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64
OBBTree: A hierarchical structure for rapid interference detection
 Proc. ACM SIGGRAPH, 171–180
, 1996
"... {gottscha,lin,manocha}©cs. unc.edu 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 mode ..."
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Cited by 671 (43 self)
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{gottscha,lin,manocha}©cs. unc.edu 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 232 (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
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 98 (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
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 87 (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 ...
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 78 (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].
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 53 (14 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
Spherical shell: A higher order bounding volume for fast proximity queries
 In Proc. of Third International Workshop on Algorithmic Foundations of Robotics
"... Hierarchical data structures have been widely used to design e cient algorithms for interference detection for robot motion planning and physicallybased modeling applications. Most of the hierarchies involve use of bounding volumes which enclose the underlying geometry. These bounding volumes are u ..."
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Cited by 46 (8 self)
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Hierarchical data structures have been widely used to design e cient algorithms for interference detection for robot motion planning and physicallybased modeling applications. Most of the hierarchies involve use of bounding volumes which enclose the underlying geometry. These bounding volumes are used to test for interference orcompute distance bounds between the underlying geometry. The e ciency of a hierarchy is directly proportional to the choice ofabounding volume. In this paper, we introduce spherical shells, a higher order bounding volume for fast proximity queries. Each shell corresponds to a portion of the volume between two concentric spheres. We present algorithms to compute tight tting shells and fast overlap between two shells. Moreover, we show that spherical shells provide local cubic convergence to the underlying geometry. As aresult, in many cases they provide faster algorithms for interference detection and distance computation as compared toearlier methods. We also describe an implementation and compare it with other hierarchies. 1
The PrioritizedLayered Projection Algorithm for Visible Set Estimation
 IEEE Trans. on Visualization & Computer Graphics
"... ..."
BOXTREE: A Hierarchical Representation for Surfaces in 3D
, 1996
"... We introduce the boxtree, a versatile data structure for representing triangulated or meshed surfaces in 3D. A boxtree is a hierarchical structure of nested boxes that supports efficient ray tracing and collision detection. It is simple and robust, and requires minimal space. In situations where sto ..."
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Cited by 43 (7 self)
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We introduce the boxtree, a versatile data structure for representing triangulated or meshed surfaces in 3D. A boxtree is a hierarchical structure of nested boxes that supports efficient ray tracing and collision detection. It is simple and robust, and requires minimal space. In situations where storage is at a premium, boxtrees are effective alternatives to octrees and BSP trees. They are also more flexible and efficient than Rtrees, and nearly as simple to implement. Keywords: collision detection, hierarchical data structures, ray shooting. 1. Introduction In 1981 Ballard 1 presented a simple data structure for representing digitized curves by means of nested strips. This work is an attempt to generalize his strip tree structure to the case of surfaces in 3D. As is well known, curves can seem quite tame when compared to surfaces. For example, collision detection in 3D is orders of magnitude more difficult than in 2D. Expectedly, generalizing a strip tree into a boxtree raises a ...