## Abstract

We address the problem of computing a measure of the distance between two configurations of a rigid or an articulated model. The underlying distance metric is defined as the maximum length of the displacement vectors over the vertices of the model between two configurations. Our algorithm is based on Chasles theorem from Screw theory, and we show that for a rigid model the maximum distance is realized by one of the vertices on the convex hull of the model. We use this formulation to compute the distance, and present two acceleration techniques: incremental walking on the dual space of the convex hull and culling vertices on the convex hull using a bounding volume hierarchy (BVH). Our algorithm can be easily extended to articulated models by maximizing the distance over its each link and we also present culling techniques to accelerate the computation. We highlight the performance of our algorithm on many complex models and demonstrate its applications to generalized penetration depth computation and motion planning.

Original language | English |
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Pages (from-to) | 489-502 |

Number of pages | 14 |

Journal | Computer Aided Geometric Design |

Volume | 25 |

Issue number | 7 |

DOIs | |

State | Published - Oct 2008 |

### Bibliographical note

Funding Information:We would like to thank Frank Chongwoo Park, Steven M. LaValle, Jean-Claude Latombe and Bert Jütler for useful discussions. We would also like to thank the anonymous reviewers for their valuable comments. This research was supported in part by ARO Contracts DAAD19-02-1-0390 and W911NF-04-1-0088, NSF awards 0400134 and 0118743, ONR Contract N00014-01-1-0496, DARPA/RDECOM Contract N61339-04-C-0043 and Intel. Young J. Kim was supported in part by the Korea Research Foundation Grant funded by the Korean Government (KRF-2007-331-D00400) and the IT R&D program of MKE/IITA (2008-F-033-01, Development of Real-time Physics Simulation Engine for e-Entertainment).

## Keywords

- Configuration space
- Distance metric