## Determining the Minimum Translational Distance between Two Convex Polyhedra (1986)

Venue: | Proceedings of International Conference on Robotics and Automation |

Citations: | 56 - 4 self |

### BibTeX

@INPROCEEDINGS{Cameron86determiningthe,

author = {S. A. Cameron and R.K. Culley},

title = {Determining the Minimum Translational Distance between Two Convex Polyhedra},

booktitle = {Proceedings of International Conference on Robotics and Automation},

year = {1986},

pages = {591--596}

}

### Years of Citing Articles

### OpenURL

### Abstract

Given two objects we define the minimal translational distance (MTD) between them to be the length of the shortest relative translation that results in the objects being in contact. MTD is equivalent to the distance between two objects if the objects are not intersecting, but MTD is also defined for intersecting objects and it then gives a measure of penetration. We show that the computation of MTD can be recast as a configuration space problem, and describe an algorithm for computing MTD for convex polyhedra.

### Citations

282 |
An algorithm for planning collision-free paths among polyhedral obstacles
- Lozano-Perez, Wesley
- 1979
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Citation Context ...pace obstacle, and it is the set of translations of A that brings it into interference with B. Configuration space has been of interest for the formulation of path planning algorithms --- for example =-=[11, 10]-=- --- and the function Con has many nice properties. In particular we can show that for any objects A and B MTD(A;B) = MTD(O;Con(A;B)) (1) where O = f 0 g is the singleton set containing the origin. To... |

135 |
Geometric modeling for computer vision
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63 |
Finding the Intersection of Two Convex Polyhedra
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- 1978
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44 |
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- 1979
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25 |
Mathematical models of rigid solid objects
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- 1977
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Citation Context ... the points then the objects do not properly overlap; that is, MTD + (A; B) = inf f ja \Gamma bj : a 2 A and b 2 B and A " (B + a \Gamma b) = ; g where " is the regularised set intersection =-=operation [15]-=-. This added complexity lead us to consider another approach to the problem. Given two objects their Minkowski difference is given by Con(A; B) = f b \Gamma a : a 2 A and b 2 B g This set is also call... |

23 |
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Citation Context ...distinguish these cases, thus: MTD(A;B) = ae +MTD + (A; B) if A intersects B \Gamma MTD + (A; B) otherwise This measure has been used to solve a collision detection problem for a robotics application =-=[7]-=-. As a simple example, if A and B are spheres of radius r A and r B , and their centres are distance d apart, then MTD(A;B) = d \Gamma r A \Gamma r B : This special case is illustrated in Fig. 1 for t... |

21 |
Modelling Solids in Motion
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8 |
A procedure for detecting intersections of three-dimensional objects
- Comba
- 1968
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Citation Context ...intersect at some given point in time. Examples include [2, 4, 12, 13, 17]. However in all of these only a Boolean value is returned, which gives no information on the 'degree' of intersection. Comba =-=[6]-=- describes a 'psuedocharacteristic' function that provides some measure of the distance between convex polyhedra; he uses this to solve an interference detection problem using a numerical minimization... |

8 |
Finding the minimum distance between two convex polygons
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- 1981
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Citation Context ...haracteristic' function that provides some measure of the distance between convex polyhedra; he uses this to solve an interference detection problem using a numerical minimization technique. Schwartz =-=[16]-=- looked at the calculation of the minimum distance between convex polygons, and Cameron [4] describes an exhaustive technique for the minimum distance between arbitrary polyhedra. Recently a couple of... |

7 |
Maitre, “Dynamic control of manipulators operating in a complex environment
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- 1978
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Citation Context ...an the one reported here, but they only return zero for intersecting objects. Interest has also been shown in the calculation of distance functions in the field of path planning. Khatib and Le Maitre =-=[9]-=- describe an algorithm that uses an approximate distance function, and Buckley [3] has recently reported a path-planning algorithm which is based on an optimisation method built around a proximity fun... |

6 |
Spatial planning---a configuration space approach
- Lozano-P'erez
- 1983
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Citation Context ...pace obstacle, and it is the set of translations of A that brings it into interference with B. Configuration space has been of interest for the formulation of path planning algorithms --- for example =-=[11, 10]-=- --- and the function Con has many nice properties. In particular we can show that for any objects A and B MTD(A;B) = MTD(O;Con(A;B)) (1) where O = f 0 g is the singleton set containing the origin. To... |

6 |
A procedure to determine intersections between polyhedral objects
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- 1972
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The computation of the distance between polyhedra
- Orlowski
- 1985
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Citation Context ...ibes an exhaustive technique for the minimum distance between arbitrary polyhedra. Recently a couple of fast solutions have been reported for calculating the minimum distance between convex polyhedra =-=[8, 14]-=-; these algorithms are asymptotically faster than the one reported here, but they only return zero for intersecting objects. Interest has also been shown in the calculation of distance functions in th... |

2 |
An efficient algorithm for computing the translational configuration space obstacle of two convex polyhedra. Unpublished internal memo
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(Show Context)
Citation Context ...se the information about sliding features which is stored during the (FV) and (VF) phases; this enables us to quickly find all the edges which can slide against a given edge. The details are given in =-=[5]-=-. 5 Calculating the Distance to the Configuration Space Obstacle We have as input a list of half-spaces, L = f hn i ; d i i g, which represents C. It turns out that we can get a good estimate of the v... |