Precise Hausdorff distance computation between polygonal meshes

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 self-bisector of the other mesh. The self-bisectors for pairs of primitives (i.e. vertex, edge, or face) are analytically constructed and they are 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. Key words: Hausdorff distance, polygonal mesh, geometric al...

• Type: Journal
• Year: 2010
• Where: CAGD
• Authors: Michael Barton, Iddo Hanniel, Gershon Elber, Myung-Soo Kim
• Keywords: CAGD 2010, Candidate Point, Conic Segment, Hausdorff Distance, Logical Reasoning