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An algorithm that finds the externally visible vertices of a polygon is described. This algorithm generates a new geometric construction, termed the convex ropes of each visible vertex. The convex ropes give the range of angles from which each vertex is visible, and they give all the pairs of vertices which are reachable by a straight robot finger. All of the convex ropes can be found in expected time order n, where n is the number of vertices of the polygon. We discuss the application of this geometric construction to automated grasp planning. The algorithm may also be useful in image interpretation and graphics where efficient computation of visible points is important. The direct application of the algorithm is restricted to two dimension since sequential ordering of vertices is required. Extension to three dimension would rely on well chosen intersecting or projective planes.