## Abstract

We present an exact algorithm for computing the precise Hausdorff distance between two general polyhedra represented as triangular meshes. The locus of candidate points, events where the Hausdorff distance may occur, is fully classified. These events include simple cases where foot points of vertices are examined as well as more complicated cases where extreme distance evaluation is needed on the intersection curve of one mesh with the medial axis of the other mesh. No explicit reconstruction of the medial axis is conducted and only bisectors of pairs of primitives (i.e. vertex, edge, or face) are analytically constructed and intersected with the other mesh, yielding a set of conic segments. For each conic segment, the distance functions to all primitives are constructed and the maximum value of their low envelope function may correspond to a candidate point for the Hausdorff distance. The algorithm is fully implemented and several experimental results are also presented.

Original language | English (US) |
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Pages (from-to) | 580-591 |

Number of pages | 12 |

Journal | Computer Aided Geometric Design |

Volume | 27 |

Issue number | 8 |

DOIs | |

State | Published - Nov 1 2010 |

## Keywords

- Bisector surface
- Geometric algorithm
- Hausdorff distance
- Low envelope
- Medial axis
- Polygonal mesh

## ASJC Scopus subject areas

- Modeling and Simulation
- Automotive Engineering
- Aerospace Engineering
- Computer Graphics and Computer-Aided Design