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Reports (Research Report) Year : 1989

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.

Domains

Other [cs.OH]
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Dates and versions

inria-00075449 , version 1 (24-05-2006)

Identifiers

  • HAL Id : inria-00075449 , version 1

Cite

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