## Fast Proximity Queries with Swept Sphere Volumes (1999)

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Citations: | 105 - 20 self |

### BibTeX

@TECHREPORT{Larsen99fastproximity,

author = {Eric Larsen and Stefan Gottschalk and Ming C. Lin and Dinesh Manocha},

title = {Fast Proximity Queries with Swept Sphere Volumes},

institution = {},

year = {1999}

}

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### Abstract

: 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 fit 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 ...

### Citations

4178 |
Pattern Classification and Scene Analysis
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- 1973
(Show Context)
Citation Context ...g volumes. Our approach is based on first and second order statistics summarizing the vertex coordinates, as used by [GLM96, BCG + 96]. They are the mean, , and the covariance matrix, C, respectively =-=[DH73]-=-. Let the vertices of the i'th triangle be the points a i , b i , and c i , then the mean and covariance matrix can be expressed in vector notation as:s= 1 3n n X i=0 (a i + b i + c i ); C jk = 1 3n n... |

1067 | The Râˆ—-Tree: an efficient and robust access method for points and rectangles - Beckmann, Kriegel, et al. - 1990 |

718 | OBBTree: A Hierarchical Structure for Rapid Interference Detection
- Gottschalk, Lin, et al.
- 1996
(Show Context)
Citation Context ...Tightness of Fit: Different BVs provide a varying tightness of fit to the underlying geometry. The RSS is the tightest BV among them. The pruning power of RSS's is similar to that of OBBs proposed in =-=[GLM96]-=-. As a result, they provide local quadratic convergence to the underlying geometry. PSS has a linear convergence to the underlying geometry. The pruning power of LSS lies somewhere between that of a P... |

298 | A fast procedure for computing the distance between complex objects in three-dimensional space
- Gilbert, Johnson, et al.
- 1988
(Show Context)
Citation Context ...elerate ray-tracing. Check out Arvo and Kirk [AK89] for a survey. 2.3 Distance Computation Given two convex polytopes, algorithms to compute distance between them have been proposed by Gilbert et al. =-=[GJK88]-=-, Lin and Canny [LC91], Cameron [Cam97], and Mirtich [Mir98]. The last three algorithms are incremental and exploit coherence between successive queries. Hamlin et al. [HKT92] present distance computa... |

271 |
Pattern Classi cation and Scene Analysis
- Duda, Hart
- 1973
(Show Context)
Citation Context ...ing volumes. Our approach is based on rst and second order statistics summarizing the vertex coordinates, as used by [GLM96, BCG + 96]. They are the mean, , and the covariance matrix, C, respectively =-=[DH73]-=-. Let the vertices of the i'th triangle be the points a i , b i , and c i , then the mean and covariance matrix can be expressed in vector notation as: Cjk = 1 3n nX i=0 = 1 3n nX i=0 (a i + b i + c i... |

250 | Efficient collision detection using bounding volume hierarchies of kDOPs - KLOSOWSKI, HELD, et al. - 1998 |

205 | Efficient distance computation between non-convex objects. Robotics and Automation
- Quinlan
- 1994
(Show Context)
Citation Context ...distance computation between a pair of spherically-extended polytopes (S-topes). The S-topes closely resemble the bounding volume shapes described in this paper. For general polygonal models, Quinlan =-=[Qui94]-=- proposed an algorithm using BVHs of spheres and also used them to compute approximate distance. Johnson and Cohen [JC98] used BVHs composed of oriented bounding boxes and also presented techniques to... |

189 |
Small-dimensional linear programming and convex hulls made easy
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- 1991
(Show Context)
Citation Context ...ficient algorithms for collision detection and distance computation have been proposed by researchers in computational geometry. These include DobkinKirkpatrick hierarchies [DK82], linear programming =-=[Sei90]-=- and algorithms for intersecting convex polytopes [Cha89]. 2.2 Hierarchical Data Structures Hierarchical data structures, such as hierarchical spatial partitions and BVHs have been widely used to desi... |

186 | Smallest Enclosing Disks (Balls and Ellipsoids
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- 1991
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Citation Context ...encloses the underlying geometry. We compute different BVs as: PSS: A number of efficient algorithms are known in computational geometry for computing the minimum enclosing sphere for a set of points =-=[Wel91]-=-. LSS: We use the largest dimension of the OBB as the central axis of the LSS. All the triangle vertices are projected onto a plane perpendicular to this axis, and a circle is computed that contains a... |

184 | V-Clip: fast and robust polyhedral collision detection
- Mirtich
- 1998
(Show Context)
Citation Context ...rvey. 2.3 Distance Computation Given two convex polytopes, algorithms to compute distance between them have been proposed by Gilbert et al. [GJK88], Lin and Canny [LC91], Cameron [Cam97], and Mirtich =-=[Mir98]-=-. The last three algorithms are incremental and exploit coherence between successive queries. Hamlin et al. [HKT92] present distance computation between a pair of spherically-extended polytopes (S-top... |

174 | On finding narrow passages with probabilistic roadmap planners - Hsu, Kavraki, et al. - 1998 |

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125 | Enhancing GJK: computing minimum and penetration distances between convex polyhedra. Robotics and Automation
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Citation Context ... Kirk [AK89] for a survey. 2.3 Distance Computation Given two convex polytopes, algorithms to compute distance between them have been proposed by Gilbert et al. [GJK88], Lin and Canny [LC91], Cameron =-=[Cam97]-=-, and Mirtich [Mir98]. The last three algorithms are incremental and exploit coherence between successive queries. Hamlin et al. [HKT92] present distance computation between a pair of spherically-exte... |

88 | Interactive collision detection
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(Show Context)
Citation Context ... using the rectangle, its center, and a radius. The idea of using any one of these shapes in proximity queries is not novel. For examples, spheres or PSS have been widely used for collision detection =-=[Hub93]-=- and distance computation [Qui94]. The LSS closely resembles a cylinder and many researchers have proposed using cylinders for proximity queries. Xiao and Zhang [XZ96] highlight all the 9 Figure 1: A ... |

88 |
Efficient algorithms for incremental distance computation
- Lin, Canny
- 1991
(Show Context)
Citation Context ...eck out Arvo and Kirk [AK89] for a survey. 2.3 Distance Computation Given two convex polytopes, algorithms to compute distance between them have been proposed by Gilbert et al. [GJK88], Lin and Canny =-=[LC91]-=-, Cameron [Cam97], and Mirtich [Mir98]. The last three algorithms are incremental and exploit coherence between successive queries. Hamlin et al. [HKT92] present distance computation between a pair of... |

81 |
Fast detection of polyhedral intersection
- Kirkpatrick
- 1983
(Show Context)
Citation Context ...etry Many asymptotically efficient algorithms for collision detection and distance computation have been proposed by researchers in computational geometry. These include DobkinKirkpatrick hierarchies =-=[DK82]-=-, linear programming [Sei90] and algorithms for intersecting convex polytopes [Cha89]. 2.2 Hierarchical Data Structures Hierarchical data structures, such as hierarchical spatial partitions and BVHs h... |

76 | V-COLLIDE: Accelerated Collision Detection for VRML - Hudson, Lin, et al. - 1997 |

69 | Evaluation of collision detection methods for virtual reality fly-throughs - Held, Klosowski, et al. - 1995 |

67 | A framework for efficient minimum distance computations
- Johnson, Cohen
- 1998
(Show Context)
Citation Context ... volume shapes described in this paper. For general polygonal models, Quinlan [Qui94] proposed an algorithm using BVHs of spheres and also used them to compute approximate distance. Johnson and Cohen =-=[JC98]-=- used BVHs composed of oriented bounding boxes and also presented techniques to compute distance between NURBS primitives. For parametric or implicit surfaces whose motion can be expressed as a closed... |

67 | der Stappen. Range searching and point location among fat objects - Overmars, van - 1996 |

67 | Interval methods for multi-point collisions between time dependent curved surfaces - Snyder - 1993 |

66 |
A survey of ray tracing acceleration techniques
- Arvo, Kirk
- 1989
(Show Context)
Citation Context ...ds [Cam91], spherical shells [KPLM98], and k-DOPs [HKM96, KHM + 98]. There is also literature on the use of spatial partitioning structures and BVHs to accelerate ray-tracing. Check out Arvo and Kirk =-=[AK89]-=- for a survey. 2.3 Distance Computation Given two convex polytopes, algorithms to compute distance between them have been proposed by Gilbert et al. [GJK88], Lin and Canny [LC91], Cameron [Cam97], and... |

65 | An optimal algorithm for intersecting three-dimensional convex polyhedra
- Chazelle
- 1992
(Show Context)
Citation Context ...omputation have been proposed by researchers in computational geometry. These include DobkinKirkpatrick hierarchies [DK82], linear programming [Sei90] and algorithms for intersecting convex polytopes =-=[Cha89]-=-. 2.2 Hierarchical Data Structures Hierarchical data structures, such as hierarchical spatial partitions and BVHs have been widely used to design efficient algorithms. Typical hierarchies include k-d ... |

64 | Solving the collision detection problem - Garica-Alonso, Flaquer - 1994 |

47 | Spherical shell: a higher order bounding volume for fast proximity queries
- Krishnan, Pattekar, et al.
- 1998
(Show Context)
Citation Context ... for BVHs include spheres [Hub93, Qui94], axis-aligned bounding boxes [BKSS90, HKM95], oriented bounding boxes [GLM96, BCG + 96], approximation hierarchies based on S-bounds [Cam91], spherical shells =-=[KPLM98]-=-, and k-DOPs [HKM96, KHM + 98]. There is also literature on the use of spatial partitioning structures and BVHs to accelerate ray-tracing. Check out Arvo and Kirk [AK89] for a survey. 2.3 Distance Com... |

43 | BOXTREE: A hierarchical representation for surfaces in 3D - Barequet, Chazelle, et al. - 1996 |

41 | The R*-tree: An e cient and robust access method for points and rectangles - Beckmann, Kriegel, et al. |

33 | Analysis of a Bounding Box Heuristic for Object Intersection - Zhou - 1999 |

31 | Fast collision detection among multiple moving spheres - Kim, Guibas, et al. - 1998 |

29 |
Approximation hierarchies and s-bounds
- Cameron
- 1991
(Show Context)
Citation Context ...94, Hub93]. The set of BVs for BVHs include spheres [Hub93, Qui94], axis-aligned bounding boxes [BKSS90, HKM95], oriented bounding boxes [GLM96, BCG + 96], approximation hierarchies based on S-bounds =-=[Cam91]-=-, spherical shells [KPLM98], and k-DOPs [HKM96, KHM + 98]. There is also literature on the use of spatial partitioning structures and BVHs to accelerate ray-tracing. Check out Arvo and Kirk [AK89] for... |

28 | Collision detection and analysis in a physically based simulation
- Bouma, Vanecek
- 1991
(Show Context)
Citation Context ...been widely used to design efficient algorithms. Typical hierarchies include k-d trees and octrees, R-trees and their variants, cone trees, BSPs [NAT90] and their extensions to multi-space partitions =-=[WG91]-=-, and spatial representations based on space-time bounds or four-dimensional tests [AANJ94, Hub93]. The set of BVs for BVHs include spheres [Hub93, Qui94], axis-aligned bounding boxes [BKSS90, HKM95],... |

23 | Real-time collision detection for motion simulation within complex environments - Held, Klosowski, et al. - 1996 |

18 |
Merging bsp trees yield polyhedral modeling results
- Naylor, Amanatides, et al.
- 1990
(Show Context)
Citation Context ... such as hierarchical spatial partitions and BVHs have been widely used to design efficient algorithms. Typical hierarchies include k-d trees and octrees, R-trees and their variants, cone trees, BSPs =-=[NAT90]-=- and their extensions to multi-space partitions [WG91], and spatial representations based on space-time bounds or four-dimensional tests [AANJ94, Hub93]. The set of BVs for BVHs include spheres [Hub93... |

18 | Curved surfaces and coherence for non-penetrating rigid body simulation - Bara - 1990 |

14 | Towards obtaining all possible contacts â€” Growing a polyhedron by its location uncertainty
- Xiao, Zhang
- 1996
(Show Context)
Citation Context ...ly used for collision detection [Hub93] and distance computation [Qui94]. The LSS closely resembles a cylinder and many researchers have proposed using cylinders for proximity queries. Xiao and Zhang =-=[XZ96]-=- highlight all the 9 Figure 1: A rendering of different swept-sphere volumes; a sphere is on the left, a line swept sphere in the center, and a rectangle swept sphere on the right. three shapes in des... |

10 |
Efficient distance calculation using the spherically-extended polytope (s-tope) model
- Hamlin, Kelley, et al.
- 1992
(Show Context)
Citation Context ...oposed by Gilbert et al. [GJK88], Lin and Canny [LC91], Cameron [Cam97], and Mirtich [Mir98]. The last three algorithms are incremental and exploit coherence between successive queries. Hamlin et al. =-=[HKT92]-=- present distance computation between a pair of spherically-extended polytopes (S-topes). The S-topes closely resemble the bounding volume shapes described in this paper. For general polygonal models,... |

7 | Interval methods for multi-point collisions between time dependent curved surfaces - al - 1993 |

4 | Real-time collision detection for haptic interaction using a 3-dof force feedback device - Gregory, Lin, et al. - 1998 |

3 |
A framework for e cient minimum distance computation
- Johnson, Cohen
- 1998
(Show Context)
Citation Context ... volume shapes described in this paper. For general polygonal models, Quinlan [Qui94] proposed an algorithm using BVHs of spheres and also used them to compute approximate distance. Johnson and Cohen =-=[JC98]-=- used BVHs composed of oriented bounding boxes and also presented techniques to compute distance between NURBS primitives. For parametric or implicit surfaces whose motion can be expressed as a closed... |

2 |
Interference Detection System. http://www.win.tue.nl/cs/tt/gino/solid
- SOLID
- 1997
(Show Context)
Citation Context ...istance between them. 6 2.4 Hybrid Combinations Several researchers have proposed hybrid combinations to accelerate proximity queries. Some of the public domain collision detection systems like SOLID =-=[Sys97]-=- and V-COLLIDE [HLC + 97] make use of AABBs for N-body tests and a combination of AABBs or OBBs for pairwise primitive tests. Recently, Gregory et al. and Kim et al. [GLGT98, KGS98] used combinations ... |