Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Determining the shape of a convex n-sided polygon by using 2n+k tactile probes
Information Processing Letters
Journal of Algorithms
An optimal O(n log n) algorithm for contour reconstruction from rays
SCG '87 Proceedings of the third annual symposium on Computational geometry
Geometric probing
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We show, in this paper, how one can probe a class of non convex polyhedra and scenes of disjoint such polyhedra. A polyhedron of that class has convex faces; any two faces are not coplanar and any two edges are not colinear. The basic step of our method is a strategy for probing a single simple polygon with no colinear edges. When each probe outcome consists of a contact point and the normal to the object at the point, we present a strategy that discovers the exact shape of a simple polygon with no colinear edges by means of at most 3n - 3 probes, which is shown to be optimal in the worst-case. This strategy can be extended to probe a family of disjoint polygons. It can also be applied in the supporting planes of the faces of a scene of polyhedra of the class above. If the scene consists of k polyhedra with altogether n faces, we show that 8n2 - 6n + k probes are sufficient to discover the exact shapes of the polyhedra.