Name
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.cagd.2010.04.004 | Computer Aided Geometric Design |
Keywords | Field | DocType |
hausdorff distance,complicated case,polygonal mesh,geometric algorithm,distance function,conic segment,medial axis,extreme distance evaluation,precise hausdorff distance,low envelope,bisector surface,candidate point,triangular mesh,exact algorithm,precise hausdorff distance computation | Hausdorff dimension,Topology,Combinatorics,Vertex (geometry),Polyhedron,Medial axis,Hausdorff distance,Conic section,Hausdorff measure,Intersection curve,Mathematics | Journal |
Volume | Issue | ISSN |
27 | 8 | Computer Aided Geometric Design |
Citations | PageRank | References |
26 | 0.84 | 18 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael Barton | 1 | 111 | 12.52 |
| Iddo Hanniel | 2 | 197 | 12.98 |
| Gershon Elber | 3 | 1924 | 182.15 |
| Myung-soo Kim | 4 | 1182 | 92.56 |