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Given a triangulation of a simple polygon P, we present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility within P. These problems include calculation of the collection of all shortest paths inside P from a given source vertex s to all the other vertices of P, calculation of the subpolygon of P consisting… (More)

diagrams of set-theoretic solid models. A retraction" method for planning the motion of a disk.

We present linear time algorithms for solving the following problems involving a simple planar polygon <italic>P</italic>: (i) Computing the collection of all shortest paths inside <italic>P</italic> from a given source vertex <italic>s</italic> to all the other vertices of <italic>P</italic>; (ii) Computing the subpolygon of <italic>P</italic> consisting… (More)

Given a convex polygonal robot B with k edges capable of translation and rotation, and a set of polygonal obstacles {A 1 ,. .. , A m } each with n i sides and n = m i=1 n i , Leven and Sharir [1] prove that the number of critical placements of B at which it makes 3 simultaneous contacts with the obstacles but does not intersect their interior is O(knλ 6… (More)

We present a relatively simple algorithm which runs in time &Ogr;(n<supscrpt>2</supscrpt>log n) for the above mentioned problem. The algorithm is an optimized variant of the decomposition technique of the configuration space of the ladder, due to Schwartz and Sharir. The algorithm is based on some ideas which may be exploited to improve the efficiency of… (More)

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