## Rapid Collision Detection by Dynamically Aligned DOP-Trees (1998)

Venue: | In Proc. of IEEE Virtual Reality Annual International Symposium; VRAIS ’98 |

Citations: | 63 - 20 self |

### BibTeX

@INPROCEEDINGS{Zachmann98rapidcollision,

author = {Gabriel Zachmann},

title = {Rapid Collision Detection by Dynamically Aligned DOP-Trees},

booktitle = {In Proc. of IEEE Virtual Reality Annual International Symposium; VRAIS ’98},

year = {1998},

pages = {90--97}

}

### Years of Citing Articles

### OpenURL

### Abstract

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.

### Citations

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Citation Context ...onhierarchical approaches have been taken as well. GarciaAlonso et al. [7] partition the set of polygons of an object by a uniform grid. Sphere trees were developed by [13, 14, 19]. Gottschalk et al. =-=[11]-=- developed a bounding box hierarchy based on oriented boxes (OBBs). Its box overlap test is much more expensive than for DOPs. Aligned Box-Trees have been presented in [21]. Barequet et al. [1] presen... |

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Citation Context ...mall [1]. ffl The tree should be balanced in terms of polygon counts. ffl The volume of overlap of two siblings should be small. Our construction of DOP-Trees can be contrasted to "insertion"=-=; methods [9, 2] and "bottom-up-=-" methods [1]. We proceed in a "top-down" fashion starting with the complete set of polygons, splitting the set at each node. For our application it is very important, that the construc... |

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Citation Context ...ions for path-planning in robotics (see [6], for example). For collision avoidance, Shaffer et al. [4] have used an octree to approximate objects. Good results have been achieved for convex polyhedra =-=[16, 3, 8]-=-. Almost all approaches for general, non-convex objects utilize some sort of BV hierarchy. A few nonhierarchical approaches have been taken as well. GarciaAlonso et al. [7] partition the set of polygo... |

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Citation Context ...me sort of BV hierarchy. A few nonhierarchical approaches have been taken as well. GarciaAlonso et al. [7] partition the set of polygons of an object by a uniform grid. Sphere trees were developed by =-=[13, 14, 19]-=-. Gottschalk et al. [11] developed a bounding box hierarchy based on oriented boxes (OBBs). Its box overlap test is much more expensive than for DOPs. Aligned Box-Trees have been presented in [21]. Ba... |

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Citation Context ...case. However, most of them are restricted to static environments and many of them have not been implemented. Configuration space has been used to detect collisions for path-planning in robotics (see =-=[6]-=-, for example). For collision avoidance, Shaffer et al. [4] have used an octree to approximate objects. Good results have been achieved for convex polyhedra [16, 3, 8]. Almost all approaches for gener... |

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Citation Context ...mall [1]. ffl The tree should be balanced in terms of polygon counts. ffl The volume of overlap of two siblings should be small. Our construction of DOP-Trees can be contrasted to "insertion"=-=; methods [9, 2] and "bottom-up-=-" methods [1]. We proceed in a "top-down" fashion starting with the complete set of polygons, splitting the set at each node. For our application it is very important, that the construc... |

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Citation Context ...f an overlap test of BVs. Our algorithm is more biased towards optimizing (2). However, the bias can be shifted to (1) by making them arbitrarily tight. Our approach is based on the BVs introduced by =-=[15]-=-. They have been named discrete orientation polytopes (DOPs) by [12]. For each object, we build a hierarchy of DOPs (DOP-Tree), each leave of which encloses a single polygon of the object. In order to... |

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Citation Context ...tion problem have been extensively studied in the literature. Computational geometry first focused on the construction of the intersection of two polyhedra [18, 17] and later on the detection problem =-=[5, 20]-=-. The algorithms are very efficient in the asymptotical worst-case. However, most of them are restricted to static environments and many of them have not been implemented. Configuration space has been... |

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Citation Context ...f intersection (a witness) in order to take reasonable steps. Fast collision detection of moving non-convex polygonal objects seems to be a "hard" problem because of its immanent "all-p=-=airs weakness" [13]-=-. Several bounding volume (BV) hierarchies have been developed to overcome this problem in order to find quickly a pair of intersecting polygons, or to reject pairs of polygons which cannot intersect ... |

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Citation Context ...elated work Interference and collision detection problem have been extensively studied in the literature. Computational geometry first focused on the construction of the intersection of two polyhedra =-=[18, 17]-=- and later on the detection problem [5, 20]. The algorithms are very efficient in the asymptotical worst-case. However, most of them are restricted to static environments and many of them have not bee... |

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Citation Context ...me sort of BV hierarchy. A few nonhierarchical approaches have been taken as well. GarciaAlonso et al. [7] partition the set of polygons of an object by a uniform grid. Sphere trees were developed by =-=[13, 14, 19]-=-. Gottschalk et al. [11] developed a bounding box hierarchy based on oriented boxes (OBBs). Its box overlap test is much more expensive than for DOPs. Aligned Box-Trees have been presented in [21]. Ba... |

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Citation Context ...for convex polyhedra [16, 3, 8]. Almost all approaches for general, non-convex objects utilize some sort of BV hierarchy. A few nonhierarchical approaches have been taken as well. GarciaAlonso et al. =-=[7]-=- partition the set of polygons of an object by a uniform grid. Sphere trees were developed by [13, 14, 19]. Gottschalk et al. [11] developed a bounding box hierarchy based on oriented boxes (OBBs). It... |

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Citation Context ...t al. [11] developed a bounding box hierarchy based on oriented boxes (OBBs). Its box overlap test is much more expensive than for DOPs. Aligned Box-Trees have been presented in [21]. Barequet et al. =-=[1]-=- presented some theoretical results on a class of BV hierarchies called BOXTREE, too. DOP-trees have been used for collision detection before by [12]. However, they seem to use more general DOPs and d... |

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Citation Context ...ions for path-planning in robotics (see [6], for example). For collision avoidance, Shaffer et al. [4] have used an octree to approximate objects. Good results have been achieved for convex polyhedra =-=[16, 3, 8]-=-. Almost all approaches for general, non-convex objects utilize some sort of BV hierarchy. A few nonhierarchical approaches have been taken as well. GarciaAlonso et al. [7] partition the set of polygo... |

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Citation Context ...izing (2). However, the bias can be shifted to (1) by making them arbitrarily tight. Our approach is based on the BVs introduced by [15]. They have been named discrete orientation polytopes (DOPs) by =-=[12]. For-=- each object, we build a hierarchy of DOPs (DOP-Tree), each leave of which encloses a single polygon of the object. In order to quickly determine ether two DOPs overlap, one of them has to be "re... |

19 |
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Citation Context ...nments and many of them have not been implemented. Configuration space has been used to detect collisions for path-planning in robotics (see [6], for example). For collision avoidance, Shaffer et al. =-=[4]-=- have used an octree to approximate objects. Good results have been achieved for convex polyhedra [16, 3, 8]. Almost all approaches for general, non-convex objects utilize some sort of BV hierarchy. A... |

15 |
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Citation Context ... 14, 19]. Gottschalk et al. [11] developed a bounding box hierarchy based on oriented boxes (OBBs). Its box overlap test is much more expensive than for DOPs. Aligned Box-Trees have been presented in =-=[21]-=-. Barequet et al. [1] presented some theoretical results on a class of BV hierarchies called BOXTREE, too. DOP-trees have been used for collision detection before by [12]. However, they seem to use mo... |

11 | Efficient Contact Determination between Geometric Models
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Citation Context ...ions for path-planning in robotics (see [6], for example). For collision avoidance, Shaffer et al. [4] have used an octree to approximate objects. Good results have been achieved for convex polyhedra =-=[16, 3, 8]-=-. Almost all approaches for general, non-convex objects utilize some sort of BV hierarchy. A few nonhierarchical approaches have been taken as well. GarciaAlonso et al. [7] partition the set of polygo... |

11 |
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Citation Context ...elated work Interference and collision detection problem have been extensively studied in the literature. Computational geometry first focused on the construction of the intersection of two polyhedra =-=[18, 17]-=- and later on the detection problem [5, 20]. The algorithms are very efficient in the asymptotical worst-case. However, most of them are restricted to static environments and many of them have not bee... |

10 |
On the detection of a common intersection of k convex polyhedra
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(Show Context)
Citation Context ...tion problem have been extensively studied in the literature. Computational geometry first focused on the construction of the intersection of two polyhedra [18, 17] and later on the detection problem =-=[5, 20]-=-. The algorithms are very efficient in the asymptotical worst-case. However, most of them are restricted to static environments and many of them have not been implemented. Configuration space has been... |

1 |
Rapid library. http://www.cs.unc.edu/ geom/OBB/- OBBT.html, Vers
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(Show Context)
Citation Context ...es. 5.2 Comparison of DOP-Trees and OBB-Trees Since there is no significant advantage in 14-DOPs over 6DOPs, we used 6-DOPs to compare DOP-Trees with OBBTrees. For OBB-Trees, the Rapid implementation =-=[10]-=- has been used. Figures 7 and 8 show the results of the benchmark for DOP-Trees and OBB-Trees. Table 4 summarizes the results for several other objects. All timings include the time to transform the (... |

1 |
On the detection of a common intersection ofk convex polyhedra
- Reichling
- 1988
(Show Context)
Citation Context ...tion problem have been extensively studied in the literature. Computational geometry first focused on the construction of the intersection of two polyhedra [18, 17] and later on the detection problem =-=[5, 20]-=-. The algorithms are very efficient in the asymptotical worst-case. However, most of them are restricted to static environments and many of them have not been implemented. Configuration space has been... |