Probing a scene of non convex polyhedra

Abstract : 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.
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Rapport
[Research Report] RR-1110, INRIA. 1989
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https://hal.inria.fr/inria-00075449
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Soumis le : mercredi 24 mai 2006 - 18:14:45
Dernière modification le : samedi 27 janvier 2018 - 01:31:11
Document(s) archivé(s) le : mardi 12 avril 2011 - 19:05:17

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Jean-Daniel Boissonnat, Mariette Yvinec. Probing a scene of non convex polyhedra. [Research Report] RR-1110, INRIA. 1989. 〈inria-00075449〉

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