in a roadmap are not on the final path; (3) the collision test for a connection is most expensive when there is no collision; and (4) any short connection between two collisionfree configurations has high prior probability of being collisionfree. The strengths of singlequery and bidirectional sampling techniques, and those of delayed collision checking reinforce each other. Experimental results