Abstract
We say that a polygon P is immobilized by a set of points I on its boundary if any rigid motion of P in the plane causes at least one point of I to penetrate the interior of P. Three immobilization points are always sufficient for a polygon with vertices in general positions, but four points are necessary for some polygons with parallel edges. An O(n log n) algorithm that finds a set of 3 points that immobilize a given polygon with vertices in general positions is suggested. The algorithm becomes linear for convex polygons. Some results are generalized for d-dimensional polytopes, where 2d points are always sufficient and sometimes necessary to immobilize. When the polytope has vertices in general position d+1 points are sufficient to immobilize.
This research is partially supported by NSERC
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© 1991 Springer-Verlag Berlin Heidelberg
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Czyzowicz, J., Stojmenovic, I., Urrutia, J. (1991). Immobilizing a polytope. In: Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1991. Lecture Notes in Computer Science, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028264
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DOI: https://doi.org/10.1007/BFb0028264
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