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inria-00075449, version 1

Probing a scene of non convex polyhedra

Jean-Daniel Boissonnat () 1, Mariette Yvinec () 2

N° RR-1110 (1989)

Résumé : We show, in this paper, how one can compute the exact shapes of a class of polyhedral scenes by means of a simple sensory device issuing probes. A scene in this class consists of disjoint polyhedra with no collinear edges, no coplanar faces and such that no edge is contained in the supporting plane of a non incident face. The basic step of our method is a strategy for probing a single simple polygon with no collinear edges. When each probe outcome consists of a contact point and the normal to the object at the point, we present a strategy that allows to compute the exact shape of a simple polygon with no collinear edges by means of at most 3n - 3 probes, where n is the number of edges of the polygon. This is optimal in the worst-case. This strategy can be extended to probe a family of disjoint polygons. It can also be applied in planar sections of a scene of polyhedra of the class above to find out, in turn, each edge of the scene. If the scene consists of k polyhedra with altogether n faces and m edges, we show that (10,3) n(m + k) - 2m - 3k probes are sufficient to compute the exact shapes of the polyhedra.

  • Domaine : Informatique/Autre
  • Référence interne : RR-1110
 
  • inria-00075449, version 1
  • oai:hal.inria.fr:inria-00075449
  • Contributeur : 
  • Soumis le : Mercredi 24 Mai 2006, 18:14:45
  • Dernière modification le : Vendredi 7 Mai 2010, 09:40:46
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